Methods of Risk Pooling in Business Logistics and Their ... · PDF fileMethods of Risk Pooling in Business Logistics and Their Application I n a u g u r a l d i s s e r t a t i o n

Methods of Risk Pooling in Business Logistics and Their Application

I n a u g u r a l d i s s e r t a t i o n

zur Erlangung des akademischen Grades „Doktor der Wirtschaftswissenschaften“

(Dr. rer. pol.)

eingereicht an der

Wirtschaftswissenschaftlichen Fakultät der Europa-Universität Viadrina

in Frankfurt (Oder) im September 2010

von

Gerald Oeser Frankfurt (Oder)

“Uncertainty is the only certainty there is,

and knowing how to live with insecurity is the only security.”

John Allen Paulos,

Professor of Mathematics at Temple University in Philadelphia

To my brother,

who never failed to support me

Acknowledgements

First and foremost I would like to express my gratitude to my Ph.D. advisor Prof. Dr.

Dr. h.c. Knut Richter, Chair of General Business Administration, especially Industrial

Management, European University Viadrina Frankfurt (Oder), Germany for his extensive

mentoring. He also kindly gave me the opportunity of gaining experience in teaching grad-

uate courses in addition to my research.

For willingly delivering his expert opinion on my thesis as the second referee I thank

Prof. Dr. Joachim Käschel, Professorship of Production and Industrial Management, Tech-

nical University Chemnitz, Germany very much.

I would also like to gratefully acknowledge the support of all employees of Prof. Rich-

ter's chair, especially Dr. Grigory Pishchulov: Among other things, he helped me carry out

the “Subadditivity Proof for the Order Quantity Function (5.1)” in Appendix E mathemati-

cally formally correctly.

Furthermore, I thank Prof. Dr. Dr. h.c. Werner Delfmann, Director of the Department of

Business Policy and Logistics, University of Cologne, Germany for the opportunity offered

and for showing me that the world cannot be explained by mathematics alone.

Moreover, I appreciate the diverse support of the following professors during my Mas-

ter's and doctoral studies: Ravi M. Anupindi (University of Michigan), Ronald H. Ballou

(Case Western Reserve University), Gérard Cachon (University of Pennsylvania), Ian

Caddy (University of Western Sydney, Australia), Sunil Chopra (Northwestern Universi-

ty), Chandrasekhar Das (emeritus, University of Northern Iowa), David Dilts (Oregon

Health and Science University), Bruno Durand (University of Nantes, France), Philip T.

Evers (University of Maryland), Amit Eynan (University of Richmond), Dieter Feige

(emeritus, University of Nuremberg, Germany), Jaime Alonso Gomez (EGADE - Tec de

Monterrey, Mexico City and University of San Diego), Drummond Kahn (University of

Oregon), Peter Köchel (emeritus, Technical University Chemnitz, Germany), David H.

Maister (formerly Harvard Business School), Alan C. McKinnon (Heriot-Watt University,

UK), Esmail Mohebbi (University of West Florida), Steven Nahmias (Santa Clara Univer-

sity), Teofilo Ozuna, Jr. (The University of Texas-Pan American), David F. Pyke (Univer-

sity of San Diego), Pietro Romano (University of Udine, Italy), Wolfgang Schmid (Euro-

pean University Viadrina Frankfurt (Oder), Germany), Yossi Sheffi (Massachusetts Insti-

tute of Technology), Edward Silver (emeritus, University of Calgary, Canada), Jacky Yuk-

Chow So (University of Macau, China), Jayashankar M. Swaminathan (University of

North Carolina), Christian Terwiesch (University of Pennsylvania), Ulrich Thonemann

(University of Cologne, Germany), Biao Yang (University of York, UK), and Walter Zinn

(The Ohio State University).

I express gratitude to the paper merchant wholesaler Papierco for the insight into its op-

erations, the opportunity of optimizing its logistics, and the financial support.

I am also thankful to my friends: Without them writing this dissertation would have

been a lonesome experience.

Finally, I thank my father for constantly pushing and financially supporting me and

proofreading my thesis.

Geleitwort

Die vorgelegte Dissertation widmet sich dem großen Thema Risk Pooling in der Business-

Logistik. Die Aggregation von Risiken der Logistikprozesse ist ein derart universelles

Problem, so dass Autoren verschiedenster Wissenschafts- und Anwendungsgebiete dazu

ihre Positionen, Lösungsansätze und Modelle dargestellt haben. Bisher hatte noch niemand

den Mut aufgebracht, diese kaum überblickbare Menge an Literaturquellen zu sichten und

nach wissenschaftlichen Kriterien zu ordnen. Herr Oeser hat sich dieser Aufgabe gestellt

und hat sie mit Bravour gemeistert.

Bei aller Bedeutung dieser aufwendigen akademischen Aktivitäten darf jedoch nicht ver-

gessen werden, dass Risk Pooling ein Problem der Praxis ist, und dass die entsprechenden

theoretischen Untersuchungen letztendlich der Praxis dienen sollen. Die Vielfältigkeit des

Problems kann dabei kaum durch ein relevantes Basismodell erfasst werden. Es ist das

Verdienst des Autors, mit der Entwicklung einer Grundkonzeption für ein Entscheidungs-

unterstützungssystem zur Auswahl der geeigneten Risk Pooling Strategien Unternehmen

und besonders Unternehmensberatungen ein Instrument in die Hand zu geben, mit dem

sich die vielfältigen Situationen der Unternehmen analysieren lassen. Er belässt es jedoch

nicht beim Entwurf der Konzeption, sondern demonstriert auch überzeugend dessen An-

wendung anhand eines Unternehmens.

Es ließen sich viele weitere Vorzüge des hier veröffentlichten Werkes nennen. Es soll an

dieser Stelle jedoch dem Leser überlassen bleiben sich ein Urteil zu bilden. Herr Oeser

bietet dem Leser mit seiner Dissertation auf jeden Fall keine „leichte Kost“, denn der be-

handelte Gegenstand lässt eine oberflächliche Betrachtung nicht zu.

Wer sollte dieses Werk lesen? Wissenschaftler und Studenten aus den Gebieten Operations

Management, Logistik, Operations Research werden hier viel Neues und Interessantes,

auch viele Probleme für die weitere Forschung finden. Unternehmensberatungen werden

viele angeführte Lösungen zur Komplexitätsbewältigung in ihren Projekten anwenden

können. Ich bin überzeugt, dass die vorgelegte Dissertation neue Forschungen und Projekte

anregen wird. Das ist das Schönste, was sich ein Autor wohl wünschen kann.

Prof. Dr. Dr. h.c. Knut Richter

VII

Table of Contents

List of Figures .................................................................................................................... X

List of Tables ..................................................................................................................... XI

List of Abbreviations, Signs, and Symbols ................................................................... XII

Abstract ................................................................................................................... XIV

1 Introduction ................................................................................................. 1

1.1 Problem: Growing Uncertainty in Business Logistics and

Need for a Tool to Choose Among Risk Pooling Countermeasures ............ 1

1.2 Objective ....................................................................................................... 3

1.3 Object and Method ........................................................................................ 3

1.4 Structure and Contents .................................................................................. 4

2 Risk Pooling in Business Logistics ............................................................. 6

2.1 Business Logistics Risk Pooling Research ................................................... 6

2.2 Placing Risk Pooling in the Supply Chain, Business Logistics,

and a Value Chain ......................................................................................... 8

2.3 Defining Risk Pooling ................................................................................. 11

2.4 Explaining Risk Pooling ............................................................................. 14

2.5 Characteristics of Risk Pooling ................................................................... 19

3 Methods of Risk Pooling ........................................................................... 24

3.1 Storage: Inventory Pooling ......................................................................... 27

3.2 Transportation ............................................................................................. 35

3.2.1 Virtual Pooling ............................................................................................ 35

3.2.2 Transshipments ........................................................................................... 35

3.3 Procurement ................................................................................................ 40

3.3.1 Centralized Ordering ................................................................................... 40

3.3.2 Order Splitting ............................................................................................ 41

3.4 Production ................................................................................................... 43

3.4.1 Component Commonality ........................................................................... 43

3.4.2 Postponement .............................................................................................. 45

3.4.3 Capacity Pooling ......................................................................................... 49

Table of Contents

VIII

3.5 Sales and Distribution ................................................................................. 51

3.5.1 Product Pooling ........................................................................................... 51

3.5.2 Product Substitution .................................................................................... 52

4 Choosing Suitable Risk Pooling Methods ............................................... 53

4.1 Contingency Theory .................................................................................... 53

4.2 Conditions Favoring the Individual Risk Pooling Methods ....................... 54

4.3 The Risk Pooling Methods' Advantages, Disadvantages,

Performance, and Trade-Offs ...................................................................... 55

4.4 A Risk Pooling Decision Support Tool ...................................................... 56

5 Applying Risk Pooling at Papierco .......................................................... 74

5.1 Papierco ....................................................................................................... 74

5.2 Problems Papierco Faces ............................................................................ 75

5.2.1 Fierce Competition in German Paper Wholesale ........................................ 75

5.2.2 Supplier Lead Time Uncertainty ................................................................. 75

5.2.3 Customer Demand Uncertainty ................................................................... 76

5.2.4 Distribution Requirements Planning (DRP) ............................................... 80

5.2.5 Demand Forecasting Methods .................................................................... 82

5.3 Solving Papierco's Problems ....................................................................... 87

5.3.1 Determining Suitable Risk Pooling Methods for Papierco ......................... 87

5.3.2 Emergency Transshipments between Papierco's German Locations .......... 91

5.3.2.1 Optimizing Catchment Areas ...................................................................... 91

5.3.2.2 Increase in Transshipments and Its Causes ................................................. 94

5.3.2.3 Transshipments Are Worthwhile for Papierco ........................................... 96

5.3.3 Centralized Ordering ................................................................................. 101

5.3.3.1 Papierco's Current Order Policy ............................................................... 101

5.3.3.2 Stock-to-Demand Order Policy with Centralized Ordering and

Minimum Order and Saltus Quantities ..................................................... 105

5.3.3.3 Benefits of Centralized Ordering for Papierco ......................................... 107

5.3.4 Product Pooling ......................................................................................... 117

5.3.5 Inventory Pooling ...................................................................................... 118

5.3.6 Challenges in IT and Organization ........................................................... 121

5.4 Summary ................................................................................................... 123

6 Conclusion ............................................................................................... 126

Table of Contents

IX

Appendix A: A Survey on Risk Pooling Knowledge and Application in

102 German Manufacturing and Trading Companies ........................ 134

1 Introduction ............................................................................................. 135

1.1 Motivation: Scarce Survey Research on Risk Pooling ............................. 135

1.2 Objective ................................................................................................... 140

2 The Survey ............................................................................................... 142

2.1 Research Design ........................................................................................ 142

2.2 Data Analysis and Findings ...................................................................... 147

2.2.1 Risk Pooling Knowledge and Utilization in

the German Sample Companies ................................................................ 147

2.2.2 Association between the Knowledge of

Different Risk Pooling Concepts .............................................................. 151

2.2.3 Association between Knowledge and Utilization of

Risk Pooling Concepts .............................................................................. 154

2.2.4 Association of the Utilization of Different Risk Pooling Concepts ........... 156

2.2.5 Risk Pooling Knowledge and Utilization in

the Responding Manufacturing and Trading Companies ......................... 161

2.2.6 Knowledge and Utilization of the Different Risk Pooling Concepts

in Small and Large Responding Companies ............................................. 164

3 Critical Appraisal .................................................................................... 166

4 Questionnaire .......................................................................................... 169

5 Answers .................................................................................................... 170

Appendix B: Proof of the Square Root Law for Regular, Safety, and

Total Stock ............................................................................................... 172

Appendix C: What Causes the Savings in Regular Stock through Centralization

Measured by the SRL? ........................................................................... 176

Appendix D: Tables ....................................................................................................... 178

Appendix E: Subadditivity Proof for the Order Quantity Function (5.1) ............... 202

Bibliography .................................................................................................................... 204

X

List of Figures

Figure 2.1: Number of Publications on Risk Pooling in Business Logistics .................. 7

Figure 2.2: Placing Risk Pooling in Business Logistics .................................................. 9

Figure 2.3: Important Value Activities Using Risk Pooling Methods .......................... 11

Figure 4.1: Risk Pooling Decision Support Tool .......................................................... 56

Figure 5.1: Total Fine Paper Sales in Tons per Month in Germany

(BVdDP 2010a: 8) ...................................................................................... 76

Figure 5.2: Papierco's Total Fine Paper Sales to Customers in Germany

in Tons per Month ....................................................................................... 77

Figure 5.3: Papierco's 2007 Warehouse Sales to Customers per Week

of Seven Standard Paper Products from the Hemmingen Warehouse ........ 78

Figure 5.4: 2007 Incoming Goods, Warehouse Sales, and Inventory at

Warehouse Hemmingen .............................................................................. 80


Warehouse Reinbek .................................................................................... 81

Figure 5.6: Comparison of Current and Optimal Catchment Areas of Papierco's

Warehouses ................................................................................................. 93

Figure 5.7: Inventory Turnover Curves for Papierco .................................................. 104

Figure 5.8a: Product Purchase Planning at Papierco's Member Companies ................. 120

Figure 5.8b: Product Purchase Planning at Papierco's Member Companies ................. 120

Figure 5.9: Stockkeeping at Papierco's Warehouses in February 2008 ...................... 121

Figure A.1: Risk Pooling Knowledge and Utilization in

the German Sample Companies ................................................................ 147

Figure A.2: Risk Pooling Knowledge and Utilization in the

Sample Manufacturing and Trading Companies ...................................... 161

Figure A.3: Knowledge and Utilization of the Different Risk Pooling Concepts in

Small and Large Responding Companies ................................................. 164

Figure A.4: Questionnaire ............................................................................................ 169

XI

List of Tables

Table 3.1: Risk Pooling Methods' Building Blocks ..................................................... 26

Table 5.1: The Extent of Transshipments at Papierco ................................................. 94

Table 5.2: Effects of Centralized Ordering at Papierco ............................................. 109

Table A.1: Comparing Respondents with the Total Population of

Manufacturing and Trading Companies in Germany ............................... 143

Table A.2: Significant Correlations at the 5 % Level of

the Knowledge of Risk Pooling Concepts ................................................ 154

Table A.3: Significant Correlations at the 5 % Level (except in the case Product

Substitution/Demand Reshape) between Knowledge and

Utilization of Risk Pooling Concepts ....................................................... 155

Table A.4: Significant Correlations at the 5 % Level between the Utilization of

Risk Pooling Concepts .............................................................................. 160

Table A.5: Survey Participants' Answers to the Questionnaire .................................. 171

Table D.1: Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies .. 178

Table D.2: Comparison of Important Inventory Consolidation Effect,

Portfolio Effect, and Square Root Law Models ........................................ 179

Table D.3: Conditions Favoring the Various Risk Pooling Methods ......................... 185

Table D.4 The Risk Pooling Methods' Advantages, Disadvantages,

Performance, and Trade-Offs .................................................................... 195

XII

List of Abbreviations, Signs, and Symbols

Common general, business, logistics, supply chain management (SCM), operations re-

search (OR), mathematical, and statistical abbreviations, signs, and symbols apply1 and are

not listed here.

CC component commonality

CE consolidation effect

CO centralized ordering

COE centralized ordering effect

COV coefficient of variation of demand

CP capacity pooling

CS cycle stock

Dipl.-Kfm. Diplomkaufmann (MBA equivalent)

DP demand pooling

DUR demand uncertainty reduction

EFR effective fill rate for the customer

ELT emergency lateral transshipment

EOS economies of scale

FR item fill rate

IC inventory holding cost

i. i. d. independent and identically distributed

IP inventory pooling

ITO in terms of

LP lead time pooling

LT lead time

LTUR lead time or lead time uncertainty reduction

n. e. c. not elsewhere classified

NLT endogenous lead times

OP order policy

OS order splitting

1 Cf. e. g. Soanes and Hawker (2008), Friedman (2007), Lowe (2002), Obal (2006), Silver et al. (1998) and

Slack (1999), Clapham and Nicholson (2009), and Dodge (2006).

List of Abbreviations, Signs, and Symbols

XIII

PCE portfolio cost effect

PE portfolio effect

PM postponement

PoD point of (product) differentiation

PP product pooling

PQE portfolio quantity effect

PRE proportional reduction of error

PS product substitution

RMSE root mean square error

RPDST risk pooling decision support tool

RS regular stock

SL transshipment sending location

SLA service level adjustment

sqrt square root

SRL square root law

SS safety stock

TC transportation cost

TS transshipments

TSC transshipment cost

VP virtual pooling

vs. versus, here: is traded off against

XLT exogenous lead times

≈ is approximately equal to

≻ is preferred to

XIV

Abstract

Purpose/topicality: Demand and lead time uncertainty in business logistics increase, but can

be mitigated by risk pooling. Risk pooling can reduce costs for a given service level, which is

especially valuable in the current economic downturn. The extensive, but fragmented and in-

consistent risk pooling literature has grown particularly in the last years. It mostly deals with

specific mathematical models and does not compare the various risk pooling methods in terms

of their suitability for specific conditions.

Approach: Therefore this treatise provides an integrated review of research on risk

pooling, notably on inventory pooling and the square root law, according to a value-chain

structure. It identifies ten major risk pooling methods and develops tools to compare and

choose between them for different economic conditions following a contingency approach.

These tools are applied to a German paper merchant wholesaler, which suffers from cus-

tomer demand and supplier lead time uncertainty. Finally, a survey explores the knowledge

and usage of the various risk pooling concepts and their associations in 102 German manu-

facturing and trading companies. Triangulation (combining literature, example, modeling,

and survey research) enhances our investigation.

Originality/value: For the first time this research presents (1) a comprehensive and

concise definition of risk pooling distinguishing between variability, uncertainty, and risk,

(2) a classification, characterization, and juxtaposition of risk pooling methods in business

logistics on the basis of value activities and their uncertainty reduction abilities, (3) a deci-

sion support tool to choose between risk pooling methods based on a contingency ap-

proach, (4) an application of risk pooling methods at a German paper wholesaler, and (5) a

survey on the knowledge and utilization of risk pooling concepts and their associations in

102 German manufacturing and trading companies.

1

1 Introduction

1.1 Problem: Growing Uncertainty in Business Logistics and

Need for a Tool to Choose Among Risk Pooling

Countermeasures

Product variety has increased dramatically in almost every industry2 particularly due to in-

creased customization3. Product life cycles have become shorter, demand fluctuations more

rapid, and products can be found and compared easily on the internet.4

This causes difficulties in forecasting for an increased number of products, demand and

lead time uncertainty, intensified pressure for product availability, and higher inventory

levels5 to provide the same service6. This trend is expected to continue and likely grow

worse.7

Supply chains8 are more susceptible to disturbances today because of their globaliza-

tion, increased dependence on outsourcing and partnerships, single sourcing, little leeway

in the supply chain, and increasing global competition.9 Disruptions, such as production or

shipment delays, affect profitability (growth in operating income, sales, costs, assets, and

inventory).10

Risk pooling is “[o]ne of the most powerful tools used to address [demand and/or lead

time] variability in the supply chain”11 particularly in a period of economic downturn12, as

it allows to reduce costs and to increase competitiveness.

2 Cox and Alm (1998), Van Hoek (1998a: 95), Aviv und Federgruen (2001a), Ihde (2001: 36), Piontek

(2007: 86), Ganesh et al. (2008: 1124f.). 3 Ihde (2001: 36), Chopra and Meindl (2007: 305), Piontek (2007: 86). 4 Rabinovich and Evers (2003a: 226), Chopra and Meindl (2007: 305, 333). 5 Dubelaar et al. (2001: 96). 6 Ihde (2001: 36), Swaminathan (2001: 125ff.), Chopra and Meindl (2007: 305, 333), Rumyantsev and

Netessine (2007: 1) 7 Cecere and Keltz (2008). 8 “A supply chain consists of all parties involved, directly or indirectly, in fulfilling a customer request.

The supply chain includes not only the manufacturer and suppliers, but also transporters, warehouses, re-tailers, and even customers themselves” (Chopra and Meindl 2007: 3).

9 Dilts (2005: 21). These ideas of Professor David M. Dilts, Owen Graduate School of Management, Van-derbilt University, have not appeared in a formal publication yet. He granted us permission to cite them as personal correspondence on July 23, 2008.

10 Hendricks and Singhal (2002, 2003, 2005a, 2005b, 2005c), Hoffman (2005). 11 Simchi-Levi et al. (2008: 48). We will differentiate between the often confused terms variability, uncer-

tainty, and risk in section 2.3. 12 Cf. Hoffman (2008), Chain Drug Review (2009a), Hamstra (2009), Orgel (2009), Pinto (2009b), Ryan

(2009).

1 Introduction

2

Although “risk pooling is often central to many recent operational innovations and

strategies”13, an important concept in business logistics and supply chain management

(SCM)14, and was already described in logistics in 196715, it is mentioned in few German

text books16 mostly limited to the square root law (SRL). Most other publications also only

consider inventory pooling17 or a single other type18 of risk pooling19. Exceptions are Neale

et al. (2003: 44f., 50, 55), Fleischmann et al. (2004: 70, 93), Taylor (2004: 301ff.), Muck-

stadt (2005: 150ff.), Reiner (2005: 434), Anupindi et al. (2006), Heil (2006), Brandimarte

and Zotteri (2007: 30, 36, 38, 39, 57, 58, 70), Sheffi (2007), Simchi-Levi et al. (2008), So-

bel (2008: 172), Van Mieghem (2008), Cachon and Terwiesch (2009), and Bidgoli (2010).

Our survey of 102 German manufacturing and trading companies of various sizes and

industries (see appendix A20) showed that the different risk pooling concepts are known

fairly well, but not widely applied despite their potential benefits. Choosing risk pooling

methods is difficult for companies, as the literature does not compare the various methods

in terms of their suitability for certain conditions holistically.21 Most of the work in risk

13 Cachon and Terwiesch (2009: 350). 14 Romano (2006: 320). 15 Flaks (1967: 266). 16 For example Pfohl (2004a: 115ff.), Tempelmeier (2006: 41f., 153f.), Bretzke (2008: 147, 152, 154). 17 For example Bramel and Simchi-Levi (1997: 219f.), Martinez et al. (2002: 14), Christopher and Peck

(2003: 132), Dekker et al. (2004: 32), Ghiani et al. (2004: 9), Daskin et al. (2005: 53f.), Li (2007: 210), Taylor (2008: 13-3), Mathaisel (2009: 19), Shah (2009: 89f.), Wisner et al. (2009: 513).

18 A type is “a category of […] things having common characteristics” (Soanes and Hawker 2008). We distinguish ten main types of risk pooling that have in common that they may reduce total demand and/or lead time variability and thus uncertainty and risk by pooling individual demand and/or lead time varia-bilities. We call them methods (e. g. in the title of this treatise), whenever we focus on the ways of risk pooling, as a method is “a way of doing something” (Soanes and Hawker 2008). If the focus is on choos-ing and implementing one or several risk pooling methods for a specific company under specific condi-tions, we refer to this as risk pooling strategy. A strategy is “a plan designed to achieve a particular long-term aim” (Soanes and Hawker 2008). In the case of risk pooling this plan can comprise one or more risk pooling methods combined in order to reduce demand and/or lead time uncertainty. We use the term con-cept, if we aim at the “abstract idea” (Soanes and Hawker 2008) or would like to include the SRL, PE, and inventory turnover curve, which are rather tools to measure the risk pooling effect on inventories than risk pooling methods.

19 Pfohl (2004b: 126, 355), Enarsson (2006: 178). 20 For the sake of readability and content unity we placed the survey in the appendix. 21 However, Evers (1999) compares inventory centralization, transshipments, and order splitting. Swamina-

than (2001) designs a framework for deciding between part and procurement standardization (component commonality), process standardization (postponement), and product standardization (substitution) accord-ing to product and process modularity, Wanke and Saliby (2009: 690) one for choosing between invento-ry centralization (demand pooling) and regular transshipments (“serving […] demands from all centra-lized facilities” and enabling demand and lead time pooling). Benjaafar et al. (2004a, 2005) find in sys-tems with endogenous supply lead times, multisourcing (Benjaafar et al. 2004a: 1441f., 1446) and capaci-ty pooling (Benjaafar et al. 2005: 550, 563) perform better than inventory pooling, if utilization (arrival rate divided by service rate) is high. Eynan and Fouque (2005) show that demand reshape is more effi-cient than component commonality.

1 Introduction

3

pooling is rather focused on one aspect and holistic treatments are rare.22 There is little

empirical and – to our knowledge – no survey research on the various methods of risk

pooling combined. Most publications develop mathematical models for a specific risk

pooling method under certain assumptions and (optimal inventory) policies that minimize

inventory for a given service level or maximize service level for a given inventory. They

do not explore whether this risk pooling method is the best for the given situation or

whether it can be combined with other ones.

1.2 Objective

Thus the objective of this treatise is to advance research on and aid practice in selecting and

applying risk pooling methods in business logistics. More specifically, the aims of this research

can be formulated as follows:

1. Develop the first comprehensive and concise definition of risk pooling.

2. Critically review and structure the research on risk pooling within a value-chain

framework according to this definition.

3. Develop tools to compare and choose appropriate risk pooling methods and mod-

els for different economic conditions with a contingency approach.

4. Apply these tools to a German paper merchant wholesaler, which faces customer

demand and supplier lead time uncertainty.

5. Examine the knowledge and usage of the various risk pooling concepts and their

associations in 102 German trading and manufacturing companies by means of a

survey.

1.3 Object and Method

The research object (German: Erfahrungsgegenstand) is an empirical phenomenon (a part of

reality) that is to be described. The scientific object or selection principle (German: Er-

kenntnisgegenstand) is the perspective and specific question used to examine the research ob-

ject.23

Our research object comprises business logistics in a company that experiences de-

mand and/or lead time uncertainty. Our scientific object is risk pooling that can decrease

this uncertainty of the company, which is perceived as a collection of value activities (val-

22 Personal correspondence with Professor Christian Terwiesch, The Wharton School, University of Penn-

sylvania on July 2, 2008. 23 Schneider (1987: 34f.), Chmielewicz (1994: 19ff.), Söllner (2008: 5), Neus (2009: 2).

1 Introduction

4

ue chain approach). Business logistics plans, organizes, handles, and controls all material,

product, and information flows across these value activities24 in an efficient, effective, and

customer-oriented manner (logistics perspective). Our main specific research questions

are: What risk pooling methods are available? What economic conditions make the indi-

vidual methods worthwhile? How can a company choose adequate risk pooling methods?

We derive the adequacy of the identified risk pooling methods from contingency factors

(contingency approach).

In order to enhance the quality of our research we use triangulation25 to gather various

types of information26 on risk pooling by literature, example, modeling, and survey re-

search. This integrated approach also accounts for our holistic ambition and leads to results

not attainable by the individual research methods separately27. Weaknesses of some me-

thods can be balanced by the strengths of others.28 Van Hoek (2001: 182f.) already pro-

posed triangulation to improve research on postponement, one type of risk pooling. For

problems of triangulation, such as coping with conflicting results, epistemological prob-

lems, and the debatable higher validity of findings, please refer to e. g. Bryman (1992:

63f.), Denzin and Lincoln (2005: 912), Blaikie (1991: 122f.), and Fielding and Fielding

(1986: 33). A holistic approach may not be as profound as an atomistic one. However, as

noted before such a holistic approach is novel to risk pooling research.

1.4 Structure and Contents

This treatise is divided into six chapters and an appendix. After this introduction (chapter 1),

we outline previous risk pooling research in business logistics, identify ten main types of risk

pooling, and place them in the supply chain, business logistics, and a value chain. This results

in the five logistics value activities storage, transportation, procurement, production, and sales

and distribution, where risk pooling is important. Completing outlining our research frame-

work, we define, explain, and characterize risk pooling in business logistics (chapter 2).

Chapter 3 defines, classifies, and characterizes the ten identified risk pooling methods

within the five logistics value activities and according to their uncertainty reduction abilities.

24 To Porter (2008: 75) inbound and outbound logistics are primary value activities themselves besides op-

erations, marketing and sales, and service. We adopt a cross-functional view of logistics. 25 Denzin (1978: 291) defines triangulation as “the combination of methodologies in the study of the same

phenomenon”. 26 Graman and Magazine (2006: 1070). 27 Jick (1979: 603f.), Fielding and Fielding (1986: 33), Graman and Magazine (2006: 1070). 28 Blaikie (1991: 115).

1 Introduction

5

Research on inventory pooling is reviewed in more detail29, as it is the earliest and most

extensive and prominent one. In particular, we attempt to remedy inconsistencies regarding

the SRL, a tool to estimate the inventory savings from risk pooling by inventory pooling:

Under what assumptions can the SRL be applied to regular, safety, and total stock, as re-

searchers do not agree on them? What causes the inventory savings measured by the SRL?

Are its results confirmed in practice? Is the SRL questioned justifiedly? After examining the

portfolio effect (PE), a generalization of the SRL, and the inventory turnover curve, we com-

pare the various SRL and PE models in a synopsis (table D.2) based on their assumptions

and assign them to groups. This facilitates choosing an appropriate model to determine stock

savings from inventory pooling for specific conditions or adapt the existing models by add-

ing or dropping assumptions.

Chapter 4 merges the results of our literature review in a synopsis about conditions

making the various risk pooling methods favorable, their advantages, disadvantages, and

basic trade-offs. Based on this synopsis and contingency theory, a Risk Pooling Decision

Support Tool is developed for choosing an appropriate risk pooling strategy for a specific

company and specific conditions.

This tool is applied to a German paper wholesaler in chapter 5 to choose suitable risk

pooling methods to cope with demand and lead time uncertainty. In this context we also

show that in contrast to Maister (1976: 132) and Evers (1995: 2, 14f.) centralization or cen-

tralized ordering can reduce cycle stocks, if the replacement principle or stock-to-demand

replenishment policy is followed in case minimum order and saltus quantities have to be

observed (section 5.3.3.2).

If risk pooling is shown to be beneficial in theory and in practice also for this German

paper wholesaler, to what extent are its different methods known, applied, and associated in

102 German manufacturing and trading companies? To answer this question we present a

survey in appendix A for the above reasons. Such a survey has not been conducted before

and is demanded by some authors30.

The conclusion (chapter 6) summarizes our findings and identifies avenues for further re-

search.

29 Professor Walter Zinn, Fisher College of Business, The Ohio State University, believes this is sorely

needed (personal correspondence on July 4, 2008). 30 For example by Thomas and Tyworth (2006: 254f.) for order splitting and by Huang and Li (2008b: 19)

for postponement.

6

2 Risk Pooling in Business Logistics

This chapter outlines our research framework: It gives an overview of previous risk pooling

research (section 2.1), identifies ten main types of risk pooling and embeds them in the supply

chain, business logistics, and a value chain (section 2.2), which sets the structure for chapter 3,

defines risk pooling in business logistics (section 2.3), explains its mathematical and statistical

foundations (section 2.4) and examines five general features of risk pooling (section 2.5).

2.1 Business Logistics Risk Pooling Research

Risk pooling in business logistics is an active field of research with well over 600 publica-

tions so far. The number of publications in this area has steadily increased since its scarce be-

ginnings in the 1960s, gained momentum especially in the 80s and 90s and reached its peak in

2003 as figure 2.1 shows. Perhaps driven by the economic downturn, research activity in 2009

was the highest after 2003. Most research focused on inventory pooling (centralization, the

square root law, portfolio effect, and inventory turnover curve), postponement and delayed

(product) differentiation, and transshipments and inventory sharing. Figure 2.1 is based on the

literature databases Business Source Complete, Business Source Premier, EconLit, and Re-

gional Business News accessed via EBSCOhost® January 11, 2010.

After the concept borrowed from modern portfolio and insurance theory has been main-

ly applied to inventory centralization, meanwhile research focuses on other forms of risk

pooling, especially postponement and transshipments, and the coordination of risk pool-

ing arrangements and cost and profit allocation through contracts31 and fair allocation

rules, schemes, or methods32 with game theory.

The academics dealing with risk pooling in business logistics are of different back-

grounds (mathematics, operations research (OR), operations management (OM), man-

agement science, decision sciences, statistics, computer sciences, engineering, business

administration, management, economics, game theory, production, marketing, logis-

tics/supply chain management, physical distribution, and transportation), orientation

(quantitative, analytical, modeling, simulation, empirical, and qualitative research), and

31 Dana and Spier (2001), Cheng et al. (2002), Cachon (2003), Wang et al. (2004), Bartholdi and

Kemahloğlu-Ziya (2005), Cachon and Lariviere (2005), Özen et al. (2008, 2010). 32 Gerchak and Gupta (1991), Robinson (1993), Hartman and Dror (1996), Anupindi et al. (2001), Lehrer

(2002), Granot and Sošić (2003), Ben-Zvi and Gerchak (2007), Dror and Hartman (2007), Wong et al. (2007a), Dror et al. (2008). Robinson (1993), Raghunathan (2003), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), and Sošić (2006) consider allocations based on the Shapley (1953) value.


7

prominence. Therefore they use inconsistent terms33, frameworks, and structures and

made our thorough literature review and definitions necessary. One might argue that due

to these differences this research must not be compared and only major research should be

cited. However, in contrast to previous research we would like to pursue a more holistic

approach to convey an integrated overview of business logistics risk pooling. Even less

prominent research can draw attention to important details and show directions for further

research. Some often cited risk pooling research has not been published in highly ranked

journals.34 Nevertheless most of the cited references are from the latter.

Most risk pooling research is quantitative and designs mathematical models of prob-

lems, develops solution methods (exact methods, algorithms, simulation methods, and heu-

ristics), and determines solutions (optimal inventory control and risk pooling, e. g. trans-

shipment, policies).

Figure 2.1: Number of Publications on Risk Pooling in Business Logistics

33 Bender et al. (2004: 233) made similar observations for location theory. 34 For example Eppen and Schrage (1981).

0

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Year of Publication

Inventory Pooling (150)

Postponement (105)

Transshipments (95)

Component Commonality (55)

Virtual Pooling (51)

Capacity Pooling (41)

Product Substitution (40)

Order Splitting (37)

Centralized Ordering (27)

Product Pooling (21)


8

2.2 Placing Risk Pooling in the Supply Chain,

Business Logistics, and a Value Chain

Business logistics35 comprises the holistic, market-conform, and efficient planning, organiza-

tion, handling, and control of all material, product, and information flows from the supplier to

the company, within the company, and from the company to the customer36 and back (reverse

logistics37).

As figure 2.2 shows, the efficient and effective material, product, and information flow

is impaired by inter alia demand and lead time uncertainty. Risk pooling methods can miti-

gate these uncertainties. They can be implemented at or between the various supply chain

members (suppliers, manufacturers, wholesalers, distribution centers, central warehouses,

delivery or regional warehouses, retailers, stores, and customers).

Thoroughly reviewing the literature referred to in section 2.1, we identified ten risk

pooling methods: capacity pooling, central ordering, component commonality, inven-

tory pooling, order splitting, postponement, product pooling, product substitution,

transshipments, and virtual pooling. We will define and characterize them in detail in

chapter 3.

They can be implemented everywhere along the supply chain. Component commonality

rather concerns production. In general capacity and inventory pooling and postponement

may pool inventories or capacities of or for different locations. Component commonality,

postponement, product pooling, and product substitution may refer to products or their

components. Transshipments and virtual pooling deal with product, material, and informa-

tion flows between supply chain members within an echelon or across echelons, and cen-

tral ordering and order splitting with procurement between supply chain members.

In our opinion, all mentioned risk pooling methods but order splitting can reduce de-

mand uncertainty, order splitting only lead time uncertainty, component commonality,

capacity pooling, inventory pooling, product pooling, and product substitution only de-

35 Business logistics (management) is difficult to distinguish from supply chain management (SCM). The

terms are often used synonymously, although logistics is majorly seen as a part of SCM and not vice ver-sa as in earlier literature (Ballou 2004b: 4, 6f., Larson and Halldórsson 2004, CSCMP 2010). According to Kotzab (2000) the German business logistics conception already comprised a holistic management along the whole value creation chain before it adopted the English term SCM. Gabler's business enzyclo-pedia defines SCM as building and administrating integrated logistics chains (material and information flows) from raw materials production via processing to end consumers (Alisch et al. 2004: 2870).

36 Wegner (1996: 8f.). 37 See e. g. Richter (1996a, 1996b, 1997), Richter and Dobos (1999, 2003a, 2003b), Dobos and Richter

(2000), Richter and Sombrutzki (2000), Richter and Weber (2001), Richter and Gobsch (2005), Gobsch (2007).


9

mand uncertainty. Transshipments and virtual pooling, postponement, and central ordering

may dampen both uncertainties. Concerning order splitting and component commonality

there are dissenting individual opinions, which we will elaborate on in section 4.4.

Various economic conditions have been found to favor the different risk pooling me-

thods. We will focus on these favorable conditions in chapter 4. They flow into a Risk

Pooling Decision Support Tool that helps to determine suitable risk pooling methods for

specific conditions (section 4.4). This tool is applied to determine adequate risk pooling

methods for a German paper merchant wholesaler for coping with its demand and lead

time uncertainty in chapter 5.

Figure 2.2: Placing Risk Pooling in Business Logistics

Supply chain member names based on Chopra and Meindl (2007: 5).

Logistics may be considered as a cross-organizational (figure 2.2) and at every member of the

above supply chain a cross-departmental coordination function across all divisions, especially

storage, transportation, procurement, production of goods and services (including R&D,

recycling, and remanufacturing), and sales and distribution (including order processing, re-

covery, return, and disposal)38 in the value chain in figure 2.3.

38 Delfmann (2000: 323f.), Ballou (2004b: 9ff., 27, 29), Kuhlang and Matyas (2005: 659f.), Grün et al.

(2009: 15, 305), Wannenwetsch (2009: 21f.).

Suppliers Manufac-turers Distributors Retailers Customers

Lead Time Uncertainty

Demand Uncertainty

EconomicConditions

Material, product, and information flow

Risk pooling methods


10

The value chain is a management concept that was developed by Porter (1985: 33ff.)

and describes a company as a collection of activities. These activities create value, use re-

sources, and are linked in processes. In our value chain, the main value activities are pro-

curement, production, and sales and distribution, which are supported by the value activi-

ties transportation and storage. Value activities are “technologically and economically dis-

tinct activities [… a company] performs to do business”39.

Inventory pooling (IP) mainly pertains to storage, virtual pooling (VP) via drop-

shipping and cross-filling and transshipments (TS) to transportation, centralized ordering

(CO) and order splitting (OS) to procurement, capacity pooling (CP), component commo-

nality (CC), and (form) postponement (PM) to production, and product pooling (PP) and

product substitution (PS) to sales. However, VP, extending a location's inventories to other

locations' ones, is also related to storage and sales, transportation and sales or service ca-

pacities may be pooled, any logistics decision may be postponed, and PP and PS may be

applied in production as well. This not mutually exclusive and exhaustive classification is

reflected in figure 2.3 and the next chapter's structure. We structured our review according

to the value chain approach, because we focus on the impact of risk pooling on the five

mentioned logistics value activities.

Risk pooling helps a company to cope with demand and/or lead time uncertainty and

thus to carry out these value activities at a lower cost for a given service level, a higher

service level for a given cost, or a combination of both40. Thus it may increase expected

profit41 by reducing expected costs and/or increasing expected revenue.

It may allow a company to win a competitive advantage over its competitors by effec-

tively combining Porter's (2008: 75) competition strategies of differentiation and cost lea-

dership, e. g. in mass customization enabled by postponement42.

39 Porter (2008: 75) 40 Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350). 41 Porter's (1985: 38) value chain considers margin instead of profit. “Margin is the difference between total

value and the collective cost of performing the value activities”. 42 For example Feitzinger and Lee (1997).


11

Figure 2.3: Important Value Activities Using Risk Pooling Methods

2.3 Defining Risk Pooling

The literature offers various definitions of and confusion about the terms variability, variance,

or volatility43, uncertainty44, and risk45. Lead time and demand uncertainty may arise from

lead time and demand variability or incomplete knowledge46. “Uncertainty is the inability to

determine the true state of affairs of a system”47. “Uncertainty caused by variability is a result

of inherent fluctuations or differences in the quantity of concern. More precisely, variability

occurs when the quantity of concern is not a specific value but rather a population of values”48.

Lead time and demand uncertainty may lead to economic risk49, the possibility50 of a negative

deviation from expected values or desired targets51. The corporate target is expected profit

(figure 2.3), the difference of expected revenue and expected cost.52 The possibility of a posi-

tive deviation from an expected value constitutes a chance.53

Despite the costs risk pooling entails54, it may reduce variability and thus uncertainty

and expected (ordering, inventory holding, stockout, and backorder) costs55 and/or increase

expected revenue (product availability, fill rate, service level)56 and thus expected profit57.

43 Hubbard (2009: 84f.). “Outside of finance, volatility may not necessarily entail risk—this excludes consi-

dering volatility alone as synonymous with risk” (Hubbard 2009: 91). 44 Knight (2005: 19ff.), Haimes (2009: 265ff.), Hubbard (2010: 49f.). 45 Wagner (1997: 51), Knight (2005: 19ff.), Hubbard (2009: 79ff., 2010: 49f.). 46 Cf. Haimes (2009: 265). For a detailed treatment of the confusion about the terms uncertainty and varia-

bility please refer to Haimes (2009: 265ff.). 47 Haimes (2009: 265). 48 Haimes (2009: 266). 49 Bowersox et al. (1986: 58), Delfmann (1999: 195), Pishchulov (2008: 17). 50 Wagner (1997: 51). 51 Cf. e. g. Wagner (1997: 51), Köhne (2007: 321). 52 Wagner (1997: 52). 53 Wagner (1997: 51). 54 Kim and Benjaafar (2002: 16), Cachon and Terwiesch (2009: 328).

StorageIP, PM, VP

Profit

TransportationCP, PM, TS, VP

Procurement

CO, OS, PM

Production

CC, CP, PM, PP, PS

Sales & Distribution

CP, PM, PP, PS, VP


12

We define risk pooling in business logistics as consolidating individual variabilities

(measured with the standard deviation58) of demand and/or lead time in order to re-

duce the total variability59 they form and thus uncertainty and risk60 (the possibility

of not achieving business objectives61). The individual variabilities are consolidated by

aggregating62 demands63 (demand pooling64) and/or lead times65 (lead time pooling66).

Consolidating and aggregating mean “combining several different elements […] into a

whole”67.

As individual variabilities68 and not individual risks69 are pooled, the term risk pooling

is misleading. Nonetheless, we use it, because it is conventional.

55 Eppen (1979), Chen and Lin (1989), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996:

114, 1997: 71f.), Cherikh (2000: 755), Eynan and Fouque (2003: 704), Kemahloğlu-Ziya (2004), Bar-tholdi and Kemahloğlu-Ziya (2005), Wong (2005), Jiang et al. (2006: 25), Thomas and Tyworth (2006: 253), Chopra and Meindl (2007: 324ff.), Pishchulov (2008: 8, 17f.), Schmitt et al. (2008a: 14, 20), Sim-chi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331, 344, 350).

56 Krishnan and Rao (1965), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996: 111, 114, 1997: 71f., 1999: 122), Eynan (1999), Cherikh (2000: 755), Ballou and Burnetas (2000, 2003), Xu et al. (2003), Ballou (2004b: 385-389), Wong (2005), Kroll (2006), Reyes and Meade (2006), Chopra and Meindl (2007: 324ff.), Cachon and Terwiesch (2009: 325, 329, 344, 350).

57 Anupindi and Bassok (1999), Cherikh (2000: 755), Lin et al. (2001a), Eynan and Fouque (2003: 704, 707, 2005: 98), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Özen et al. (2005), Chopra and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: 234-238), Cachon and Terwiesch (2009: 331), Yang and Schrage (2009: 837).

58 Sussams (1986: 8), Romano (2006: 320). “The standard deviation is the most commonly used and the most important measure of variability” (Gravetter and Wallnau 2008: 109). Zinn et al. (1989: 2) and Cho-pra and Meindl (2007: 307) consider the standard deviation a measure of uncertainty. Cachon and Ter-wiesch (2009: 331f., 282f.) and Chopra and Meindl (2007: 307) use the derived coefficient of variation (standard deviation divided by mean) as a measure for demand variability or uncertainty. Pooling independent random variables does not change total variability measured with the variance. Of course, one could argue that the measuring unit of the variance is squared and therefore difficult to interp-ret and that the standard deviation and not the variance is used to calculate safety stock. Pooling variabili-ties measured with the range may even increase total variability.

59 Cf. e. g. Chopra and Meindl (2007: 336). 60 Cf. e. g. Pishchulov (2008: 18). 61 Wagner (1997: 51). 62 Cf. e. g. Anupindi et al. (2006: 167), Chopra and Meindl (2007: 336). 63 Gerchak and Mossman (1992: 804), Swaminathan (2001: 131), Hillier (2002b: 570), Randall et al. (2002:

56), Gerchak and He (2003: 1027), Özer (2003: 269), Chopra and Sodhi (2004: 55, 60), Nahmias (2005: 334), Anupindi et al. (2006: 167, 187), Çömez et al. (2006), Romano (2006: 320), Chopra and Meindl (2007: 177), Pishchulov (2008: 8, 18, 26), Simchi-Levi et al. (2008: 48, 196, 281, 348), Yu et al. (2008: 1), Yang and Schrage (2009: 837), Bidgoli (2010: 209).

64 Evers (1997: 55, 57, 1999: 121f.), Benjaafar and Kim (2001), Benjaafar et al. (2004a: 1442, 2004b: 91), Chopra and Sodhi (2004: 59ff.), Tomlin and Wang (2005: 37), Gürbüz et al. (2007: 302), Van Mieghem (2007: 1270f.), Ganesh et al. (2008: 1134), Cachon and Terwiesch (2009: 332), Wanke and Saliby (2009: 690), Yang and Schrage (2009: 837).

65 Thomas and Tyworth (2006: 254). 66 Evers (1999: 121f.), Cachon and Terwiesch (2009: 336). 67 Soanes and Hawker (2008). 68 Gerchak and He (2003: 1028). 69 The business logistics risk pooling literature finds “the risk related to the uncertainty” of individual de-

mands (Zinn 1990: 12), risk “over uncertainty in customer demand” (Anupindi and Bassok 1999: 187), standard deviations (Zinn 1990: 13) or variances of individual demands (Zinn 1990: 16), risk “over de-mand uncertainty” (Weng 1999: 75) or risk “over random supply lead time” (Weng 1999: 82), “inventory


13

Among others Hempel (1970: 654), Wacker (2004: 630), and the references they give

make requirements for a “good”70 definition. To our knowledge previous attempts to de-

fine risk pooling do not satisfy them. They merely describe its causes71, effects72, or aim73,

only target demand pooling74, and equate risk pooling with inventory pooling75 and the

square root law76. Moreover they do neither define nor differentiate between variability77,

uncertainty, and risk. The business logistics risk pooling literature states risk pooling re-

duces

variability78, “lead-time variability”79, lead time demand variability80, demand va-

riability81, demand variation82, variation83, “demand variance”84, variance of deli-

very time85, “the variance of the retailers' net inventory processes”86, “the mean and

variance of cycle stock”87,

uncertainty88, demand uncertainty89, “the uncertainty the firm faces”90, “the effect

of uncertainty”91,

risks” (Van Hoek 2001: 174, Pishchulov 2008: 27), “inventory risk” (Kemahlioğlu-Ziya 2004: 76), “fore-cast risk” (Chopra and Sodhi 2004: 58, 60), risk (Schwarz 1989: 830, 832, McGavin et al. 1993: 1093, Chopra and Sodhi 2004: 58, 60f., Simchi-Levi et al. 2008: 357, Yang and Schrage 2009: 837), risks (Aviv and Federgruen 2001a: 514, Gerchak and He 2003: 1027), “risk over the outside-supplier leadtime” (Schwarz 1989: 828, McGavin et al. 1993: 1093), “lead-time risk” (Thomas and Tyworth 2006: 245f., 2007: 169), “lead-time uncertainty” (Evers 1997: 70, Thomas and Tyworth 2006: 245), “lead-time fluctu-ations” (Evers 1997: 70), “demand uncertainty” (Evers 1997: 70), uncertainty (Evers 1994: 51, Rabino-vich and Evers 2003a: 206), or “quantity and timing uncertainty” (Collier 1982: 1303) is or are pooled.

70 “A ‘good’ [formal conceptual] definition […] is a concise, clear verbal expression of a unique concept that can be used for strict empirical testing” (Wacker 2004: 631). Hempel (1970: 654) requires inclusivi-ty, exclusivity, differentiability, clarity, communicability, consistency, and parsimony.

71 Nahmias (2005: 334), Anupindi et al. (2006: 168), Romano (2006: 320), Simchi-Levi et al. (2008: 48), Wisner et al. (2009: 513), Bidgoli (2010: 209).

72 Gerchak and He (2003: 1027), Özer (2003: 269), Romano (2006: 320), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 350), Bidgoli (2010: 209).

73 Chopra and Meindl (2007: 212), Cachon and Terwiesch (2009: 321). 74 Flaks (1967: 266), Gerchak and Mossman (1992: 804), Gerchak and He (2003: 1027), Özer (2003: 269),

Nahmias (2005: 334), Anupindi et al. (2006: 187), Chopra and Meindl (2007: 212). 75 Anupindi et al. (2006: 168). 76 Wisner et al. (2009: 513). 77 Tallon (1993: 192, 199f.) equates variability with uncertainty. 78 Eynan and Fouque (2005: 91), Anupindi et al. (2006: 167). 79 Thomas and Tyworth (2007: 171). 80 Benjaafar and Kim (2001). 81 Flaks (1967: 266), Zinn (1990: 11), Randall et al. (2002: 56), Eynan and Fouque (2003: 705, 2005: 91),

Romano (2006: 320), Thomas and Tyworth (2006: 255, 2007: 188), Chopra and Meindl (2007: 212), Pishchulov (2008: 18), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331), Wisner et al. (2009: 513), Bidgoli (2010: 209).

82 Eynan and Fouque (2005: 91), Nahmias (2005: 334). 83 Evers (1999: 133). 84 Kemahlioğlu-Ziya (2004: 71). 85 Masters (1980: 71), Ihde (2001: 33). 86 Schwarz (1989: 830). 87 Thomas and Tyworth (2006: 247f.) 88 Pishchulov (2008: 22), Simchi-Levi et al. (2008: 281). 89 Eynan and Fouque (2003: 714), Pishchulov (2008: 17).


14

“the risk associated to the variability”92, the “impact of individual risks”93, “risks

associated with forecasting errors and inventory mismanagement”94, and “inventory

risk”95.

Risk pooling is described “to hedge uncertainty so that the firm is in a better position to miti-

gate the consequence of uncertainty”96, “enables one to avoid […] uncertainty”97, or “removes

some of the uncertainty involved in planning stock levels”98.

It is also referred to as “statistical economies of scale”99, “portfolio efficiencies”100,

“Pooling Efficiency trough Aggregation” or “Principle of Aggregation”101, and “IMPACT

OF AGGREGATION ON SAFETY INVENTORY”102.

Risk pooling is also considered a form of operational hedging. “Hedging is the action

of a decision maker to mitigate a particular risk exposure. Operational hedging is risk miti-

gation using operational instruments”103, e. g. pure diversification or demand pooling104.

For more on operational hedging please refer to Boyabatli and Toktay (2004) and Van

Mieghem (2008: 313-350).

2.4 Explaining Risk Pooling

Risk pooling can be shown e. g. for inventory or location pooling: Let a single product be

stocked at n separate locations. Demand for this product is a normal random variable105 xi with

known mean µi and standard deviation106 σi for each location i = 1, …, n. The standard devia-

90 Cachon and Terwiesch (2009: 321). 91 Özer (2003: 269). 92 Risk pooling “is applied to portfolio theory in finance here [sic!] the risk associated to the variability in

the return from individual stocks is diluted when an investor keeps a portfolio of stocks“ (Zinn 1990: 12). 93 Dilts (2005: 23). 94 Yang and Schrage (2009: 837). 95 Chopra and Sodhi (2004: 59). 96 Cachon and Terwiesch (2009: 321). 97 Pishchulov (2008: 26) remarks this for risk pooling through delayed differentiation. 98 Jackson and Muckstadt (1989: 2). 99 Eppen (1979: 498), Eppen and Schrage (1981: 52), Evers (1994: 51), Özer (2003: 269), Rabinovich and

Evers (2003a: 206). 100 Eppen and Schrage (1981: 52). 101 Anupindi et al. (2006: 187, 189). 102 Chopra and Meindl (2007: 318). 103 Van Mieghem (2007: 1270). 104 Van Mieghem (2007: 1270f.). 105 A random variable is a variable that takes its values (realizations) with certain probabilities respectively

whose values are assigned to certain probability densities (Alisch et al. 2004: 3454). 106 If (the empirical distribution of) demand is forecast (Thonemann 2005: 255f.), σi is the standard deviation

of the distribution of the forecast error in formula (2.1) for calculating safety stock (Caron and Marchet 1996: 239, Pfohl 2004a: 114, Thonemann 2005: 255f., Chopra and Meindl 2007: 306). An estimate of expected demand (forecast value) is ordered to satisfy the expected value of demand and safety stock is


15

tion σi is a measure of dispersion of individual values of the random variable xi around the

mean µi for every entity i and therefore a measure of xi's variability107.

If each location just satisfies its own demand, location i needs to hold an amount of

safety stock that allows it to hedge against the demand uncertainty associated with xi. Let

the optimal safety stock at location i in accordance with the newsboy model108 be

, (2.1)

where z is the safety factor that corresponds to a certain target service level. Therefore,

the total safety stock across all locations is

∑ . (2.2)

If all inventory holding is centralized at one location, this location needs to serve the to-

tal demand

∑ . (2.3)

The individual demands are aggregated across all locations. Safety stock in the centra-

lized system is

, (2.4)

where

∑ 2∑ ∑ 109 (2.5)

is the standard deviation of x and ρij is the correlation coefficient of the value of the random

variable for locations i and j. It can be formally shown that the aggregated variability (standard

deviation of total demand σa) is less than or equal to the sum of the individual variabilities

built up as protection against the forecast error, which is at least as high as the demand uncertainty or standard deviation of demand (personal correspondence with Professor Ulrich W. Thonemann, University of Cologne, in 2008), and not against uncertainty in demand (Thonemann 2005: 255f.). A high safety stock is needed, if the (standard deviation of the) forecast error is high. The size of demand fluctuations is irrelevant (Thonemann 2005: 257). If the distribution of demand is known, σi is the standard deviation of demand (Zinn et al. 1989: 4) and safety stock is held to hedge against uncertainty in demand. The higher the uncertainty in demand, the higher is the safety stock. The standard deviation of demand is zero and no safety stock is needed, if there is no demand uncertainty (Thonemann 2005: 238) and no lead time uncer-tainty either. Nonetheless, some companies forecast demand, but wrongly use the standard deviation of demand instead of the standard deviation of the forecast error in calculating safety stock (Korovessi and Linninger 2006: 489f.).

107 Gravetter and Wallnau (2008: 109). 108 See e. g. Thonemann (2005: 220), Cachon and Terwiesch (2009: 235). 109 Cf. Mood et al. (1974: 178), Zinn et al. (1989: 5), Jorion (2009: 43). This expression is also written

∑ 2∑ ∑ (Eppen 1979: 500) or ∑ 2∑ ∑ (cf.

Weisstein 2010). “The double summation sign ∑∑ indicates that all possible combinations of i and j should be included in calculating the total value” (Moyer et al. 1992: 222), where j is larger than i.


16

(sum of standard deviations of demand at the n locations σ) because of the subadditivity prop-

erty of the square root of non-negative real numbers110:

∑ ∑ 2∑ ∑ . (2.6)

Therefore the safety stock in the centralized system is less than or equal to the one in the

decentralized one

∑ ∑ 2∑ ∑ . (2.7)

Inequality (2.6) is a special case of the known Minkowski inequality for p = 2. It is al-

ways correct, if the variances exist, therefore also for the Poisson and Binomial distribu-

tion.111

Hence, the standard deviation of the aggregate demand is lower than or equal to the sum

of the standard deviations of the individual demands. Consequently, inventory pooling or

centralization at a single location can reduce the amount of safety stock necessary to en-

sure a given service level. The reduction in safety stock depends on the correlations be-

tween xi, i = 1, …, n. Inventory pooling does not always reduce safety stock due to the

less-than-or-equal sign.

Yet, the sum of the individual variabilities (standard deviations) only equals the total

aggregated variability (the square root of the sum of the individual variances plus two

times the covariance of the random variable's value for two entities i and j) in two cases:

(1) The random variables xi are perfectly positively correlated (the coefficient of

correlation ρij equals 1, i, j):

∑ 2∑ ∑ ∑ ∑ 112

∑ ∑ 1 ∑ ∑ .

(2.8)

(2) Random variables xi cannot mutually balance their fluctuations, if at least

n-1 σi equal zero: If n-1 σi equal zero, (2.6) becomes

(2.9)

for this single non-zero σi. If all σi are zero, (2.6) becomes

110 Gaukler (2007). 111 Minkowski (1896), Abramowitz and Stegun (1972: 11), Bauer (1974: 72), Gradshteyn and Ryzhik (2007:

1061). 112 Cf. Moyer et al. (1992: 222). This expression is also written ∑ ∑ ∑ , (cf.

Jorion 2009: 43).


17

0 . (2.10)

Apart from this, for independent (the correlation coefficient ρij is equal to 0, i, j) nor-

mally distributed random variables risk pooling leads to variability reduction:

∑ ∑ . (2.11)

The highest possible variability reduction is achieved, if there are negative correla-

tions which make the second term under the square root equal to minus the first term113 in

(2.6).

Some authors114 give the impression that risk pooling always reduces total variability or

enables to reduce inventory, although this must not be the case as shown above.

Likewise industry and academia often assume that inventory pooling, a type of risk

pooling, always is beneficial, i. e. it either reduces costs or increases profits, and that the

value of inventory pooling increases with increasing variability of demand.115

Kemahlioğlu-Ziya (2004: 40) states this was only always correct for normally distributed

demand such as in Eppen (1979) or Eppen and Schrage (1981). She neglects though that

this is not correct for perfectly positively correlated demands and if at least n-1 σi equal

zero.

Furthermore, for uncertain demand and certain conditions more willingness to substitute

may not lead to higher expected profits or “lower optimal total inventory”116 for full117 and

partial substitution or risk pooling118.

113 Cf. Eppen (1979: 500). 114 Tallon (1993: 186) imprecisely remarks, “Mathematically, the square root of the sum of the variances is

less than the sum of the individual standard deviations”. Likewise, Anupindi et al. (2006: 191) inaccu-rately state “the inventory benefits” from physical centralization “result from the statistical principle called the principle of aggregation, which states that the standard deviation of the sum of random vari-ables is less than the sum of the individual standard deviations”. Gaukler (2007) uses the less-than-or-equal sign, but inconsistently says the standard deviation of the aggregate demand was lower than (not lower than or equal to) the sum of the standard deviations of the individual demands. Although Gaukler (2007) states his remarks were not intended to be a rigorous derivation of this concept, they should be consistent. “It is well known that the pooled demand has a lower standard deviation than the sum of stan-dard deviations of individual demands. Thus, the safety stock as well as inventory holding and shortage costs are lower when products are more substitutable” (Ganesh et al. 2008: 1134). “Inventory pooling represents a strategy of consolidating inventories and aggregating stochastic demands, enabling reduc-tions in inventory holding and shortage costs” (Pishchulov 2008: 8). “Risk pooling suggests that demand variability is reduced if one aggregates demand across locations” (Romano 2006: 320, Simchi-Levi et al. 2008: 48). “The aggregation of demand stemming from risk pooling leads to reduction in demand varia-bility, and thus a decrease in safety stock and average inventory” (Simchi-Levi et al. 2008: 50). “Centra-lizing inventory reduces both safety stock and average inventory in the system” (Simchi-Levi et al. 2008: 51). Finally, inventory pooling does not automatically reduce inventory, but it may allow to reduce the inventory necessary to provide a given service level.

115 Kemahlioğlu-Ziya (2004: 40). 116 Yang and Schrage (2009: 837). 117 Baker et al. (1986), Pasternack and Drezner (1991), Gerchak and Mossman (1992). 118 McGillivary and Silver (1978), Parlar and Goyal (1984), Anupindi and Bassok (1999), Ernst and Kouve-

lis (1999), Rajaram and Tang (2001), Netessine and Rudi (2003).


18

Yang and Schrage (2009) show this “inventory anomaly” (after demand substitution or

risk pooling the company ought to hold more stock rather than less) for full substitution

with any right skewed demand distribution119 if the shortage is somewhat higher than the

holding cost per unit, for partial substitution with exponential, Normal, Poisson, and uni-

form demands even if they are negatively correlated, as well as for more than one period,

with backlogging, lost sales, more than two products, and with setup costs. The inventory

anomaly is increasing as the underage is close to the overage cost per unit and as the cor-

relation between demands decreases.120 The relative difference of the shortage to holding

cost for which the anomaly arises increases with increasing right skewedness. A company

will not face the inventory anomaly, if it uses a shortage penalty, but minimizes inventory

carrying costs subject to a fixed target service level. However, it may not seize the chance

to increase sales and profits, if it augments demand pooling without raising inventory. The

likelihood of the inventory anomaly is higher with short lead times and lower with less

frequent but larger orders, e. g. with high setup costs.121

Inventory pooling may reduce costs and increase profits for the supply chain party hold-

ing inventory122, but may reduce the total supply chain profits. In a two-echelon supply

chain, where the upper echelon (the supplier) carries inventory, the lower echelon (the re-

tailers), whose revenues depend only on sales, may lose profits due to pooling.123 The sup-

plier and the retailers are likely to benefit from risk pooling inventory, if the stockout pe-

nalty cost is high.124

The normal random variable xi in our derivation of risk pooling can also be the demands

for i unique components, product versions, substitute products, customized products, or

(replenishment) lead times to i locations. They are aggregated to the demand for a common

component in component commonality125, universal product in product pooling, all substi-

tutes in product substitution or demand reshape, the undifferentiated generic product in

postponement or delayed product differentiation, or to an aggregated lead time across all

locations, suppliers, or deliveries in lead time pooling (emergency transshipments and or-

der splitting). The aggregated demand and/or lead time x may fluctuate less, as the stochas-

119 “Actual demand distributions tend to be right skewed” (Yang and Schrage 2009: 847). 120 Yang and Schrage (2003: 1). 121 Yang and Schrage (2009: 847). 122 Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005). 123 Anupindi and Bassok (1999). 124 Dai et al. (2008: 411). 125 Dogramaci (1979: 130) shows that “the standard deviation of demand for the common component (σc)

would be less than or equal to” the sum of “the standard deviation[s] of lead time demand” of the compo-nents it replaces.


19

tic fluctuations (σi) of the individual demands and/or lead times usually balance each other

to a certain extent (equation 2.6).

Risk pooling by demand pooling in transshipments, virtual pooling, centralized order-

ing, and capacity pooling can be derived in the same manner as shown for inventory pool-

ing: Demands are pooled across locations.

2.5 Characteristics of Risk Pooling

We now turn to describing five important characteristics common to most risk pooling me-

thods: (1) increasing returns, but (2) diminishing marginal returns with increasing application

as well as increasing benefit with (3) increasing demand variability, (4) decreasing demand

correlation, and (5) decreasing concentration of uncertainty.

(1) The benefit of or return on risk pooling is variability reduction and thus enabled in-

ventory reduction for a given service level or increase in service level for a given invento-

ry. The risk pooling return generally (in the following cases) increases with increasing

application or the number of participants:

It augments with the number of

participating stock-keeping locations in inventory pooling126, time and logistics

postponement127, transshipments128, and cross-filling129,

(substitutable) products and degree of substitution in product substitution, demand

reshape130, and resource flexibility131,

products in the product line132 or products being postponed133 in manufacturing

postponement,

products sharing components (increasing commonality) in component commonali-

ty134, as well as

126 Lin et al. (2001a), Heil (2006: 170), Netessine and Rudi (2006), Milner and Kouvelis (2007), Cachon and

Terwiesch (2009: 282f.). 127 Zinn and Bowersox (1988: 133), Heil (2006: 170). 128 Jönsson and Silver (1987a: 224), Robinson (1990), Diks and de Kok (1996: 378), Tagaras (1999), Evers

(2001: 313), Herer et al. (2002), Tagaras and Vlachos (2002), Dong and Rudi (2004), Burton and Baner-jee (2005), Hu et al. (2005), Heil (2006: 170).

129 Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389). 130 Eynan and Fouque (2003, 2005), Ganesh et al. (2008: 1124). 131 Tomlin and Wang (2005: 51). 132 Zinn (1990: 14), Swaminathan and Tayur (1998). 133 Graman and Magazine (2006: 1075). 134 Collier (1982: 1303), Srinivasan et al. (1992: 26), Grotzinger et al. (1993: 532f.), Eynan and Fouque

(2005), Chew et al. (2006: 247).


20

retailers in pooling over the outside-supplier lead time or centralized ordering135

and risk pooling by drop-shipping or virtual pooling136.

(2) However, the marginal benefit of risk pooling commonly decreases with each addi-

tional increase in risk pooling or participant. There appear to be diminishing marginal

returns to risk pooling137, e. g. to cross-filling138 and transshipments with increasing num-

ber of locations transshipping139 or increasingly even allocation of demand across loca-

tions140, to virtual pooling by drop-shipping with increasing number of retailers141, to com-

ponent commonality142, postponement143, product substitution144, capacity pooling, and

location pooling145.

The marginal benefit of location pooling decreases with increasing number of pooled

locations146, so that the main benefit is gained by consolidating a few locations and it might

not be necessary to pool all locations147. The same applies to transshipments.148

Capacity pooling with a little bit of flexibility149 as long as it is designed with long

chains150 almost has the same benefit as full flexibility. Companies can benefit from any

135 Jackson and Muckstadt (1989: 14), Kumar and Schwarz (1995), Gürbüz et al. (2007). 136 Netessine and Rudi (2006: 845). 137 Similarly, in corporate finance we can observe diminishing marginal risk reduction with increasing num-

ber of securities: At first diversification reduces portfolio risk (standard deviation or volatility) rapidly, then more slowly with increasing number of randomly chosen stocks (Statman 1987: 353, 355). In recent years stocks have become individually more volatile but are increasingly less than perfectly correlated. Therefore an investor needs to hold more stocks to capture the majority of benefits from diversification than before (Campbell et al. 2001: 40).

138 Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389). Based on Ballou's (2003b: 81) numerical example, we devise the general formula for the effective fill rate EFR for the customer in dependence of the for all locations equal item fill rate FR (0 1) and the number n of locations that cross-fill as

1 1 . The first derivative of EFR with respect to n shows that the more locations cross-fill the higher is the EFR: ⁄ 1 · ln 1 0. However, the incremental in-crease in EFR diminishes with increasing number of locations taking part in cross-filling: ⁄1 · ln 1 · ln 1 0.

139 Evers (1997: 70). 140 Evers (1996: 128). 141 Netessine and Rudi (2006: 852). 142 Chopra and Meindl (2007: 327f.) find by a numerical example that “the marginal benefit [… marginal

reduction in safety stock] decreases with increasing commonality” for independent and normally distri-buted end-product demand, but formulate this result as if generally valid. Bagchi and Gutierrez (1992) show by two numerical examples (817) that “increasing component commonality results in increasing marginal returns when the criteria are aggregate service level and aggregate stock requirement” (815) for two end-products that face independent, identically exponentially, geometrically, or Poisson distributed demands and share up to three components (815, 817f., 824). They do not give an intuitive explanation (829).

143 Zinn (1990: 14), Graman and Magazine (2006: 1075, 1080). 144 Eynan and Fouque (2003: 707, 2005: 96). 145 Cachon and Terwiesch (2009: 323, 349). 146 Cachon and Terwiesch (2009: 323, 349). 147 Cachon and Terwiesch (2009: 323f.). 148 Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389), Kranen-

burg and Van Houtum (2009).


21

amount of risk pooling as long as they implement it appropriately151 and demand is not

perfectly positively correlated. Graman and Magazine (2006: 1075) similarly observe per-

taining to postponement “that it is only necessary to postpone a portion of a product to

realize most of the benefits of such a strategy”. “The mathematical inventory model shows

that almost all of the positive benefits of postponement (such as lower inventories) can be

achieved with a partial (low-capacity) postponement scenario”152.

Cachon and Terwiesch (2009: 324) show diminishing marginal returns of location pool-

ing with increasing mean for independent Poisson demands.153 This must not necessarily

hold for other distributions such as the normal one.154

(3) The (demand) risk pooling effect decreases with increasing demand correlation155

and any Magnitude (relative sizes of the standard deviations of demand), and increases

149 Flexibility means that a plant is capable of producing more than one product. With no flexibility each

plant can only produce one product; with total flexibility every plant can produce every product (as in manufacturing postponement). Graphically lines called links indicate which plant is capable of producing which product. Flexibility allows production shifts to high selling products to avoid lost sales (Cachon and Terwiesch 2009: 344f.).

150 “A chain is a group of plants and [… products] that are connected via links” (Cachon and Terwiesch 2009: 346).

151 Cachon and Terwiesch (2009: 349). 152 Graman and Magazine (2006: 1080). 153 “[T]he standard deviation of a Poisson distribution equals the square root of its mean. Therefore, Coeffi-

cient of variation of a Poisson distribution √

√ […].

As the mean of a Poisson distribution increases, its coefficient of variation decreases, that is, the Poisson distribution becomes less variable. Less variable demand leads to less inventory for any given service level. Hence, combining locations with Poisson demand reduces the required inventory investment be-cause a higher demand rate implies less variable demand. However, because the coefficient of variation decreases with the square root of the mean, it decreases at a decreasing rate. In other words, each incre-mental increase in the mean has a proportionally smaller impact on the coefficient of variation, and hence on the expected inventory investment” (Cachon and Terwiesch 2006: 324). This can also be derived for-mally: The first derivative of the coefficient of variation √ ⁄⁄ with respect to the mean λ

is smaller than zero, the second one larger than zero: ⁄ 0, ⁄ 0. 154 For the normal distribution it depends on how the coefficient of variation changes with respect to the

mean. With the Poisson distribution it decreases as the mean increases, but this is not necessarily the case with the normal distribution. However, we find that there are at least diminishing marginal returns to pooling of normally distributed independent demands with the same standard deviation and mean. For normally distributed independent demand the coefficient of variation of pooled demand is ∑

∑. If the standard deviation and mean is the same at each pooled location i, this expression simpli-

fies to √

√. The first and second derivative of COV with respect to the number n of

pooled locations shows that as n increases COV decreases at a decreasing rate: ⁄ 0,

⁄ 0. 155 Eppen (1979), Zinn et al. (1989: 12), Inderfurth (1991: 109, 111), Netessine and Rudi (2003: 329), Alfaro

and Corbett (2003), Corbett and Rajaram (2004, 2006), Heil (2006: 170), Chopra and Meindl (2007: 319), Cachon and Terwiesch (2009: 349). In serial or divergent multi-stage base-stock production/distribution systems the lower the demand correlation, the further upstream safety stocks should be held and vice ver-sa and the lower the worth of safety stocks because of product-dependent risk diversification (risk pool-


22

with decreasing correlation and Magnitude156. Likewise the value of lead time risk pooling

(order splitting157 and transshipments) increases with decreasing correlation of replenish-

ment lead times.

Therefore, many “companies attempt to reduce inventory and manufacturing costs by

manipulating correlated demand sources, or inducing demand patterns that balance each

other in an average sense”158, i. e. by risk pooling, while maintaining sales.159

The bullwhip effect160 can be reduced by risk pooling (effects)161, production smooth-

ing, and seasonality162, so that it may be overestimated163.

Evers and Beier (1993) and Evers (1995) debatably show that there are no further sav-

ings in safety stock after a first consolidation because of the arising perfectly positive cor-

relation.

Tyagi and Das (1999: 211) show that if demands are correlated and one appropriately

takes advantage of their characteristics, a partial may be more cost-efficient than complete

pooling of customers.

On the other hand, Xu and Evers (2003) claim that partial can never outperform com-

plete pooling only based on demand correlation. Examples suggesting that one should pre-

fer partial to complete aggregation were based on inconsistent correlation matrices.

(4) The benefits of risk pooling generally increase with a structured (“a common linear

transformation”164) increase in demand variability165, if lead times are exogenous (for in-

ventory pooling, product consolidation, and delayed differentiation166). Gerchak and He

ing) (Inderfurth 1991: 109, 111). Nonetheless, the total safety stock size may increase with decreasing correlation due to the impact of time-dependent risk diversification on carrying safety stocks at the still more costly final stage level because of long replenishment lead times (Inderfurth 1991: 111).

156 Zinn et al. (1989: 3, 12), cf. Tallon (1993: 201), Tyagi and Das (1998: 201), Wanke (2009: 122). 157 Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188). 158 Burer and Dror (2006: 1). 159 Gerchak and Gupta (1991), Ruusunen et al. (1991), Hartman and Dror (2003: 243f.), Tyagi and Das

(1999). 160 The bullwhip effect describes that demand (order) variabilities are amplified as they move upstream the

supply chain (Lee et al. 1997a: 93, 1997b: 546, 2004: 1875, Sucky 2009: 311). It is caused by demand forecast updating or demand signaling, order batching, price fluctuation, as well as rationing and shortage gaming (Lee et al. 1997a: 95, 1997b: 546, 2004: 1883) and can be counteracted by avoiding multiple de-mand forecast updates, breaking order batches, stabilizing prices, and eliminating gaming in shortage sit-uations (Lee et al. 1997a: 98ff., 1997b: 555ff., 2004: 1883ff.).

161 Hartman and Dror (2003: 244), Lee et al. (2004: 1882), Cachon et al. (2007: 475), Chen and Lee (2009: 781), Sucky (2009: 311).

162 Cachon et al. (2007). 163 Cachon et al. (2007), Sucky (2009). 164 Gerchak and He (2003: 1027). 165 Kemahlioğlu-Ziya (2004: 22), Zinn et al. (1989), Alfaro and Corbett (2003), Eppen (1979). 166 Benjaafar and Kim (2001: 19f.), Benjaafar et al. (2004b: 90f., 2005).


23

(2003) provide a newsvendor counterexample with convex ordering where increased va-

riability of two individual demands reduces the benefits of risk pooling.

If supply lead times are endogenous in multi-item finite capacity production-inventory

systems, both higher demand variability167 and capacity utilization (arrival rate divided by

service rate)168 or asymmetric backordering or holding costs make risk (inventory) pool-

ing169 less valuable170.

(5) Assuming a multivariate normal distribution and uncorrelated demands, the value of

pooling is lower when uncertainty is more concentrated, i. e. the less uniform or more

dispersed the values of the standard deviations of the demands are.171 Correspondingly,

“the PE will be larger when variances are of similar rather than highly varying magni-

tude”172.

167 Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1446). 168 Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1438, 2004b: 71,

2005: 550). 169 “While the relative benefit of inventory pooling tends to diminish with utilization, the relative benefit of

capacity pooling tends to increase with utilization” (Benjaafar et al. 2005: 550). 170 Kim and Benjaafar (2002: 15). 171 Alfaro and Corbett (2003: 24). 172 Tyagi and Das (1998: 201), cf. Zinn et al. (1989).

24

3 Methods of Risk Pooling

After clarifying the prerequisites in the previous chapter, we will now enumerate the ten identi-

fied risk pooling methods and their synonyms, present a classification according to their ability

to pool demands and/or lead times, and define, classify, and characterize them correspondingly

within the structure of the aforementioned five logistics value activities.

First, under the heading storage we deal with inventory pooling and centralization, the

SRL, PE, and inventory turnover curve, as this area shows the earliest and most extensive

research in risk pooling (cf. figure 2.1) and requires a review173. The various SRL and PE

models are compared in a synopsis (table D.2) based on their assumptions. This facilitates

choosing an appropriate model to determine stock savings from inventory pooling for spe-

cific conditions or adapt the existing models by adding or dropping assumptions and re-

lates our centralized ordering considerations in section 5.3.3.2 to these models.

Afterwards, virtual pooling, which is related to inventory pooling, and transshipments

are examined (transportation). Upon considering risk pooling in these two original (tradi-

tional) logistics duties that refer to the transfer of objects (above all of goods)174, we survey

it in the derivative logistics areas175 procurement (centralized ordering and order splitting),

production (component commonality, postponement, and capacity pooling), and sales and

distribution (product pooling and substitution) downstream the value chain.

Perhaps since risk pooling and centralization of inventories (distribution or warehouse

networks) are closely related, the terms inventory pooling176 or just pooling177 are often

used interchangeably and ambiguously for risk pooling (methods), although inventory

pooling literally merely refers to the consolidation or centralization of inventory, is a

type178 or manifestation179 of risk pooling, and takes advantage of the possible benefits of

risk pooling.

173 Personal correspondence with Professor Walter Zinn, Fisher College of Business, The Ohio State Univer-

sity on July 4, 2008. 174 Delfmann (2000: 323). 175 Delfmann (2000: 323). 176 Benjaafar and Kim (2001: 13), Kemahlioğlu-Ziya (2004: 11), Gaur and Ravindran (2006: 482), Pishchu-

lov (2008: iii, 23f., 26, 28ff., 133), Simchi-Levi et al. (2008: 239). 177 Evers (1999: 121), Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Kemahlioğlu-Ziya

(2004: 11), Pishchulov (2008: iv, vi, vii, 8, 17f.). 178 “A finite set of outlets with randomly fluctuating demands bands together to reduce costs by buying,

storing and distributing their inventory jointly. This is termed inventory centralization and is a type of risk pooling” (Burer and Dror 2006: 1). Cachon and Terwiesch (2009: 321).

179 Gerchak and He (2003: 1027).


25

After a thorough literature review we conclude that apart from

(1) inventory pooling180, location pooling181, or (physical) inventory or ware-

house centralization182 (SRL, PE, selective stock keeping, inventory turnover

curve),

risk pooling in business logistics can also be achieved by

(2) virtual pooling183, virtual inventory or inventories184, “electronic invento-

ry”185, virtual centralization186, virtual warehouse187 or warehousing188, “vir-

tually aggregating inventories”189, or information centralization190,

(3) transshipments (stock sharing between inventory locations)191 or “location

substitution”192,

(4) centralized ordering193, “consolidated distribution”194, “risk pooling over the

outside-supplier lead time”195, or ”warehouse risk-pooling”196,

(5) order splitting or multiple suppliers197,

(6) component commonality198, component sharing199, part standardization200, or

procurement standardization201,

180 Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 13), Anupindi et al. (2006: 189, 273), Heil

(2006), Yang and Schrage (2009: 837). Cf. also references in section 1.1. 181 Cachon and Terwiesch (2009: 321ff.). 182 Eppen (1979), Zinn (1990: 12), Benjaafar and Kim (2001: 13), Martinez et al. (2002: 14), Ghiani et al.

(2004: 9), Reiner (2005: 434), Anupindi et al. (2006: 187-194), Sheffi (2006: 117f., 2007), Brandimarte and Zotteri (2007: 57f.), Chopra and Meindl (2007: 336), Pishchulov (2008: iii, 17, 133).

183 Cachon and Terwiesch (2009: 321, 350, 469), Mahar et al. (2009: 561). 184 Snyder (1995), Christopher (1998: 135), Hutchings (1999), Caddy and Helou (2000: 1715), Planning &

Reporting (2001), Randall et al. (2002: 56), Sawyers (2003), Ballou (2004b: 335, 385-389), Kroll (2006). 185 Christopher (1998: 135). 186 Anupindi et al. (2006: 194f., 314, 335). 187 Electrical Wholesaling (1997), Faloon (1999), Franse (1999), Duvall (2000), Purchasing (2000), AFSAC

(2001), Gourmet Retailer (2002). 188 Verkoeijen and deHaas (1998). 189 Chopra and Meindl (2007: 336). 190 Chopra and Meindl (2007: 321f.). 191 Benjaafar and Kim (2001: 13), Taylor (2004: 301ff.), Diruf (2005, 2007), Nonås and Jörnsten (2005:

521), Muckstadt (2005: 150ff.), Heil (2006), Sheffi (2006: 248, 2007), Yang and Schrage (2009: 837). 192 Yang and Schrage (2009: 838). 193 Diruf (2005, 2007), Nonås and Jörnsten (2005: 521), Heil (2006). 194 Cachon and Terwiesch (2009: 336ff.). 195 Schwarz (1989: 828), Pishchulov (2008: iii, 133). 196 Schwarz (1989: 828). 197 Sheffi (2007: 99f., 215-222). 198 Alfaro and Corbett (2003: 15), Neale et al. (2003), Reiner (2005: 434), Anupindi et al. (2006: 192, 194,

273), Sheffi (2006, 2007: 184-186), Brandimarte and Zotteri (2007: 30, 36, 38f.), Chopra and Meindl (2007: 326ff.), Yang and Schrage (2009: 837), Bidgoli (2010: 21).

199 Benjaafar and Kim (2001: 13). 200 Zinn (1990: 12), Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 201 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.).


26

(7) postponement, delayed (product) differentiation,202 process standardiza-

tion203, or “modularization strategies”204,

(8) capacity pooling and flexible manufacturing205,

(9) product pooling206, stock keeping unit (SKU) rationalization207, universal or

generic design208, or product standardization209, as well as

(10) product substitution210, “item substitution”211, interchangeability212, “de-

mand reshape”213, or “product commonalities”214.

Risk Pooling Methods

Building Blocks IP VP TS CO OS CC PM CP PP PS

DP 1 1 1 1 0 1 1 1 1 1

LP 0 0 1 0 1 0 0 0 0 0

Table 3.1: Risk Pooling Methods' Building Blocks

As highlighted in our definition in section 2.3, risk pooling (methods) may take advantage of

demand pooling (DP) and/or lead time pooling (LP). DP aggregates stochastic demands, so

that higher-than-average demands may balance lower-than-average ones.215 LP balances high-

er-than-average and lower-than-average lead times: A late-arriving order may be compensated

by an early-arriving one216, so that safety stock can be reduced, inventory availability in-

202 Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Neale et al. (2003), Fleischmann et al.

(2004: 93), Taylor (2004: 301ff.), Sheffi (2004: 95f., 100, 2006: 297, 2007), Hwarng et al. (2005: 2841, 2842), Reiner (2005: 434), Anupindi et al. (2006: 167, 169, 193), Enarsson (2006: 178), Heil (2006), Brandimarte and Zotteri (2007: 39, 70), Chopra and Meindl (2007: 328f.), Pishchulov (2008: iii, 27, 133), Sobel (2008: 172), Cachon and Terwiesch (2009: 341ff.), Yang and Schrage (2009: 837). Many authors consider postponement and delayed (product) differentiation synonyms (e. g. Lee and Tang 1997, John-son and Anderson 2000, Aviv and Federgruen 2001a: 512, 2001b: 578, Swaminathan and Lee 2003, Mat-thews and Syed 2004, Anupindi et al. 2006: 193, Caux et al. 2006: 3244, Anand and Girotra 2007, Li et al. 2007, Simchi-Levi et al. 2008: 190, 346, Graman and Sanders 2009, LeBlanc et al. 2009). At least form postponement can be equated with delayed (product) differentiation and therefore the latter be con-sidered a subform of postponement. For a distinction of these terms, which is not relevant for our further considerations, please refer to Pishchulov (2008: 24-29).

203 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 204 Reiner (2005: 434). 205 Anupindi et al. (2006: 224), Graves (2008: 36), Cachon and Terwiesch (2009: 344ff.). 206 Cachon and Terwiesch (2009: 321, 330ff.). 207 Alfaro and Corbett (2003: 12), Neale et al. (2003), Sheffi (2006: 119, 2007), Sobel (2008: 172). 208 Pishchulov (2008: 17), Cachon and Terwiesch (2009: 330). 209 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 210 Anupindi et al. (2006: 192), Chopra and Meindl (2007: 324ff.), Yang and Schrage (2009: 837). 211 Benjaafar and Kim (2001: 13). 212 Sheffi (2006: 210, 2007). 213 Eynan and Fouque (2003, 2005). 214 Reiner (2005: 434). 215 Evers (1997: 55), Chen and Chen (2003). 216 Evers (1999: 122).


27

creased, or both217. Transshipments pool both lead times and demands, order splitting only the

former.218

Cachon and Terwiesch (2009: 336) consider consolidated distribution and delayed dif-

ferentiation types of LP: Lead times between the supplier and the retail stores in the direct-

delivery model are combined to a single lead time between the supplier and the distribution

center (DC) in the consolidated-distribution model.219 Actually (forecast) demands are

pooled over or during the outside-supplier lead time220. Thus it is likely that higher-than-

average and lower-than-average demands balance each other and inventory can be reduced

for a given service level (DP).

All risk pooling building blocks can reduce variability and thus inventory221 for a given

service level, increase the service level for a given inventory, or a combination of both222.

Table 3.1 can result in a classification according to the notation DP/LP that indicates

which risk pooling properties the risk pooling method of concern relies upon. A 1 indicates

that the respective property applies, a 0 the contrary. IP would be classified as a 1/0 – risk

pooling method.

3.1 Storage: Inventory Pooling

Inventory pooling is the combination of inventories and satisfying various demands from it in

order to reduce inventory holding and shortage costs through risk pooling.223 It is also called

vendor pooling224, product consolidation225, demand pooling226, pooling227, distributor integra-

tion228, location pooling229, or inventory centralization230. It can e. g. be achieved by invento-

ry231 or warehouse (system) centralization232 or selective stock keeping respectively specializa-

217 Evers (1997: 71, 1999: 122). 218 Evers (1997, 1999: 121). 219 Cachon and Terwiesch (2009: 339). 220 Eppen and Schrage (1981), Schwarz (1989), Schoenmeyr (2005: 4), Gürbüz et al. (2007: 293). 221 Cf. Romano (2006: 320), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 350), Bidgoli

(2010: 209). 222 Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350). 223 Benjaafar and Kim (2001: 13), Kim and Benjaafar (2002: 12), Gerchak and He (2003: 1027), Benjaafar et

al. (2005), Anupindi et al. (2006: 191), Pishchulov (2008: 8, 17), Cachon and Terwiesch (2009: 322). 224 Monezka and Carter (1976: 207). 225 Benjaafar et al. (2004b: 73). 226 Benjaafar et al. (2004a: 1442, 2004b: 91). 227 Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Benjaafar et al. (2005). 228 Simchi-Levi et al. (2008: 261, 263). 229 Cachon and Terwiesch (2009: 322). 230 Monezka and Carter (1976: 207). 231 Benjaafar et al. (2004a: 1438). 232 Eppen (1979), Benjaafar and Kim (2001: 13), Taylor (2004: 304f.), Reiner (2005: 434), Heil (2006).


28

tion233. The latter strives to reduce inventory carrying cost treating products differently without

reducing the service level substantially. For example, products with a low turnover might be

stocked only at few locations due to cost considerations.234

Inventory pooling is e. g. considered in location and allocation decisions235, satisfying

both on-line and store demand236, speculative online exchanges237, airline revenue man-

agement238, for spare parts of airlines239 and of U.S. manufacturing companies240, and for

Saturn241, General Motors242, Intel243, and Airbus244.

Inventory pooling is a 1/0 – risk pooling method: Inventories are consolidated and sto-

chastic demands aggregated, as they are satisfied from the consolidated inventory245. Thus

demand variabilities may balance each other (demand pooling). The lead times to the sepa-

rate inventories are pooled to the lead time to the consolidated stock according to Cachon

and Terwiesch's (2009: 336, 339) notion of lead time pooling, but this actually is demand

pooling during the replenishment lead time. Inventory pooling does not pool lead times, so

that their variabilities may balance each other according to Evers (1997: 69ff., 1999: 121)

and Wanke and Saliby (2009: 678f.).

Inventory centralization can reduce expected costs in a cost minimization model246 or

increase profits and service level247 in a profit maximization model248 or in incentive-

compatible laboratory experiments in behavioral operations management (OM)249, even if

233 Anupindi et al. (2006: 191f.), Chopra and Meindl (2007: 322ff.) 234 Pfohl (2004a: 122f.). 235 Nozick and Turnquist (2001), Teo et al. (2001), Shen et al. (2003), Miranda and Garrido (2004), Hall

(2004), Croxton and Zinn (2005), Klijn and Slikker (2005), Shu et al. (2005), Snyder et al. (2007), Vi-dyarthi et al. (2007), Naseraldin and Herer (2008), Ozsen et al. (2008), Taaffe et al. (2008), Lee and Jeong (2009).

236 Bendoly (2004), Bendoly et al. (2007: 426). 237 Milner and Kouvelis (2007). 238 “Airline revenue management involves dynamically controlling the availability and prices of many dif-

ferent classes of tickets to maximize revenues” (Zhang and Cooper 2005: 415). 239 Hearn (2007), Burchell (2009), Cattrysse et al. (2009). 240 Carter and Monczka (1978). 241 Treece (1996). 242 Kisiel (2000). 243 Johnson (2005). 244 Aviation Week & Space Technology (2006). 245 Pishchulov (2008: 8, 17). 246 For example Eppen (1979), Chen and Lin (1989). 247 Eynan (1999). 248 For example Cherikh (2000), Lin et al. (2001a). 249 Ho et al. (2009).


29

locations differ in profitability (selling price and stockout costs)250, because “of risk pool-

ing over uncertainty in customer demand”251 and economies of scale252 and scope253.

Centralization (decreasing the number of warehouses) generally reduces inbound trans-

portation costs from the supplier to the warehouses because of a higher utilization of trans-

portation means (economies of density254), possibly the distances between the production

facility and the central warehouse(s)255, and the unit costs256 in the warehouse system due

to higher utilization (economies of scale). The systemwide total throughput is distributed

over a smaller number of warehouses and thus the average throughput per warehouse in-

creases.257 The warehouse costs per item (unit costs for space, product handling, and per-

sonnel) decrease through economies of scale.258 The fixed costs per order and per unit

holding costs usually diminish with centralization.259 Fixed warehouse costs, especially

personnel costs, are distributed over a larger warehouse throughput so that the unit costs

decrease with increasing utilization260 and the return on rationalization investments in more

productive low-cost methods increases (economies of scale)261. Variable warehouse costs,

particularly handling costs, diminish by mechanization or automation.262 However, increas-

ing mechanization or automation reduces flexibility263.

250 Eynan (1999: 38ff.) considers a central warehouse for a single product that supplies retailers from differ-

ent markets, which differ in product prices and stockout costs, according to the first come, first served principle. Surprisingly the centralized system usually performs better than the decentralized one: Consi-dering the whole system, possible cannibalization effects of low-price-market demands at the expense of high-price-market ones are overcompensated.

251 Anupindi and Bassok (1999: 187), cf. Teo et al. (2001), Lim et al. (2002: 668), Snyder and Shen (2006), Schmitt et al. (2008a, 2008b), Ho et al. (2009).

252 Lim et al. (2002: 668), Rabinovich and Evers (2003a). Economies of scale are decreasing unit costs with increasing output (Adam 1979: 950, Gutenberg 1983, Busse von Colbe and Laßmann 1986: 197, Mono-polkommision 1986: 231, Chandler 1990: 17, Bohr 1996: 375, Samuelson and Nordhaus 1998, Alisch et al. 2004: 771).

253 Rabinovich and Evers (2003a). Economies of scope arise as cost synergy effects, if the combined produc-tion of goods is cheaper than the separate one (Alisch et al. 2004: 771). In the literature among others the portfolio effect is given as an economic reasoning for them: Diversification in different projects reduces the total investment risk. Fritsch et al. (2001: 96) observe this effect with research and development in a multi-product company, Bohr (1996: 382f.) with the general use of financial means.

254 Economies of density are cost advantages due to increasing utilization in a transportation system (Harris 1977, Caves et al. 1984: 472).

255 Fawcett et al. (1992: 37), Pfohl (1994: 141), Delfmann (1999: 193). 256 Unit costs are the costs that are defined by the distribution of total costs to the output to be produced

(Kistner and Steven 2002: 88). 257 Vahrenkamp (2000: 32). 258 Williams (1975), McKinnon (1989: 104). 259 Maister (1976: 132), McKinnon (1989: 102f.), Lim et al. (2002: 668). 260 Schulte (1999: 377), Vahrenkamp (2000: 34). 261 Paraschis (1989: 16), Pfohl (1994: 142), Vahrenkamp (2000: 34), Ihde (2001: 316). 262 Beuthe and Kreutzberger (2001: 249). 263 Stein (2000: 486), Ackerman and Brewer (2001: 231).


30

Centralization can lead to economies of massed reserves, if it is used to lower system-

wide safety stock through risk pooling and thus unit holding costs.264 The latter are further

reduced by less inventory loss and thus lower risk costs in the centralized system.265 Econ-

omies of massed reserves are cost savings due to centralized reserve holding with increas-

ing firm size.266 Among others Bowersox et al. (1986: 283ff.), Fawcett et al. (1992: 5),

Pfohl (1994: 141), and Delfmann (1999: 193) argue that in spite of constant basic invento-

ry and increasing in transit inventory total inventory is lowered by reducing safety stock in

the centralized system. Higher utilization of inbound transportation means with centraliza-

tion decreases the number of stock placements and removals.267 Therefore setups are re-

duced and larger loading and unloading equipment can be used saving time in the transpor-

tation system. Reducing idle time leads to a higher utilization in time and therefore to

economies of density using larger means of transportation.268

On the other hand, in a centralized logistics system outbound transportation costs may

be higher because of lower utilization269 and longer distances from the central ware-

house(s) to customers270 and thus perhaps the service level might be lower271. Centraliza-

tion may entail diseconomies of scale mostly in organization.272 With increasing size there

are no gains from rationalization anymore, but increasing transaction and coordination

costs and thus increasing warehouse unit costs in big warehouse systems.273

Das and Tyagi (1997) develop an optimization model for determining the optimal de-

gree of centralization as a tradeoff between inventory and transportation costs.

Inventory centralization games optimize and allocate the savings from a centralized

inventory, so that the participants' cooperation is maintained.274

264 Bowersox et al. (1986: 286), Paraschis (1989: 16), Vahrenkamp (2000: 34f.), Ihde (1976: 39f., 2001:

316). 265 Vahrenkamp (2000: 32). 266 Scherer and Ross (1990: 100). 267 Schulte (1999: 377). 268 Pfohl (1994: 142), Vahrenkamp (2000: 35). 269 In the medium term smaller transportation vehicles might be used to increase utilization (Fawcett et al.

1992: 5, Delfmann 1999: 193, Vahrenkamp 2000: 31). 270 Delfmann (1999: 193), Ballou (2004b: 573f.). 271 Schulte (1999: 377), Vahrenkamp (2000: 31), Lee and Jeong (2009: 1169), Wanke (2009: 122). 272 Chandler (1990: 25), Scherer and Ross (1990: 103f.), Bohr (1996: 385f.). 273 Pfohl (1994: 143), Delfmann (1999: 194). 274 Hartman et al. (2000), Anupindi et al. (2001), Slikker et al. (2001, 2005), Müller et al. (2002: 118f.),

Granot and Sošić (2003), Hartman and Dror (2005: 93), Özen and Sošić (2006), Ben-Zvi and Gerchak (2007), Chen and Zhang (2007, 2009), Drechsel and Kimms (2007), Dror et al. (2008), Özen et al. (2008), Chen (2009), Zhang (2009).


31

The risk pooling effect on (safety) stock levels evoked by inventory pooling or centrali-

zation can be quantified with the square root law (SRL), portfolio effect (PE), and inven-

tory turnover curve.

Maister's (1976) SRL states that the total system wide stock of n decentralized ware-

houses is equal to that of a single centralized one multiplied with the square root of the

number of warehouses n. There is some confusion about which part of inventory275 it can

be applied to and about its underlying assumptions276.

Nevertheless, it applies to regular stock277, if an economic order quantity (EOQ) order

policy is followed, the fixed cost per order and the per unit stock holding cost, demand at

every location, and total system demand is the same both before and after centralization.278

It holds for safety stock, if demands at the decentralized locations are uncorrelated279, the

variability (standard deviation) of demand at each decentralized location280, the safety fac-

tor (safety stock multiple)281 and average lead time are the same at all locations both before

and after consolidation, average total system demand remains the same after consolida-

tion282, no transshipments occur283, lead times and demands are independent and identical-

ly distributed random variables and independent of each other284, the variances of lead time

are zero285, and the safety-factor (kσ) approach is used to set safety stock for all facilities

both before and after consolidation286. It applies to total inventory, the sum of regular and

safety stock287, if the aforementioned assumptions of the SRL as applied to regular and

safety stock hold collectively. A formal proof is given in appendix B.

The savings in regular stock measured by the SRL stem from the assumption of constant

275 Heskett et al. (1974: 462), Ballou (2004b: 380). Professor emeritus Ronald H. Ballou, Weatherhead

School of Management, Case Western Reserve University, agreed with us in a personal correspondence on May 15, 2007.

276 Sussams (1986: 9), Bowersox et al. (2002: 469), Coyle et al. (2003: 259f.), Ballou (2004b: 380), Chopra and Meindl (2007: 320).

277 Regular or cycle stock is the inventory “necessary to meet the average demand during the time between successive replenishments. The amount of cycle stock is highly dependent on production lot sizes, eco-nomical shipment quantities, storage space limitations, replenishment lead times, price quantity discount schedules, and inventory carrying costs” (Ballou 2004b: 331), and “affected by inventory policy” (Ballou 2004b: 379).

278 Maister (1976: 125, 127, 131). 279 Maister (1976: 132). 280 Maister (1976: 130). 281 Maister (1976: 132). 282 Evers and Beier (1993: 110), Evers (1995: 4). 283 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 284 Evers and Beier (1993: 110), Evers (1995: 4). 285 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 286 Maister (1976: 129). 287 Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou

2004b: 330f.), which is neglected here.


32

fixed costs per order, holding costs, and total demand for all locations before and after centrali-

zation. Thus, if an EOQ policy is followed, the total order fixed cost usually is lower because

of less orders and the inventory holding cost is lower due to a smaller total EOQ in the centra-

lized than in the decentralized system. For the proof please refer to appendix C. This is called

“EOQ cost effect” by Schwarz (1981: 147) and “order quantity effect” by Evers (1995: 5).

Savings in safety stock stem from the subadditivity of the square root (the square root of

the sum of the individual demand variances of the decentralized locations is usually less than

the sum of the standard deviations of demand of the decentralized locations), i. e. from ba-

lancing demand variabilities (demand risk pooling). Schwarz (1981: 147), Zinn et al. (1989:

3), and Evers (1995: 5) identify this as the portfolio effect.

Total cost savings from centralizing safety stock are probably larger than the ones from

cycle stock centralization288, because centralized cycle stocks have to be transported to the

customer eventually, so that extra transportation costs are probably high. Centralized safety

stocks only have to be transported to the customer in the less frequent case of a stockout, so

that additional expenses for premium transportation are relatively small. If both cycle and

safety stocks are centralized some warehouses might be closed and fixed costs saved.289

Although some researchers290 claim the SRL estimated real savings well, in 13291

of 14292 practical cases we reviewed it overestimated actual inventory savings often sig-

288 Maister (1976: 134), Evers (1995: 17). 289 Maister (1976: 134), Evers (1995: 17). 290 Pfohl (1994: 141). Sussams (1986: 10) gives an example where a company's savings in safety stock (cal-

culated with the standard deviation of demand of the decentralized and centralized depots) from reducing the number of depots from five to one would only be 2.76 % higher than the ones predicted by the SRL, although the variability (standard deviation) of demand at the decentralized depots is not the same, de-mands are not uncorrelated as the correlation coefficients we calculated show, but all locations use the same safety stock multiple (two times the standard deviation of demand). The SRL assuming uncorrelated demands coincidentally predicts similar savings to the ones calculated on the basis of the actual standard deviations in this case. Here the correlations of sales between the different depots balance each other when demands are consolidated, so that Zinn et al.'s (1989: 3) portfolio effect (percent reduction of safety stock due to centralization of correlated demands) of 57.25 % resembles the savings of the SRL of 55.27 %. However, as Zinn et al. (1989: 6, 10) show this need not be the case at all. Note that Sussams (1986: 10) compares two theoretical savings calculated with the SRL and on the basis of calculated stan-dard deviations and not the theoretical savings estimated by the SRL with the actual savings realized by the company and his table contains mistakes. He concludes that the SRL “has been tested against 24 dif-ferent situations, and in all cases there was close agreement between the theoretical and the practical re-sults. It was concluded that, subject to the reservations concerning the normality of the demand pattern, the square root law may be used with confidence to estimate differences in buffer stock requirements for different configurations of depots”. However, it is not clear whether the savings theoretically predicted with the SRL were compared to actually realized or calculated savings and whether the assumptions of the SRL as applied to safety stock were fulfilled in the practical cases. Therefore Sussams' (1986: 10) conclusion is not intersubjectively verifiable.

291 Newson (1978), Voorhees and Sharp (1978: 75f.). Ballou (1981: 148ff.) shows for several real companies from different industries that the inventory savings predicted by the SRL are higher than the actual sav-ings. This might be caused by joint ordering (to benefit from volume buying and shipping, which in-creases inventory levels), forward buying, diversion from the EOQ pull policy for some products, use of


33

nificantly. This means its assumptions are not fulfilled293 in these cases or there were other

inventory-294 or service-related changes. It is difficult to isolate the effect of inventory cen-

tralization.295 The SRL shows the inventory necessary for a given service level in depen-

dence of the number of stocking locations, if its underlying assumptions are fulfilled. This

does not mean that reducing the number of warehouses automatically reduces inventory.

None of the aforementioned sources states whether the assumptions to the SRL were

fulfilled. Therefore actually no statements can be made about the accuracy of the SRL's

results. However, it seems that the SRL “tends to over-predict”296 actual inventory savings,

as its assumptions are not fulfilled: In a survey that we conducted in the winter of 2008

none of the eleven participating companies from different countries and industries fulfilled

all assumptions of the SRL when applied to safety stock (table D.1). They fulfilled at least

two (respondents 1, 4, and 5) and at the most seven (respondent 10) of these eleven as-

sumptions. Only one company (respondent 3) fulfilled all five assumptions necessary for

applying the SRL to regular stock. Two companies (respondents 4 and 11) did not fulfill

any of the assumptions of the SRL when applied to regular stock. Evers (1995: 17) already

remarked that the SRL is “based on numerous limiting assumptions which collectively are

not likely to be found in practice”, although Coyle et al. (2003: 259) call them “reasona-

ble”.

push distribution (where production considerations are more important than inventory replenishment ones) or a stock-to-demand order policy (relates inventory levels directly to demand), multiple product types with different service policies in the aggregated product group, no equal product service levels and costs, and poor inventory management. According to Ashford (1997: 20), Nike Europe intended to reduce its footwear storage locations from 20 to 2 and was predicted by the consultancy Touche Ross to save 11 % of inventory costs (calculated by us with the given data) instead of 68 % as predicted by the SRL. Nike planned to reduce its apparel storage locations from 20 to 1 with predicted savings of 12 % (calcu-lated by us) as opposed to 78 %. Close-outs were estimated to decrease by 33 % for footwear and 50 % for apparel. It is not stated how the inventory savings were predicted and whether they were actually real-ized. McKinnon (1997: 81), Watson and Morton (2000), Hammel et al. (2002). McKinnon (2003: 24) considers two companies. Lovell et al. (2005), Progress Software Corporation (2007), clearpepper supply chain consulting & education (2009). We interviewed the Supply Chain Manager of a U.S. wireless tele-communication device production company with 6,000 employees. This manufacturer reduced the num-ber of warehouses from 80 to 15 and thus reduced regular stock by 50, safety stock by 75, and total aver-age inventory by 50 %. The SRL predicts inventory savings of 56.70 % and thus estimates the savings in regular and total stock fairly well in this case. Table D.1 shows which assumptions of the SRL this res-pondent 10 fulfilled.

292 A U.S. chemical company went from 100 to 89 warehouses. Inventory costs (including order processing and warehousing costs) were reduced (projected by DISPLAN and later verified from accounting records) by 76 % (compared to 6 % predicted by the SRL). These savings resulted not only from closing 11 ware-houses, but also from reallocating demand among the remaining warehouses while maintaining the com-pany's high level of customer service (Ballou 1979: 68).

293 Cf. Ballou (1981: 148ff.). 294 Ballou (1979: 68), McKinnon (1997: 81). 295 McKinnon (1997: 81). 296 McKinnon (1997: 81).


34

Researchers questioning Maister's (1976) SRL challenge its assumptions illogically297, do

make other assumptions and therefore arrive at different results298, or give no clear reason299.

Nonetheless, the other SRL- and PE-models compared in table D.2 might be applied

as their assumptions are fulfilled.

Eppen (1979) showed for the assumptions listed in table D.2 that the expected total sys-

tem inventory holding and penalty costs increase with the square root of the number of

warehouses.300 His research was extended to Poisson demand301, any (non-negative) de-

mand distributions with concave holding and penalty cost functions302, and to include costs

for the transportation of goods between locations with overage and underage in the centra-

lized system303.

Zinn et al.'s (1989) portfolio effect (PE) is a generalization of the SRL and shows the

reduction in aggregate safety stock by centralizing several warehouses' inventories in one

warehouse in percent for the assumptions listed in table D.2. The PE was used to estimate

the effect of postponement on safety stock304 and extended to include holding, transporta-

tion, facility investment, and procurement costs305, multiple consolidation points306, varia-

ble lead times307, both safety and cycle stocks (“consolidation effect”) as well as various

assumptions308, the effect of non-emergency309 and emergency transshipments310, and un-

equal demand variances and possibly unequal capacities of centralized locations311.

297 Durand (2007). 298 Das (1978), Evers and Beier (1993), Evers (1995). 299 Durand and Paché (2006). 300 Kemahlioğlu-Ziya (2004: 9) wrongly states that Eppen (1979) “is the first to model and analyze the

benefits of inventory centralization”. 301 Stulman (1987). 302 Chen and Lin (1989). 303 Chang and Lin (1991). They are extended by Chang et al. (1996), who consider delay supply product

cost. 304 Zinn (1990). 305 Mahmoud (1992: 203ff.). 306 Evers and Beier (1993). 307 Tallon (1993). 308 Evers (1995). 309 Evers (1996). In nonemergency transshipments a certain proportion of demand is always filled from other

locations' inventory (Evers 1996: 129). The PE model of Evers and Beier (1993) can be utilized to deter-mine the percentage reduction in safety stocks from nonemergency transshipments without considering the effect on cycle stocks and transportation costs (Evers 1996: 111).

310 Evers (1997). The PE model of Evers (1996) underestimates the benefits of an emergency transshipment policy, as it does not adequately consider the number of locations, lead times, and desired fill rates (Evers 1997: 68ff.).

311 Tyagi and Das (1998: 197). Savings in aggregate safety stocks are maximal, if every centralized location delivers the same portion of each decentralized location's demand. Centralization can be beneficial, even if customers have unequal demand variances and more centralized locations are established than there are customer ones (Tyagi and Das 1998: 201f.).


35

The inventory turnover curve shows average inventory in dependence of the inventory

throughput for a specific company. It can be constructed from a company's stock status

reports and be used to estimate the average inventory (not only safety stock as with the PE)

for any (planned) warehouse throughput (shipments from the warehouse or sales) without

the limitations of the SRL. Thus one can assess the effect of centralization, decentralization

(changing the number and/or size of warehouses), or combining warehouses on average

inventory as well as the performance of inventory management and control policies for a

specific company.312

3.2 Transportation

3.2.1 Virtual Pooling

Virtual pooling extends a company's warehouse or warehouses beyond its or their physical

inventory to the inventory of other own or other companies' locations313 by means of informa-

tion and communication technologies (ICT)314, drop-shipping315, and cross-filling316.

“[D]emand across [these locations] is pooled, which smoothes demand fluctuations”317. There-

fore inventory availability is improved for a given “inventory investment” or maintained with

less inventory.318 If virtual pooling entails cross-filling, it may pool lead times. However, this

corresponds to transshipments and is considered in the next section. Therefore virtual pooling

is a 1/0 – risk pooling method.

3.2.2 Transshipments

Lateral transshipments are monitored company internal or external product shipments on the

same level or echelon of the value or supply chain, e. g. among retailers.319 They are also

called intra-echelon transshipments320, stock transfer321, lateral (re)supply322, inventory shar-

ing323, stock redistribution324, virtual pooling325, or information pooling326.

312 Ballou (1981, 2000, 2004a, 2004b: 381f., 2005). 313 Caddy and Helou (2000: 1715), Planning & Reporting (2001), Kroll (2006). 314 Memon (1997), Christopher (1998: 135), Planning & Reporting (2001), SDM (2001), Frontline Solutions

Europe (2002), Electrical Wholesaling (2003), Mason et al. (2003), Fung et al. (2005), Kroll (2006), Ci-oletti (2007), Cachon and Terwiesch (2009: 350, 469).

315 Planning & Reporting (2001), Randall et al. (2002, 2006), Netessine and Rudi (2006). 316 Ballou (2004b: 335, 385-389). 317 Randall et al. (2002: 56). 318 Cachon and Terwiesch (2009: 350). 319 Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Simchi-Levi et al. (2008: 239), Yang and

Schrage (2009: 838). 320 Burton and Banerjee (2005), Chiou (2008: 439). 321 Archibald et al. (1997).


36

Emergency or reactive327 lateral transshipments (ELT) transfer products from a loca-

tion with a surplus to a location that faces a stockout328. Yang and Schrage (2009: 838)

regard ELT as “location substitution”.

Preventive or proactive329 lateral transshipments are conducted, if a retailer anticipates

a stockout before demands are realized330. Lee et al. (2007) combine emergency and pre-

ventive lateral transshipments in their transshipment policy “service level adjustment”

(SLA).

In virtual lateral transshipments a capacitated manufacturing plant designates arriving

demands to be served by another, more remote one. This can help capacitated plants to

work together to better deal with random demands and save costs. In contrast to the source

plant of real lateral transshipments the one of the virtual lateral transshipment may have

negative inventory levels throughout the transshipment process.331

All of the above lateral transshipments must not be confused with cross-docking (re-

loading of goods at transfer points or hubs)332 or shipping goods from a warehouse to a

demand-satisfying location333, which is also called transshipments sometimes.

If locations from the same echelon cannot transship inventory to prevent a stockout, an

upper-level supplier can fill the demand via a cross-level, inter-echelon, or vertical

transshipment334. This might resemble virtual pooling carried out by drop-shipping335.

Emergency transshipments pool both demands across locations or retailers336 (by per-

mitting alternative locations to satisfy customer demands) and lead times (by providing

the whole system with the possibility of partial stock replenishments) and allow a company

322 Sherbrooke (1992), Yanagi and Sasaki (1992). 323 Anupindi et al. (2001), Grahovac and Chakravarty (2001), Zhao et al. (2005), Herer et al. (2006), Sošić

(2006), Chiou (2008: 427), Kutanoglu (2008). 324 Das (1975), Jönsson and Silver (1987a, 1987b), Bertrand and Bookbinder (1998), Tagaras and Vlachos

(2002), Hu et al. (2005). 325 Çömez et al. (2006). 326 Herer et al. (2006: 185), Özdemir et al. (2006a). 327 Herer et al. (2006: 185f.). 328 Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Yang and Schrage (2009: 838). 329 Herer et al. (2006: 185f.). 330 Tagaras (1999), Lee et al. (2007). Preventive lateral transshipments are not useful in two-location periodic

review inventory systems with nonzero replenishment lead times and uncertain future material require-ments and availability (Tagaras and Cohen 1992).

331 Yang and Qin (2007). 332 Campbell (1993), Hoppe and Tardos (2000), Petering and Murty (2009). 333 Köchel (2007). 334 Chiou (2008: 427, 439, 443). 335 Netessine and Rudi (2006). 336 Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Çömez et al.

(2006), Wanke and Saliby (2009), Yang and Schrage (2009: 837).


37

to remain close to customers337. They enable a company to exploit risk pooling338 or statis-

tical economies of scale339, i. e. “advantages that result from the pooling of uncertainty”340.

As a result (safety) stock341 and (inventory holding, shortage, backorder, or total sys-

tem) costs342 can be reduced for a given service level, which leads to leanness343, cus-

tomer service level (fill rates, product availability, or delivery time) can be improved

without raising inventory levels344, which enables agility or flexibility345, or a combina-

tion of both (increasing service while decreasing inventory levels)346, which is called “lea-

gility”347. Transshipments may decrease lost sales, the rejection rate of returns348, and rep-

lenishment lead times349 and improve revenues350 and performance351.

In a static stochastic demand system, transshipments balance stock levels at different lo-

cations through emergency stock transfers from one location with overage to another one

with underage. In a dynamic deterministic demand system, transshipments may save fixed

and variable replenishment costs352, if e. g. one location makes a larger replenishment or-

der to transship some of it to other locations353 (cf. section 3.3.1 on centralized ordering).

Inventory consolidations do not pool lead times, may close stock keeping installa-

tions near markets354, restructure the logistics network fundamentally, which is difficult to

change or undo at least in the short term355, and increase order cycle times and/or transpor-

337 Evers (1997, 1999), Wanke and Saliby (2009). 338 Tagaras and Vlachos (2002), Tagaras (1999), Dong and Rudi (2002, 2004), Çömez et al. (2006), Zhao

and Atkins (2009: 667). 339 Evers (1997, 1999). 340 Evers (1994: 51). 341 Jönsson and Silver (1987a: 224), Tagaras (1989), Diks and de Kok (1996: 378), Evers (1996), Mercer and

Tao (1996), Evers (1997: 71f.), Köchel (1998a: 190), Evers (1999), Kukreja et al. (2001), Herer et al. (2002), Minner et al. (2003), Minner and Silver (2005).

342 Das (1975), Lee (1987), Robinson (1990), Evers (1996: 114), Köchel (1998a: 190), Alfredsson and Ver-rijdt (1999), Evers (2001: 313), Grahovac and Chakravarty (2001), Kukreja et al. (2001), Herer et al. (2002), Tagaras and Vlachos (2002), Daskin (2003), Minner et al. (2003), Kukreja and Schmidt (2005), Minner and Silver (2005), Wong (2005), Çömez et al. (2006), Yang and Qin (2007), Chiou (2008: 428), Kutanoglu and Mahajan (2009: 728).

343 Herer et al. (2002). 344 Krishnan and Rao (1965), Tagaras (1989), Chang and Lin (1991), Sherbrooke (1992), Evers (1996, 1997:

71f., 1999), Hong-Minh et al. (2000), Herer et al. (2002), Minner et al. (2003), Xu et al. (2003), Minner and Silver (2005), Zhao et al. (2005), Chiou (2008: 427), Kutanoglu (2008: 356).

345 Herer et al. (2002), Zhao et al. (2008). 346 Evers (1997), Needham and Evers (1998), Evers (1999), Minner et al. (2003), Minner and Silver (2005),

Zhao et al. (2008: 400). 347 Herer et al. (2002). 348 Ching et al. (2003). 349 Herer et al. (2002). 350 Reyes and Meade (2006). 351 Wong (2005), Wong et al. (2007b: 1045), Chiou (2008: 429). 352 Herer and Rashit (1999: 525), Herer and Tzur (2003: 419). 353 Herer and Tzur (2003: 419). 354 Evers (1999: 122). 355 Domschke and Drexl (1996: 1), Klose and Stähly (2000: 434), Klose (2001: 3).


38

tation costs to customers356. The stockout probability for a given system inventory level is

lower in a decentralized system with emergency transshipments than in a centralized

one.357 Therefore these two systems are not generally equal as in Chang and Lin (1991)

with no replenishment times and no transshipment transportation costs.358

Transshipments are similar to order splitting359, but orders from facilities employing

transshipments are not necessarily placed at the same time, while split orders are360 and

order splitting only pools lead times361.

Transshipments may decrease customer service (increase the number of receipts per or-

der and/or order cycle times) and increase transportation or rebalancing362, transaction

(shipment documentation, receiving, handling and administration) costs363, the sending

location's cost of reordering the transshipped product from the supplier and its probability

of a stockout364, and daily average inventories365, and require willingness to share stock366.

Not all supply chain members may benefit from transshipments: they can increase

overall or retailer inventories and harm the distributor or individual retailers in a supply

chain, in which a manufacturer supplies integrated or autonomous retailers with a one-for-

one inventory policy via a central depot.367

Dong and Rudi (2002, 2004) find that if the wholesale price is endogenous, a single

manufacturer benefits from its retailers' transshipments, the more, the larger the risk pool-

ing effect. The identical (except in their normal demands) retailers in many situations are

worse off under transshipment due to a higher wholesale price, especially if the risk pool-

ing effect is large. Zhang (2005) extends Dong and Rudi's (2004) results under normal de-

mand to general demand distributions.

Shao et al. (2009) also conclude that a manufacturer and the decentralized retailers via

which he sells may be hurt by transshipments. If the manufacturer controls the transship-

ment price, he prefers selling through decentralized retailers. If the latter control the trans-

356 Evers (1999: 122). 357 Evers (1997: 69ff., 1999: 121). 358 Evers (1997: 69ff.). 359 Sculli and Wu (1981), Hayya et al. (1987), Sculli and Shum (1990). 360 Evers (1997: 75). 361 Evers (1999: 122, 132). 362 Jönsson and Silver (1987a: 224), Diks and de Kok (1996: 378), Evers (1997: 56), Evers (1999: 122),

Burton and Banerjee (2005: 169). 363 Evers (1999: 122, 2001: 312f.). 364 Evers (2001: 312f.). 365 Reyes and Meade (2006). 366 Evers (1999: 122). 367 Grahovac and Chakravarty (2001).


39

shipment price, they realize higher profits than a chain store and the manufacturer may

prefer selling via a chain store.

Most research deals with transshipments of goods or commodities between warehouses,

retailers, or production locations. Cohen et al. (1980) consider transfers of patients between

hospitals and capacity decisions. Lue (2006) introduces transshipments to chemical manu-

facturing systems with continuous material flows to maintain non-stop operations, since it

is costly to shut down and restart the production process.

Transshipments affect the ordering policy and should be considered in it.368 The majori-

ty of publications model transshipments and determine (optimal) replenishment order and

transshipment369, ordering370, stocking, or inventory control371, stocking or inventory con-

trol and transshipment372, production and transshipment373, and transshipment374 policies,

rules, heuristics, or algorithms under different assumptions.

Similarly to the inventory centralization games in section 3.1, Anupindi et al. (2001),

Granot and Sošić (2003), Sošić (2006), and Zhao et al. (2005) study the conditions (profit

allocations) that make retailers jointly share their residual supply/demand with the other

retailers in a manner that maximizes the additional profit in inventory sharing games.

Small incentives for transshipments can achieve the benefits of a full-inventory sharing

policy.375

Köchel (1998a) provides a survey on multi-location inventory models with lateral

transshipments, foremost on research conducted at the Technical University Chemnitz,

Germany concerning the coordination of ordering decisions of all locations. Chiou (2008)

and Paterson et al. (2009) present more general reviews of transshipment problems in

supply chain systems and inventory models with lateral transshipments.

In summary, transshipments are a 1/1 – risk pooling method.

368 Robinson (1990), Hu et al. (2005), Kukreja and Schmidt (2005). 369 For example Köchel (1975, 1977, 1982, 1988), Tagaras (1989), Arnold and Köchel (1996), Arnold et al.

(1997), Köchel (1998b), Herer and Rashit (1999), Bhaumik and Kataria (2006). 370 For example Robinson (1990), Tagaras and Vlachos (2002), Hu et al. (2005), Herer et al. (2006), Olsson

(2009). 371 For example Das (1975), Lee (1987), Tagaras and Cohen (1992), Kukreja et al. (2001), Jung et al. (2003),

Kukreja and Schmidt (2005), Wong (2005), Wong et al. (2005a, 2005b, 2007b), Gong and Yucesan (2006), Lue (2006), Yang and Qin (2007), Kranenburg and Van Houtum (2009).

372 Diks and de Kok (1996), Archibald et al. (1997), Hu et al. (2008). 373 Zhao et al. (2008). 374 Tagaras (1999), Evers (2001), Axsäter (2003a), Minner et al. (2003), Burton and Banerjee (2005: 169),

Minner and Silver (2005), Wee and Dada (2005), Çömez et al. (2006), Zhao et al. (2006), Archibald (2007), Lee et al. (2007), Archibald et al. (2009).

375 Zhao et al. (2005).


40

3.3 Procurement

3.3.1 Centralized Ordering

Centralized ordering376 places joint orders for several locations and later allocates the orders

(perhaps by a depot) to the requisitioners or distribution points in consolidated distribution

according to current demand information.377 This is also called pooling risk over (the) outside-

supplier lead time(s)378, “lead time pooling […] achieved by consolidated distribution”379,

“coordinated replenishment”380, “central ordering”381, or “centralized purchasing”382.

The allocation decision is postponed and stochastic demands can be treated in an aggre-

gate form until it is made. This reduces uncertainty and system stock “because of a portfolio

effect over the lead time from the supplier”383, “portfolio efficiencies”384, or “statistical

economies of scale”385. As explained at the beginning of this chapter, centralized ordering

does not entail lead time pooling, so that lower-than-average supplier lead times may not

balance higher-than-average ones. Consequently, centralized ordering is a 1/0 – risk pooling

method.

Compared to independent and individual or local386 ordering centralized ordering can lead

to economies of scale, i. e. it can take advantage of quantity discounts (“joint ordering ef-

fect”387) and save ordering388 and shipping costs389. It can make more frequent shipments

economical in comparison to direct delivery from the suppliers and thus reduce inventory

even further or increase the service level390.

If a warehouse, depot, or distribution center (DC) is introduced to allocate the stock391,

DC operating and extra transportation costs from the DC to the requisitioners or retailers are

incurred.392 A unit must travel a longer distance from the supplier to the retailer. However,

376 Eppen and Schrage (1981: 51), Erkip et al. (1990: 381), Ganeshan et al. (2007: 341), Gürbüz et al. (2007:

293). 377 Eppen and Schrage (1981), Cachon and Terwiesch (2009: 336-341). 378 Eppen and Schrage (1981), Schwarz (1989: 828), Schoenmeyr (2005: 4). 379 Cachon and Terwiesch (2009: 336). 380 Gürbüz et al. (2007: 293). 381 Ganeshan et al. (2007: 341). 382 Anupindi et al. (2006: 149f.). 383 Eppen and Schrage (1981: 67). 384 Eppen and Schrage (1981: 52). 385 Eppen (1979: 498), Eppen and Schrage (1981: 52). 386 Ganeshan et al. (2007: 341). 387 Eppen and Schrage (1981: 67). 388 Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293). 389 Gürbüz et al. (2007: 293), Cachon and Terwiesch (2009: 341). 390 Cachon and Terwiesch (2009: 341). 391 Eppen and Schrage (1981), Schwarz (1989: 828), Cachon and Terwiesch (2009: 336ff.). 392 McGavin et al. (1993: 1094), Cachon and Terwiesch (2009: 341).


41

the holding cost for each unit of inventory at the DC is probably lower than at the retail

stores.393

The value of risk pooling through holding inventory at the warehouse, depot, or DC (“de-

pot effect”394) and using this inventory “between system replenishments to ‘rebalance’ retail-

er inventories which have become ‘unbalanced’ due to variations in individual retailer de-

mands” (between replenishment risk pooling)395 can be substantial396 (cf. inventory pooling).

Schwarz et al. (1985) and Badinelli and Schwarz (1988) find it is not significant, perhaps

because the model of Deuermeyer and Schwarz (1981) that they use does not allow the

warehouse to balance retailer inventory levels, if system stocks are low397.

3.3.2 Order Splitting

Order splitting is simultaneously partitioning a replenishment order into multiple orders with

multiple suppliers398 or into multiple deliveries (scheduled-release)399. The single order and

thus its lead time are split into multiple orders or deliveries and their lead times, so that the

variabilities of these lead times may balance each other400. Thus safety stock needed for a giv-

en service level (inventory availability, expected number of backorders or shortage cost) can be

reduced, service level increased for a given safety stock level, or both.401 It can also reduce

cycle stock due to successive deliveries of smaller split orders.402 Consequently, order splitting

only pools lead times, not demands403 and constitutes a 0/1 – risk pooling method.

Disadvantages of order splitting might include no “quantity and transportation dis-

counts” because of smaller orders, a higher “administrative effort”, which electronic data

interchange might mitigate, and no “long-term partnership with a single supplier”, but mul-

tiple “suppliers may ensure competitive pricing and other favorable terms”.404

Thomas and Tyworth (2006: 246f., 2007: 170f.) critically review the literature on order

splitting: On the one hand, the literature assesses the effect of order splitting on the distri-

393 Cachon and Terwiesch (2009: 341). 394 Eppen and Schrage (1981: 67). 395 McGavin et al. (1993: 1093), cf. Schwarz (1989: 830). 396 Jackson and Muckstadt (1984a, 1984b, 1989), Jönsson and Silver (1987a, 1987b), Jackson (1988),

McGavin et al. (1993: 1104). 397 McGavin et al. (1993: 1093). 398 Evers (1999: 123), Thomas and Tyworth (2006: 245), Qi (2007). 399 Hill (1996), Chiang (2001), Mishra and Tadikamalla (2006), Thomas and Tyworth (2007: 188). 400 Evers (1999: 122). 401 Evers (1997: 71), Evers (1999: 123), Thomas and Tyworth (2006: 245f.). 402 Thomas and Tyworth (2006: 245). 403 Evers (1999: 123f.). 404 Evers (1999: 123).


42

bution of effective lead times405 and safety stock carrying and shortage costs with statis-

tics.406 On the other hand, it compares the average total cost (inventory holding, ordering,

shortage, and purchase cost) of order splitting with the one of not order splitting407 and

finds that it reduces cycle stock408. Order splitting and the just-in-time inventory strategy

are analyzed by Pan and Liao (1989), Ramasesh (1990), Hong and Hayya (1992), Hong et

al. (1992), Kelle and Miller (2001), and Ryu and Lee (2003). Simultaneously splitting an

order among suppliers does not decrease the sum of in-transit and cycle stock, but only

total safety stock in the system409 and increases ordering410 and shipping costs411. Most

researchers neglect transportation economies of scale, the size of transportation costs com-

pared to inventory costs, in-transit inventory412, the probability of lead time correlation413,

order dependent supply lead times and unit purchasing prices, and the derived disadvan-

tages and advantages of order splitting414.

Options other than simultaneously splitting replenishment orders among several suppli-

ers might be more promising:415 Delivering an order in sequential shipments can reduce

demand and production variability because of advance demand and delivery informa-

tion.416 Orders can also be split between a fast, reliable and a cheaper, less reliable mode or

supplier in order to take advantage of cost-performance differences in transportation mod-

es417 or between capacitated suppliers418. Lead time variability and freight rates could be

405 “The effective lead time in this case will be that of the minimum of the set of random variables

representing the lead time of each supplier” (Sculli and Wu 1981: 1003). 406 Sculli and Wu (1981), Hayya et al. (1987), Kelle and Silver (1990a, 1990b), Sculli and Shum (1990), Pan

et al. (1991), Ramasesh (1991), Fong (1992), Fong and Ord (1993), Guo and Ganeshan (1995), Fong and Gempeshaw (1996), Fong et al. (2000), Geetha and Achary (2000), Kelle and Miller (2001), Mishra and Tadikamalla (2006).

407 Ramasesh (1990), Ramasesh et al. (1991), Hong and Hayya (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Lau (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Mohebbi and Posner (1998), Ganeshan et al. (1999), Sedarage et al. (1999), Tyworth and Ruiz-Torres (2000), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003).

408 Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Hong et al. (1992), Zhou and Lau (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsy-pour and O'Brien (2001), Ryu and Lee (2003).

409 Thomas and Tyworth (2006: 254). 410 Sajadieh and Eshghi (2009). 411 Thomas and Tyworth (2006: 246). 412 Thomas and Tyworth (2006: 254, 2007: 188). 413 Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188). 414 Sajadieh and Eshghi (2009: 3272). 415 Thomas and Tyworth (2006: 255). 416 Hill (1996), Janssen et al. (2000), Minner (2003: 276), Thomas and Tyworth (2006: 255). 417 Ganeshan et al. (1999), Minner (2003). 418 Qi (2007).


43

reduced by stable, periodic, long-term transportation commitments.419 Using emergency

transshipments instead of order splitting to reduce variation is attractive in many situations,

not only because order splitting is contrary to current theory and practice of vendor rela-

tions and lean production.420

3.4 Production

3.4.1 Component Commonality

Component commonality or part standardization421 designs products that share parts or com-

ponents422. These common components can be used for several products.423

Component commonality is a 1/0 – risk pooling method: Demand for the individual

components is aggregated (pooled424) to the demand for the (fewer) generic common com-

ponent(s).425

This may426 reduce the variability of demand (quantity and timing uncertainty) and the

required (safety) stock for any constant service level427, increase the service level for a

given inventory, or lead to a combination of both, inventory reduction and service in-

crease428 due to risk pooling429. Furthermore, component commonality can lower setup,

ordering, inventory holding430, manufacturing431, logistics432, and part costs433 due to econ-

419 Thomas and Hackman (2003), Henig et al. (1997). 420 Evers (1999: 133). 421 Wacker and Treleven (1986: 219), Swaminathan (2001: 129), Simchi-Levi et al. (2008: 345). 422 Srinivasan et al. (1992), Jönsson et al. (1993), Meyer and Lehnerd (1997), Ma et al. (2002), Mirchandani

and Mishra (2002), Kim and Chhajed (2001), Labro (2004), Van Mieghem (2004), Ashayeri and Selen (2005), Chew et al. (2006), Humair and Willems (2006). Swaminathan (2001: 131) and Simchi-Levi et al. (2008: 348) also consider commonality in procurement standardization, which exploits commonality in part and equipment purchasing. Demand can be pooled across a large variety of end products, if they are produced on similar machines and/or use common components. Procurement standardization is most ef-fective, if the product is nonmodular and the process modular.

423 Grotzinger et al. (1993: 524). 424 Yang and Schrage (2009: 837). 425 Dogramaci (1979: 129), Guerrero (1985: 409), Vakharia et al. (1996: 15), Kreng and Lee (2004), Labro

(2004: 363), Kulkarni et al. (2005: 247), Graman and Magazine (2006: 1074), Bidgoli (2010: 21). 426 Component commonality does not always reduce inventory in a dynamic inventory system with lead

times under some common allocation rules (Song and Zhao 2009: 493). 427 Roque (1977), Collier (1981: 95, 1982: 1303), McClain et al. (1984), Baker et al. (1986), Gerchak and

Henig (1986, 1989), Wacker and Treleven (1986: 219), Gerchak et al. (1988). 428 Bagchi and Gutierrez (1992: 824f., 829), Srinivasan et al. (1992), Grotzinger et al. (1993: 525f.),

McDermott and Stock (1994: 65), Eynan (1996), Eynan and Rosenblatt (1996), Thonemann and Bran-deau (2000), Hillier (2002a, 2002b), Thomas et al. (2003), Labro (2004: 363), Mohebbi and Choobineh (2005: 481), Chopra and Meindl (2007: 326ff.).

429 Srinivasan et al. (1992: 26f.), Grotzinger et al. (1993: 524), Swaminathan (2001: 129), Labro (2004: 363), Chew et al. (2006), Simchi-Levi et al. (2008: 345).

430 Dogramaci (1979: 129), Collier (1981: 95, 1982: 1303), Guerrero (1985: 402), Thonemann and Brandeau (2000), Swaminathan (2001: 129, 131), Hillier (2002b: 570), Ma et al. (2002: 524), Mirchandani and Mishra (2002), Mohebbi and Choobineh (2005: 473), Simchi-Levi et al. (2008: 345, 348).


44

omies of scale434 or order pooling435, as well as product design costs436 and design and

manufacturing time437. The order-pooling benefit may be more important than the risk-

pooling one.438 Component commonality increases the survival probability of start-up

companies439 and possibly revenue440.

Total stock of product-specific components may increase though441 depending on the

used service-level measure442. Although component commonality may reduce the average

work load, it may increase workload variability and work-in-process inventory variabili-

ty.443

Excessive part commonality can reduce product differentiation, so that less expensive

customization options might cannibalize sales of more expensive parts.444 While customer

valuation for the high-value product and the chargeable price may be reduced, the ones for

the low-value one may be increased by using commonality in vertical product line exten-

sions.445

Sometimes, it is necessary to redesign products and/or processes to achieve commonali-

ty.446 This may result in a smaller and more economical set of components though.447 The

431 Collier (1981: 95), Hayes and Wheelwright (1984: 229-274), Walleigh (1989), Kim and Chhajed (2001:

219). 432 Kim and Chhajed (2001: 219). 433 Collier (1982: 1303). 434 Collier (1982: 1303), Kim and Chhajed (2001: 219), Swaminathan (2001: 129, 131), Simchi-Levi et al.

(2008: 345, 348). 435 Hillier (2002b: 570). 436 Desai et al. (2001). 437 Maskell (1991: 184f.), Berry et al. (1992), McDermott and Stock (1994: 65), Sheu and Wacker (1997),

Mirchandani and Mishra (2002). 438 Hillier (2002b: 570). 439 Thomas et al. (2003). 440 Component commonality allows to produce more of a higher-margin product instead of a low-margin

one, if demand exceeds capacity. Therefore it may be optimal even for perfectly positively correlated de-mands (no risk-pooling benefit), if products have sufficiently different margins (“revenue-maximization option”) (Van Mieghem 2004: 422).

441 Baker et al. (1986), Gerchak and Henig (1986: 157), Gerchak et al. (1988), Gerchak and Henig (1989: 61), Van Mieghem (2004: 423).

442 Gerchak et al. (1988). 443 Guerrero (1985: 409), Vakharia et al. (1996: 3), Ma et al. (2002). 444 Ulrich and Ellison (1999), Kim and Chhajed (2000, 2001: 219), Desai et al. (2001), Krishnan and Gupta

(2001), Ramdas and Sawhney (2001), Simpson et al. (2001), Swaminathan (2001: 131), Heese and Swa-minathan (2006), Simchi-Levi et al. (2008: 348).

445 Kim and Chhajed (2001: 219). 446 Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129), Ma et al. (2002: 536), Simchi-Levi et al.

(2008: 345). 447 Whybark (1989).


45

common component may be more expensive than the unique components it replaces.448

Still component commonality may reduce total cost.449

Using commonality as backup safety stock, if unique parts are not available, is better

than no commonality or pure commonality, where only common parts are used.450 Pure

commonality is not optimal unless it is free or there are high fixed product and process

redesign or complexity costs for procuring and handling two inputs.451

A component-mismatch problem due to demand uncertainty for end products may

arise.452 The equal-fractile allocation policy453 that allocates the components so that all

products have an equal probability of being out of stock at the end of the period can help to

reduce the required safety stock for a given target service level. However, it may keep

amply available components at the component level for the product with the highest de-

mand variability (“worst-case product”), although they may be employed to manufacture

other end products. This can be avoided by modifying the policy accordingly.454

Although some publications assert that cost decreases with commonality in general,

there are contradictory claims on the effect of commonality on various cost elements and

commonality's impact on total cost cannot be determined in general yet.455

Wazed et al. (2008) review the literature on component commonality. For a review of

advantages and disadvantages of component commonality in manufacturing and degree of

commonality indices in designing new or assessing existing product families please refer to

Wazed et al. (2009). Boysen and Scholl (2009) develop a general solution framework for

component-commonality problems.

3.4.2 Postponement

Postponement in general means delaying a decision in production, logistics, or distribution in

order to be able to use more accurate information because of a shorter forecast period and an

aggregate forecast456, especially in industries with high demand uncertainty,457 and commit-

448 Hillier (2002a, 2002b), Van Mieghem (2004: 419), Zhou and Grubbström (2004), Mohebbi and Choobi-

neh (2005: 473). 449 Van Mieghem (2004: 419), Hillier (2002a, 2002b). 450 Hillier (2002a). 451 Van Mieghem (2004: 423). 452 Baker (1985), Chew et al. (2006: 240). 453 Cf. Eppen and Schrage (1981), Bollapragada et al. (1998). 454 Chew et al. (2006: 239f., 248). 455 Labro (2004: 358, 366). 456 Aggregate forecasts usually are more accurate than disaggregate ones (Lawrence and Zanakis 1984: 25,

Neumann 1996: 9f., Swaminathan 2001: 126f., Sheffi 2004: 93f., Alicke 2005: 44, Nahmias 2005: 55, Anupindi et al. 2006: 168, 187, Donnellan et al. 2006: x, Chopra and Meindl 2007: 188f., Simchi-Levi et al. 2008: 190, 194, 345, Shah 2009: 166, Bretzke 2010: 77f., Schnuckel 2010: 152) because of statistical


46

ting resources rather to demand than to a forecast458. The opposite strategy of holding finished

goods at locations close to customers in anticipation of sales is called speculation.459

Postponement strategies can be applied to form, time, and place.460 This can include

product development461, purchasing462, order(ing)463, fulfillment assignment464, produc-

tion465, manufacturing466, assembly467, packaging468, labeling469, delivery470, and pricing

postponement471. Form postponement delays product finalization or differentiation until

after customer orders have been received.472 Time postponement delays the forward

movement of stock.473 Rabinovich and Evers (2003b: 36, 41f.) consider emergency trans-

shipments and inventory centralization forms of time postponement. Place postponement

keeps inventories in centralized locations until customer orders are received.474 Logistics or

geographic postponement combines time and place postponement.475 It delays the transpor-

tation to individual market areas.476 Pull postponement moves the decoupling point477 up-

balancing effects, statistical economies of scale, or risk pooling (Bretzke 2010: 77f.). For further explana-tions please refer to e. g. Neumann (1996: 9f.), Sheffi (2004: 93), Alicke (2005: 44), Nahmias (2005: 55), Donnellan et al. (2006: x), Simchi-Levi et al. (2008: 60), and Schnuckel (2010: 152).

457 Pfohl (1994: 143), Swaminathan and Tayur (1998), Swaminathan (2001: 129f.), Sheffi (2004: 95f., 100), Anupindi et al. (2006: 192f.), Chopra and Meindl (2007: 362), García-Dastugue and Lambert (2007: 57f.), Piontek (2007: 86f.), Simchi-Levi et al. (2008: 346), LeBlanc et al. (2009: 19).

458 Bucklin (1965), Van Hoek (2001: 161). 459 Bucklin (1965). 460 Van Hoek et al. (1998: 33). 461 Yang et al. (2004: 1052), Piontek (2007: 86). 462 Yang et al. (2004: 1052). 463 Granot and Yin (2008), Chen and Lee (2009), Li et al. (2009). 464 Allowing online sales to accumulate and postponing assigning them to fulfillment sites can reduce hold-

ing, backorder, and transportation costs (Mahar et al. 2009: 561). 465 Yang et al. (2004: 1052), Anupindi and Jiang (2008: 1876). 466 Zinn and Bowersox (1988), Huang and Lo (2003). 467 Zinn and Bowersox (1988). 468 Zinn and Bowersox (1988), Howard (1994), Graman and Magazine (1998), Cholette (2009), Graman

(2010). 469 Zinn and Bowersox (1988), Cholette (2009). 470 Anupindi and Jiang (2008: 1876). 471 Van Mieghem and Dada (1999), Boone et al. (2007: 597), Granot and Yin (2008). 472 Bowersox and Closs (1996), Lee (1998), Van Hoek (2001: 167), Rabinovich and Evers (2003b: 33), Li et

al. (2007: 31), Harrison and Skipworth (2008), Wong et al. (2009). 473 Zinn and Bowersox (1988), Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and

Evers (2003b: 33), Nair (2005: 449). 474 Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and Evers (2003b: 33), Nair (2005:

449). 475 Pfohl (1994: 145), Bowersox and Closs (1996: 473), Lee (1998), Van Hoek (1998a), Van Hoek et al.

(1998: 33), Özer and Xiong (2008). 476 Pfohl (1994: 145). 477 Up to the decoupling point, order-penetration-point, variant determination point, freeze point (Piontek

2007: 86f.), or point of (product) differentiation (PoD) (Lee 1996, Lee and Tang 1997, Meyr 2003) stan-dardized products are made to stock customer-anonymously based on sales forecasts (push strategy). Af-ter an order has been received, the standardized products are transformed into various variants customer-individually (make-to-order pull strategy) (Piontek 2007: 86f., Harrison and Skipworth 2008).


47

stream to assemble to order478. Waller et al. (2000: 138) consider upstream postponement,

e. g. delaying ordering of raw materials, and downstream postponement, e. g. distribution

or place postponement.

Postponement allows to ship a single common generic product longer down the supply

chain and change it to individual products (differentiate it) more responsively according to

more recent demand information later.479 On the preceding levels of the supply chain the

demands for the individual products are aggregated to the demand for the generic prod-

uct (demand pooling480), which fluctuates less, since the stochastic fluctuations of the indi-

vidual demands balance each other to a certain extent because of the risk pooling effect.481

Postponement constitutes a 1/0 – risk pooling method.

Furthermore, inventories of the common intermediate product can function as a com-

mon buffer.482 A learning effect may arise, if forecasts can be improved on the basis of

observed sales data.483 Thus the total inventory holding costs and stockouts can be reduced

and customer service level484 and profits increased485 by better matching supply and de-

mand486.

Besides this risk and cost reduction, postponement can lead to economies of scale, syn-

ergistic effects, delayed increase in costs in the value chain and thus decreased capital

commitment, and higher flexibility or leagility.487 However, it is usually necessary to rede-

sign488 the product specifically for delayed differentiation and to modify the order of man-

ufacturing steps (resequence or operations reversal)489. This may decrease production vo-

lume variability though.490 Time-based postponement at the company level can increase

478 Lee (1998). 479 Lee (1996), Aviv and Federgruen (2001b: 579). 480 Yang and Schrage (2009: 837). 481 Lee and Tang (1997: 52), Aviv and Federgruen (2001a: 514, 2001b: 579), Alfaro and Corbett (2003: 12,

15), Piontek (2007: 87), Dominguez and Lashkari (2004: 2113), Anupindi et al. (2006: 192f.), Caux et al. (2006), Jiang et al. (2006), Cholette (2009).

482 Weng (1999), Aviv and Federgruen (2001b: 579). 483 Aviv and Federgruen (2001b: 579). 484 Lee (1996), Lee and Tang (1997), Jiang et al. (2006), Davila and Wouters (2007), Li et al. (2008, 2009),

LeBlanc et al. (2009: 19), Mahar and Wright (2009), Wong et al. (2009). 485 Jiang et al. (2006), Chopra and Meindl (2007: 364), Cholette (2009). 486 Chopra and Meindl (2007: 364). 487 Aviv and Federgruen (2001b: 579), Herer et al. (2002), Piontek (2007: 86f.). 488 Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994), Davila and Wouters

(2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 346). 489 Lee and Tang (1997: 40, 1998), Kapuscinski and Tayur (1999), Jain and Paul (2001), Swaminathan

(2001: 129f.), Shao and Ji (2008), Simchi-Levi et al. (2008: 346). 490 Jain and Paul (2001).


48

supply chain inventory, as other members of the supply chain may be forced to use more

speculation, i. e. hold more inventories.491

Postponement reduces risk associated with order mix and order quantity, but may in-

crease stockouts or lost sales due to longer lead, delivery, or order cycle times.492 Specula-

tion provides a high availability and flexibility because of short lead times and few stock-

outs.493 Decreasing (increasing) speculation and increasing (decreasing) postponement

increases (decreases) transportation costs and decreases (increases) inventory holding

costs.494

Postponement and speculation can be combined installing an intermediary stage be-

tween the suppliers and the buyers close to the buyers and holding uncommitted, anticipa-

tory inventory of the suppliers ready to be shipped on request495 or “postponing only the

uncertain part of the demand and producing the predictable part at a lower cost without

postponement” in “tailored postponement”496. “The combined principle of postponement-

speculation”497 may lower both inventory risk by centralization and order fulfillment times

and lost sales.498 Internet retailers, for instance, depend more on both inventory location

speculation (in-stock inventory) and postponement (drop-shipping) to fulfill their orders as

their market share and product popularity increase.499

As products are only delivered after a customer order is received, in general postpone-

ment leads to a centralized logistics system.500 Speculation rather has a decentralizing

effect on the logistics system501 and finished products inventory is stored as close as possi-

ble to customers. At the same time speculative processes lead to consolidated flows of

goods because of higher order quantities.502 Consolidated flows of goods support the ten-

dency towards centralized logistics systems.503 These opposite movements are no contra-

491 García-Dastugue and Lambert (2007). 492 Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al.

(2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13). 493 Bucklin (1965: 27), Delfmann (1999: 195). 494 Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Graman and Magazine (1998), Delfmann (1999:

195), Van Hoek (2001: 161). 495 Bucklin (1965: 31). 496 Chopra and Meindl (2007: 366). 497 Bucklin (1965: 28). 498 Bucklin (1965: 31), Pishchulov (2008: 27). 499 Bailey and Rabinovich (2005). 500 Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper

(1998: 14), Van Hoek (1998a: 95), Van Hoek et al. (1999b: 506), Nair (2005: 458). 501 Shapiro and Heskett (1985: 53), Klaas (2002: 154). 502 Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157). 503 Pfohl et al. (1992: 95), Kloster (2002: 122).


49

diction, but rather proof of the complex interdependencies between process and structure

variables in logistics systems.504

In practice there is a trend towards customer order oriented logistics systems505 or post-

ponement as a logical consequence to centralization506, increasing uncertainty in buyer

markets, increasing product variety, individualization of demands, and regional expansion

of supply in a globalized economy507.

Postponement is analyzed by Eppen and Schrage (1981) in the steel industry, Heskett

and Signorelli (1984) at Benetton, Fisher and Raman (1996) at Sport Obermeyer, Feitzin-

ger and Lee (1997) at HewlettPackard, Magretta (1998), Van Hoek (1998b), and Kumar

and Craig (2007) at Dell, Inc., Van Hoek (1998b) with the SMART car, Battezzati and

Magnani (2000) for industrial and fast moving consumer goods in Italy, Brown et al.

(2000) at a semiconductor firm, Chiou et al. (2002) in the Taiwanese IT industry, Huang

and Lo (2003) in the Taiwanese desktop personal computer industry, Dominguez and

Lashkari (2004) at a major household appliance manufacturer in Mexico, Caux et al.

(2006) in the aluminum-conversion industry, Davila and Wouters (2007) at a disk drive

manufacturer, Cholette (2009) in wine distribution, ElMaraghy and Mahmoudi (2009) in

the optimal location of nodes of a global automobile wiper supply chain considering cur-

rency exchange rates and the optimal modular product structure, Kumar et al. (2009) at 3M

Company, Kumar and Wilson (2009) in off-shored manufacturing, and Wong et al. (2009)

in terms of the optimal differentiation point positioning and stocking levels.

Van Hoek (2001) reviews the literature on postponement dating back to 1965 and puts

it in a systematic framework. Boone et al. (2007) review postponement literature published

from 1999 to 2006 and conclude research should be extended to non-manufacturing post-

ponement, investigate the slow rate of postponement adoption among practitioners, and

continue assessing the relationship between postponement and uncertainty.

3.4.3 Capacity Pooling

Capacity pooling is the consolidation of production508, service509, transportation510, or invento-

ry capacities of several facilities.511 Without pooling every facility fulfills demand just with its

504 Klaas (2002: 157f.). 505 Van Hoek et al. (1999b: 506). 506 Van Hoek (1998a: 95). 507 Ihde (2001: 36). 508 Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281). 509 Cachon and Terwiesch (2009: 149ff., 325, 349, 467). 510 Masters (1980: 71), Evers (1994), Ihde (2001: 33), Chen and Chen (2003), Chen and Ren (2007).


50

own capacity. With pooling demand is aggregated and fulfilled by a single (perhaps virtually)

joint facility.512 If demand is stochastic, a higher service level can be attained with the same

capacity or the same service level can be offered with less capacity.513 It is also advantageous,

if there are economies of scale in obtaining capacity or satisfying demand.514 Capacity pooling

may pool supplier lead times, if the capacities receive separate deliveries from the suppliers

and provide the whole system with the possibility of partial stock replenishments515. However,

this is considered under stock sharing (transshipments). Consequently, capacity pooling is re-

garded as a 1/0 – risk pooling method.

It is predominantly associated with combining manufacturing capacity516 and thus creat-

ing manufacturing flexibility517. We adopt this view in the following and subsume pooling

of inventory capacity under inventory pooling. Manufacturing flexibility means that a plant

is capable of producing more than one product. With no flexibility each plant can only

produce one product, with total flexibility every plant can produce every product (as in

manufacturing postponement). Flexibility allows production shifts to high selling products

to avoid lost sales.518

Capacity pooling can increase effective capacity to serve more demand, which leads to

higher expected sales, profits, and capacity utilization519 or lower manufacturing flow

time.520 Aggregating demands which were served by individual capacities before and are

now served with pooled capacity can reduce demand variability and thus the demand-

capacity mismatch cost. However, installing flexibility is expensive521. If demands are of

different variability, pooling production capacities may increase inventory costs for the

low-demand-variability facility522 or total cost523.

511 Anupindi et al. (2006: 223), Yu et al. (2008: 1), Cachon and Terwiesch (2009: 463). 512 Yu et al. (2008: 1). 513 Anupindi et al. (2006: 224), Yu et al. (2008: 1). 514 Yu et al. (2008: 1). 515 Cf. Evers (1997, 1999), Wanke and Saliby (2009). 516 Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281). 517 Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Pringle (2003), Chopra and Sodhi (2004:

59), Goyal et al. (2006), Van Mieghem (2007), Mayne et al. (2008), Cachon and Terwiesch (2009: 344-351).

518 Cachon and Terwiesch (2009: 344f.). 519 Pooling server capacity in a queuing system does not affect utilization, as demand is never lost, but might

have to wait longer than desired. The amount of demand fulfilled is independent of the capacity structure (Cachon and Terwiesch 2009: 346).

520 Weng (1998: 587), Chen and Chen (2003), Plambeck and Taylor (2003), Chen and Ren (2007), Van Mieghem (2007: 1251), Cachon and Terwiesch (2009: 344).

521 Cachon and Terwiesch (2009: 151, 348). 522 Iyer and Jain (2004). 523 Jain (2007).


51

3.5 Sales and Distribution

3.5.1 Product Pooling

Product pooling is the unification of several product designs to a single generic or “universal

design”524 or reducing the number of products or stock-keeping units (“SKU rationaliza-

tion”525) thereby serving demands that were served by their own product variant before with

fewer products.526

The demands for the different products are aggregated to the demand for the universal

design or the reduced number of SKUs, which fluctuates less thanks to risk pooling. Thus

product pooling can reduce demand variability, improve matching of supply and demand,

reduce the demand-supply mismatch cost527, and increase sales and profit or lower invento-

ry for a given target service level.528 Thus, product pooling constitutes a 1/0 – risk pooling

method.

However, a universal design might not provide the desired functionality to consumers

and therefore might not achieve the same total demand as a set of focused designs. It does

not permit price discrimination and may be more expensive than focused designs, because

the components or quality of components of the universal design targeted to many different

uses might not be necessary to some consumers. There might be economies of scale in

production and procurement of a single universal component relative to small quantities of

several components and lower labor costs though.529 The risk pooling benefits of selling a

universal product may compensate its higher cost.530

Product pooling is closely related to postponement, where the differentiation of a uni-

versal product to individual ones is delayed531, standardization, and component commonal-

ity. It may prohibit risk pooling benefits from product substitution.

524 Cachon and Terwiesch (2009: 330). 525 Jabbonsky (1994), Lahey (1997), Kulpa (2001), Pamplin (2002), Alfaro and Corbett (2003: 12), Neale et

al. (2003), HTT (2005), Sheffi (2006: 119, 2007), Covino (2008), Harper (2008), Sobel (2008: 172), Chain Drug Review (2009a, 2009b), Hamstra (2009), MMR (2009), Orgel (2009), Pinto (2009a, 2009b), Ryan (2009), Thayer (2009).

526 Alfaro and Corbett (2003: 12), Cachon and Terwiesch (2009: 330-336, 467). 527 The demand-supply mismatch cost is the cost of left over inventory (overage cost) and the opportunity

cost of lost sales (underage cost) (Cachon and Terwiesch 2009: 257-263, 433f.). 528 Cachon and Terwiesch (2009: 331), Hamstra (2009), Ryan (2009), Thayer (2009: 23). 529 Cachon and Terwiesch (2009: 335), Hamstra (2009), Ryan (2009), Thayer (2009: 23). 530 Cattani (2000). 531 Alfaro and Corbett (2003: 25).


52

3.5.2 Product Substitution

In product substitution one tries to make customers buy another alternative product, because

the original customer wish is out of stock532 or although it is available (“demand reshape”533).

In manufacturer-driven substitution the manufacturer or supplier makes the decision to

substitute. Typically the manufacturer or supplier substitutes a higher-value or functionality

product, component, or service for a lower-value or functionality one that is not available

(downward substitution).534 Axsäter (2003b: 438) compares this to unidirectional transship-

ments, where transshipments are only allowed in one direction, perhaps because warehouses

differ in their shortage costs. Swaminathan (2001: 130) and Simchi-Levi et al. (2008: 348) relate

substitution to product standardization: With risk pooling through product standardization a

large variety of products may be offered, but only a few kept in inventory. If a product not kept

in stock is ordered, either the product is made or procured or the order filled by downward substi-

tution.

In customer-driven substitution, a customer makes the decision to substitute, because his

original wish is not available.535

If only one of two products is a substitute for the other one, this is called one-way substitu-

tion. In two-way substitution either product substitutes for the other one.536

Substitution allows the manufacturer or retailer to aggregate demand across substitutable

components or products537 (demand pooling538). Demand reshape increases the demand mean

and variability of one product while reducing them for the other product. Substitution and de-

mand reshape reduce total demand variance539 (“demand-pooling effect of substitution”540) and

thus allow to reduce the safety stock for a given customer service level (product availability, fill

rate, or average backlogged demand)541, increase service level without increasing inventory, or a

combination of both542 or increase total profit and raise the customer service level simultaneous-

ly by risk pooling543. Product substitution is a 1/0 – risk pooling method.

532 Swaminathan (2001: 130), Chopra and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: 348). 533 Eynan and Fouque (2003, 2005). 534 Gerchak et al. (1996), Hsu and Bassok (1999), Bassok et al. (1999), Swaminathan (2001: 130), Chopra

and Meindl (2007: 324), Simchi-Levi et al. (2008: 348). 535 Netessine and Rudi (2003), Chopra and Meindl (2007: 324). 536 Chopra and Meindl (2007: 325). 537 Chopra and Meindl (2007: 324ff.). 538 Yang and Schrage (2009: 837). 539 Eynan and Fouque (2003, 2005). 540 Ganesh et al. (2008: 1124). 541 Chopra and Meindl (2007: 326). 542 Liu and Lee (2007). 543 Weng (1999), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348).

53

4 Choosing Suitable Risk Pooling Methods

Findings from our thorough literature review are now merged in a synoptic comparison about

conditions favoring the ten identified risk pooling methods, their advantages, disadvantages,

and basic trade-offs. Based on this synopsis a decision support tool is developed for choosing

appropriate risk pooling methods for a specific situation. Therefore a situational approach is

used.

4.1 Contingency Theory

We adopt a situational approach similar to contingency theory. It claims that there is no “one

best way” as e. g. in Weberian bureaucracy544 to manage a company or make decisions.545 It

depends (is contingent) on internal and external conditions (contingency factors).546 “The best

way to organize depends on the nature of the environment to which the organization must re-

late”547.

Contingency theory is mainly criticized for its positivist548, deterministic, unidirectional,

linear relationships and reduction of complex situations to a limited number of contingency

factors.549

Different from the usual contingency approach we not only use quantitative, empiri-

cal550, but mainly qualitative analysis based on reviewed quantitative analyses, which Do-

naldson (1999) rejects. Kieser and Kubicek (1992: 220ff.), on the other hand, propose to

use empirical correlations not as causalities, but for further interpretations, hypotheses, and

empirical analyses. Höhne (2009: 89) and the references she gives support that contingen-

cy factors are based on both empirical analyses and plausibility assumptions.

We cannot confirm that there is “[o]ne best way for each given situation”551 as our con-

tingency factors are not exhaustive and mutually exclusive and thus several risk pooling

methods may be adequate. However, Donaldson (1996: 118ff.) remarks there are as many

544 Weber (1980: 124ff., 551ff.). 545 Scherer and Beyer (1998: 333f.). 546 Drazin and van de Ven (1985), Miller and Friesen (1980: 268), Scherer and Beyer (1998: 334). 547 Scott (1981: 114). 548 Positivism is “a system recognizing only that which can be scientifically verified or logically proved”

(Soanes and Hawker 2008). 549 Miller and Friesen (1978: 921), Miller (1981: 2f.), Meyer (1993: 1176), Staehle (1994: 49f., 54), Schrey-

ögg (1995: 159ff., 217f., 219), Frese (1992: 193), Scherer and Beyer (1998: 334ff.), Klaas (2002: 99f.), Höhne (2009: 92f.).

550 Scherer and Beyer (1998: 334), Höhne (2009: 89, 91, 94). 551 Scherer and Beyer (1998: 334).


54

combinations of environment, strategy, and structure (“fits”) as there are different envi-

ronmental situations. Thus, for every situation (combination of contingency factors) there

may be one best risk pooling strategy, i. e. combination and implementation of risk pooling

methods.

Starbuck (1981, 1982: 3), Frese (2000: 488f.), and Schreyögg (2008: 54) consider the

contingency approach obsolete. Others, however, deem it important552, popular, often used,

and useful553, as it is open and flexible554, allows to be combined with other approaches to

advance research555, to make action and design recommendations556, to systematize contin-

gency factors557, and to conduct a practice-oriented analysis558. Therefore it seems ade-

quate for our research.

4.2 Conditions Favoring the Individual Risk Pooling Methods

Table D.3 is based on our thorough literature review and shows which conditions render which

risk pooling methods favorable. The favorable conditions are demand-, lead-time-, transporta-

tion-, service-level-, order-policy-, storage-, product-, process-, company-, and competition-

related. The risk pooling methods (columns) are arranged according to the previous chapter's

structure.

Further research is needed to complete this table and confirm the favorable conditions

for the different risk pooling methods, especially for product pooling, central ordering,

(particularly non-manufacturing) capacity pooling, virtual pooling, and product substitu-

tion/demand reshape. We could only speculate and hypothesize about which risk pooling

methods the stated favorable conditions also apply to. Therefore, we only check marked

them for methods where there is confirmation in the literature and the table is not exhaus-

tive. References and explanations are given in footnotes.

552 Pugh (1981), Donaldson (2001), Daft (2009: 26). 553 For example in management (Hiddemann 2007: 16, Schröder 2008: 68, Müller-Nedebock 2009: 22,

Sommerrock 2009: 88, 93f., Segal-Horn and Faulkner 2010: 157f.), organization (Dzimbiri 2009: 86, Güttler 2009: 73f., Höhne 2009: 83, 91, 93f., March 2009: 25, Nobre et al. 2009: 31), finance (Pfeifer 2010: 253), information systems (Andres and Zmud 2001, Sugumaran and Arogyaswamy 2003, Khazan-chi 2005), supply management (Staudinger 2007), business logistics and SCM (Hult et al. 2007, Huang et al. 2008, Doch 2009: 39ff.), and supply chain risk management (Wagner and Bode 2008) research. The li-terature database Business Source Complete accessed via EBSCOhost® showed 1,139 results for the search term “contingency theory” on June 18, 2010.

554 Staudinger (2007: 41), Güttler (2009: 73f.). 555 Sommerrock (2009: 144), Güttler (2009: 73f.). 556 Hiddemann (2007: 16), Schröder (2008: 69), Doch (2009: 39ff.), Pfeifer (2010: 262). 557 Doch (2009: 41). 558 Staudinger (2007: 41), Sommerrock (2009: 94).


55

4.3 The Risk Pooling Methods' Advantages, Disadvantages,

Performance, and Trade-Offs

Table D.4 presents the considered risk pooling methods' possible advantages, disadvantages,

and basic trade-offs in choosing or rejecting them and compares their performance vis-à-vis

other ones.

In summary, the risk pooling methods may, on the one hand, reduce demand and/or lead

time variability, (safety) stock, lead time, as well as procurement, production, transporta-

tion, personnel, and warehouse cost and increase service level (product availability and

fill-rate), utilization, sales, profit, and competitiveness.

On the other hand, they may increase R&D, redesign, component, product, procure-

ment, production, transportation, transaction, and warehousing cost, as well as cycle stock

and cycle time, and decrease customer service, sales, profit, and product functionality. We

only check marked the respective risk pooling method's most important effects that are

confirmed in the studied literature. References are given in footnotes. Explanations are

only given where essential, as we already dealt with the individual risk pooling methods in

detail earlier. These three choices maintain the readability of the table.

Tables D.3 and D.4 can be used to choose suitable risk pooling methods for a specific

company under specific conditions. Scoring methods could be applied or the risk pooling

method with the highest net present value or profit (advantages minus disadvantages ex-

pressed in monetary units) could be chosen. However, the following decision support tool

condenses the most definite distinguishing factors and helps to make a first decision on

possible risk pooling methods elegantly, before carrying out a more thorough cost-benefit

analysis.


56

4.4 A Risk Pooling Decision Support Tool

Figure 4.1: Risk Pooling Decision Support Tool


57

The Risk Pooling Decision Support Tool (RPDST) depicted by a flow chart in figure 4.1 helps

in choosing a risk pooling strategy to cope with demand and/or lead time uncertainty (1), if

it cannot be reduced more efficiently by other means559.

To facilitate the reader's orientation we introduced numbers in round brackets in this

explanation and the flow chart. We will guide you through the flow chart step by step and

critically revisit it at the end.

(2) If product variety is important, inventory pooling (IP)560, capacity pooling

(CP)561, component commonality (CC)562, postponement (PM)563, product substitution

(PS)564, transshipments (TS)565, virtual pooling (VP)566, centralized ordering (CO), and

order splitting (OS) are a possibility. IP, CP, TS, VP, CO, and OS may also be applied, if

product variety is not important. The first four methods might make more sense, if product

variety is important. CC, PM, and PS are not expedient without product variety.

If product variety is not important, product pooling (PP), IP, CP, TS, VP, CO, and

OS are considered. PP is only meaningful, if product variety is not important. The other

methods may also be applied, if product variety is important.

(3) If product variety is important and the stockout penalty cost high compared to in-

ventory carrying cost (savings), PS567, TS568, VP, CP, CC, PM569, CO570, and OS571 may be

559 In addition to risk pooling it may be reduced by e. g. adding inventory or capacity, having redundant

suppliers, which resembles order splitting, increasing responsiveness (Chopra and Sodhi 2004: 55, 60) (quick response (Heil 2006)), flexibility, and capability (Chopra and Sodhi 2004: 55, 60), and improving forecasting (Heil 2006). In LeBlanc et al.'s (2009: 29) model, for instance, PM is favorable unless the forecast is completely accurate.

560 Pfohl (1994: 142), Schulte (1999: 378), Weng (1999: 80), Vahrenkamp (2000: 221), Alfaro and Corbett (2003: 28).

561 Jordan and Graves (1995: 577), Cachon and Terwiesch (2009: 344). 562 Srinivasan et al. (1992: 27), Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348), Song and Zhao

(2009: 493). 563 Zinn (1990: 14), Lee and Tang (1997: 52), Pagh and Cooper (1998: 24), Swaminathan and Tayur (1998),

Van Hoek (1998b, 2001: 161, 173), Van Hoek et al. (1998), Aviv and Federgruen (2001a: 514), Ihde (2001: 36), Matthews and Syed (2004: 34), Graman and Magazine (2006: 1072), Chopra and Meindl (2007: 363f.), Cachon and Terwiesch (2009: 342, 363). “The potential benefits of postponement in the presence of product variety are reduced inventory levels and/or improved service levels” (Graman and Magazine 2006: 1072). “In general, delayed differentiation is an ideal strategy when […] Customers de-mand many versions, that is, variety is important” (Cachon and Terwiesch 2009: 342).

564 Weng (1999: 80), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348). 565 Grahovac and Chakravarty (2001), Wong (2005), Simchi-Levi et al. (2008: 231). 566 Guglielmo (1999), Randall et al. (2002: 56f., 2006: 567), Kroll (2006). 567 Liu and Lee (2007: 1, 41). Only the risk pooling effect is considered, the financial aspect of different

product margins neglected. 568 TS reduce demand and lead time variability by pooling demand and lead times, decrease stockouts, and

thus are sensible, if stockout costs are high (Evers 1997, Needham and Evers 1998, Evers 1999: 133, 2001: 313, Jung et al. 2003, Hu et al. 2005, Wee and Dada 2005: 1519, 1529, Zhao et al. 2005: 545, Lue 2006, Chiou 2008: 428). However, in Jung et al. (2003) the savings from lateral TS decrease with increas-ing shortage cost from a certain value upwards.


58

applied. PS (costs of persuading a customer to buy a substitute in case of a stockout and

possible customer dissatisfaction because he did not obtain the desired product572), TS

(transshipping costs), VP (drop-shipping or cross-filling costs), CP (large costs to have

flexibility), and CC (common component costs) may only be worthwhile, if stockout costs

are high. PS573, PM574, CO575, and OS576 may also be considered, if the stockout penalty

cost is low. IP is suitable, if the stockout cost is low compared to the inventory (carrying

cost) savings from combining inventories, as it increases the distance between the invento-

ry and the buyer and thus delivery time and therefore might increase stockouts577. As noted

earlier in section 2.4 and table D.3, Dai et al. (2008: 407, 410f.) show when IP by a suppli-

er for two retailers may increase the supplier's and retailers' total profits. We consider IP

for low stockout costs only, as the decision for or against inventory pooling vis-à-vis the

other risk pooling methods is considered.

(4) If (2) is answered in the affirmative, (3) with “High”, and the supplier lead time is

highly variable/uncertain or long, TS578, VP, PM579, CO, and OS580 are considered. TS

569 PM may increase flexibility and responsiveness to customer demand (Zinn and Bowersox 1988: 133,

Herer et al. 2002, Davila and Wouters 2007), increase customer service, decrease stockout costs, and thus may be sensible, if stockout costs are high.

570 Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5). CO may increase responsiveness to customer demand, if the allocation of the central order to the delivery warehouses, retailers, or stores can be post-poned and made more responsively according to more recent demand information (Cachon and Terwiesch 2009: 341), decrease stockout costs, and thus may be sensible, if stockout costs are high.

571 OS can reduce lead time (variability) through lead time pooling and increase inventory availability. Therefore it can be reasonable, if stockout costs are high (Evers 1999: 122, 132).

572 Swaminathan (2001: 131). 573 PS may be worthwhile in case of low stockout costs, if the sold substitute's profit margin is higher than

that of the original product wish. Besides, even if the original customer wish is available, PS or demand reshape lowers the total variability of demand and thus inventory costs (Eynan and Fouque 2003, 2005).

574 Besides the risk and stockout cost reduction, PM can lead to economies of scale, synergistic effects, de-layed increase in costs in the value chain and thus decreased capital commitment, and higher flexibility (Lee and Tang 1997: 52, Van Hoek 2001: 162, Aviv and Federgruen 2001b: 579, Herer et al. 2002, Kim and Benjaafar 2002: 16, Ma et al. 2002: 534, Graman and Magazine 2006: 1078, Piontek 2007: 86f.). Therefore it may be worthwhile, even if stockout costs are not particularly high.

575 PM (Zinn and Bowersox 1988: 125f., Van Hoek 2001: 161, Rabinovich and Evers 2003b: 35, Yang et al. 2005b: 994, Graman and Magazine 2006: 1078, Pishchulov 2008: 13, Mahar and Wright 2009: 3061) and CO (McGavin et al. 1993: 1094, Cachon and Terwiesch 2009: 341) may lead to a longer delivery time (from the supplier to the retailer) and more stockouts, and therefore stockout costs should be low. Bucklin (1965: 27) remarks that speculation, the opposite strategy to postponement, “limits the loss of consumer goodwill due to stockouts”. CO may also increase stockouts, if it decreases local knowledge (Ganeshan et al. 2007: 341).

576 Although OS may reduce lead time variability, the split orders are delivered sequentially and thus may lead to more stockouts than a single order or delivery and stockout costs should be low (Chiang 2001: 73, cf. Chiang and Chiang 1996).

577 McKinnon (1989: 104), Fawcett et al. (1992: 36ff.), Schulte (1999: 80, 377), Vahrenkamp (2000: 31f.), Bowersox et al. (1986: 278f.), Evers (1999: 122f.), Ballou (2004b: 573f.), Schmitt et al. (2008a: 14), Ca-chon and Terwiesch (2009: 336).

578 Evers (1999: 132), Herer et al. (2002), Hu et al. (2005), Wanke and Saliby (2009). However, Evers (1996) finds the percentage reduction in safety stocks obtained by using non-emergency transshipments decreases with increasing coefficient of variation of lead time (lead time variability) and average lead


59

and VP by cross-filling may pool demands and lead times, i. e. reduce demand and lead

time variability.581 Long order cycles582 and inflexible production processes583 favor TS.

Long supplier/production lead times support CO.584 For CO the lead time before the distri-

bution center (DC) should be longer than the one after it.585 PM and CO may also reduce

lead time (variability/uncertainty): “Postponement permits firms to be more responsive and

other advantages that are often mentioned are risk-pooling and lead-time uncertainty re-

duction”586. If, for instance, in CO or consolidated distribution product differentiation is

delayed (PM) in the DC, total lead time may be reduced587. Since larger common orders

for multiple locations make more frequent shipments economically possible between the

suppliers and the DC and the DC and the retailers588, consolidated distribution might de-

crease lead time (uncertainty) despite the additional lead time from the DC to the various

retailers. If there is no DC and the retailers merely place joint orders with the suppliers

which are then allocated according to more recent demand information to the retailers just

before the delivery means leave the suppliers, there is no additional lead time between the

DC and the retailers. The retailers' higher demand power through CO and closer collabora-

tion between the retailers and the suppliers might further reduce average lead times and

lead time fluctuations. OS only pools lead times589 and is only worthwhile, if lead time

time at each market (Evers 1996: 126ff.). It increases at a decreasing rate as the proportion of demand at market i retained at facility i approaches the point where demand at i is spread evenly among all locations (Evers 1996: 128). By spreading the demands, and therefore the variability, more evenly across locations, the opportunity to smooth demand fluctuations increases at a decreasing rate (Evers 1996: 128).

579 Transhipments may be seen as a type of time postponement (Rabinovich and Evers 2003b). 580 Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1997, 1999: 122, 132), Kelle and Miller

(2001), Thomas and Tyworth (2006, 2007: 178, 188). According to Thomas and Tyworth (2007: 188), sequentially releasing a split order according to more recent demand information may reduce demand va-riability. Chiang and Chiang (1996) and Chiang (2001: 67, 73), however, recommend “splitting an order into multiple deliveries“ for low demand variability or service level only. The number of stockout possi-bilities is proportional to the number of deliveries. Thus OS increases stockouts, the more, the more vari-able demand is. Kelle and Miller (2001: 407) find dual sourcing may decrease stockouts, if there is no “single, reliable supplier [… and] the variability of the lead-time demand is considerable”, but is only suitable, if lead time uncertainty cannot be reduced. According to Evers (1999: 123) and Wanke and Sali-by (2009: 679) splitting a replenishment order into multiple orders only pools lead times, not demand. Consequently, we recommend OS only for high lead time variability and its lead time pooling, but not its debatable demand variability reduction effect.

581 Evers (1997, 1999: 121), Zhao et al. (2008). 582 Jönsson and Silver (1987a: 224). 583 Grahovac and Chakravarty (2001: 580). 584 Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5). 585 Cachon and Terwiesch (2009: 341), cf. Kumar and Schwarz (1995). 586 Caux et al. (2006: 3243). 587 Dilts (2005: 43). Personal correspondence with Professor David M. Dilts on July 7, 2009. 588 Cachon and Terwiesch (2009: 341). 589 Evers (1999: 122, 132).


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variability590 and unit values are (unusually) high (in relation to industry standards)591. For

high stockout costs per unit (3), high lead time variability (4), low order quantity and/or

safety stock levels emergency TS perform particularly well compared to OS.592

In case (4) lead times are neither highly variable/uncertain nor long, but rather de-

mand is variable/uncertain and thus demand pooling important, PS593, CP594, CC595, PM596

and CO597 may be appropriate.

590 Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1999: 132), Thomas and Tyworth (2007:

178, 188). 591 Thomas and Tyworth (2007: 178, 188). 592 Evers (1999: 132). 593 Eynan and Fouque (2003, 2005), Chopra and Meindl (2007: 324ff.), Ganesh et al. (2008: 1124). 594 Yu et al. (2008: 1). 595 We will now examine whether CC reduces (the effects of) lead time variability/uncertainty and therefore

should be considered, if it is high: Benton and Krajewski (1990: 407) show in a computer simulation experiment with 320 observations that manufacturing “environments with intermediate stocking points and commonality significantly dampen the effects of lead time uncertainty” (410), “tend[…] to reduce the level of backlogs as well as dampen their sensitivity to lead time uncertainty” (412), because “commonality causes intermediate inventories to increase” (413, cf. 410). However, they are more sensitive to vendor quality (“the ability to supply the re-quested quantity of nondefective parts or raw materials” (404)) and therefore might increase backlogs (413). Yet, the ambition of risk pooling is to decrease inventory for a given service level or vice versa or a combination of both. If there are no intermediate stocking points, they are more sensitive to lead time un-certainty (410). Hence, CC by itself does not reduce “the effects of lead time uncertainty”. Benton and Krajewski (1990) give no intuitive explanation for the increasing total inventory. Usually common com-ponents reduce safety and thus total stock, because they are used in several products (Labro 2004: 362). Eynan and Rosenblatt (1996), Chandra and Kamrani (2004: 175), and Mohebbi and Choobineh (2005: 473) cite Benton and Krajewski (1990) in a truncated manner, aiming at the reduction of lead time uncer-tainty through CC. Labro (2004) deals with Benton and Krajewski (1990) more accurately. Although Ma et al. (2002) assume “deterministic replenishment leadtimes” (Ma et al. 2002: 526), they find “the major benefits of commonality are risk-pooling and lead time uncertainty reduction. These lead to a safety stock reduction and have been studied extensively by many researchers, including, but not li-mited to, Baker et al. (1986), Collier (1982), Guerrero (1985), Gerchak et al. (1988), Eynan and Rosen-blatt (1996), and Grotzinger et al. (1993)” (Ma et al. 2002: 524). Like most CC research (e. g. McClain et al. 1984, Eynan 1996, Thonemann and Brandeau 2000, Hillier 2002a, 2002b, Thomas et al. 2003, Labro 2004: 359), all these researchers mention demand uncertainty reduction as a benefit of CC (Baker et al. 1986: 983, Collier 1982: 1300, 1303, Guerrero 1985: 396, Ger-chak et al. 1988: 755), only Eynan and Rosenblatt (1996) lead time uncertainty reduction in the inade-quate manner described above. Under restrictive assumptions, Mohebbi and Choobineh (2005: 476, 481) conclude CC tends to be more beneficial with both random component procurement order delays and demand uncertainty than with only one of these uncertainties. They assume, for instance, that the component procurement lead time can only be longer not shorter than the planned one. Actual uniformly distributed demand for finished products, however, can be higher or lower than the forecast (476). Costs (481), safety stock and safety lead times are neglected. Backorders are filled after current demand (475). These researchers do not ex-plain the causes for their observations. Lead time delays mostly reduce average total inventory per com-ponent per period (477f.), as they perhaps reduce the time a component remains in storage. This effect in-creases with increasing demand uncertainty (477), perhaps because a longer-than-planned delivery time may be offset by lower-than-forecast actual demand. This may be amplified by CC and lead to a higher service level than without commonality. However, the product with the lowest number of (three) compo-nents and without commonality shows the lowest inventory per component and the highest service levels (478f.). Song and Zhao (2009: 22) even find that in dynamic assemble-to-order systems commonality may not decrease inventories under the first-in-first-out (FIFO) with identical and under the FIFO and modified FIFO (MFIFO) rule for dynamically allocating common components to demand with non-identical com-


61

(5) If (2) is “Yes”, (3) “High”, (4) “Yes”, and the fixed cost per order high, TS598, VP,

PM, and CO599 are favorable. If the replenishment order cost is high, one rather resorts to

other cheaper and/or faster possibilities (TS, VP, and PM) than placing a replenishment

order or tries to combine orders by CO to reduce the number of orders and exploit econo-

mies of scale (EOS) and thus lower ordering costs. If it is low600 and there are no transpor-

tation EOS601, OS may be considered. Due to smaller orders OS cannot take advantage of

quantity and transportation discounts and a long-term partnership with a single supplier,

but several suppliers may guarantee competitive pricing and other advantageous terms.602

TS603, VP, and PM may also be applied, if the fixed order cost is low.

(6) In case (2) is “Yes”, (3) “High”, (4) “Yes”, (5) “High”, and the transshipment or

transportation cost is high and there are EOS in ordering, CO604 or PM605 can be

worthwhile. If the transshipment or transportation cost is low and there are no EOS in

ordering, TS606, VP607 or likewise PM608 can be applied. PM may forego EOS:609 Zinn and

ponent replenishment lead times. “The value of commonality tends to decrease as [… the common com-ponent replenishment lead time] increases under either FIFO or MFIFO”. If the common component replenishment lead time fluctuates strongly and the common component is not available, all the products using this component cannot be built. Thus lead time variability/uncertainty of the common component supplier might be more severe than of a specific component supplier (cf. Benton and Krajewski 1990: 413, Labro 2004: 363). All these findings led us to not recommend CC by itself for coping with high lead time variability/un-certainty and to only consider it for the low lead time variability/uncertainty case.

596 Jain and Paul (2001: 595ff.), Anupindi et al. (2006: 193), Chopra and Meindl (2007: 365), Pishchulov (2008: 24).

597 If we follow Cachon and Terwiesch (2009: 336, 339, 341f., 349), CO may only pool demands and may also be applied if lead time (variability) is low. PM or delayed differentiation and CO may increase lead time and only pool demands during lead time.

598 Herer and Rashit (1999: 525), Daskin (2003), Herer and Tzur (2003: 419). 599 Schwarz (1981: 147), Evers (1995: 5, 1999: 133), Gürbüz et al. (2007: 294). 600 Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188). 601 Evers (1999: 122f.), Thomas and Tyworth (2006, 2007), Sajadieh and Eshghi (2009). 602 Evers (1999: 122f.). 603 For TS the fixed order cost is irrelevant (Evers 1999: 132). 604 Eppen and Schrage (1981: 67), Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293), Cachon and Ter-

wiesch (2009: 341). 605 Allowing online sales to accumulate and postponing assigning them to a fulfillment site can lead to lower

inventory costs (Mahar and Wright 2009), higher utilization of transportation means, and EOS in order-ing. PM does not necessarily increase transportation distance, so that transportation costs may be irrele-vant. Customers may be willing to wait, so that no premium transportation cost is incurred. The product and process are usually designed, so that the delayed differentiation can be conducted fast (Lee and Tang 1997), the delivery delay is insignificant, and no premium transportation cost is incurred. PM can exploit EOS (Piontek 2007: 87).

606 Jönsson and Silver (1987a: 224), Robinson (1990), Evers (1999: 132f.), Grahovac and Chakravarty (2001), Jung et al. (2003), Hu et al. (2005), Anupindi et al. (2006: 191), Kutanoglu (2008: 356f.). Still TS may save fixed and variable replenishment costs (Herer and Rashit 1999: 525, Herer and Tzur 2003: 419), if e. g. one location makes a larger replenishment order to transship some of it to other locations especial-ly in a dynamic deterministic demand environment (Herer and Tzur 2003: 419). Herer and Rashit (1999) consider a single period random demand environment.

607 Anupindi et al. (2006: 191). In VP small-orders may be drop-shipped more expensively than full truck loads (Randall et al. 2002, Cachon and Terwiesch 2009: 328f.).


62

Bowersox (1988: 124f.) find that labeling, packaging, and manufacturing PM can lead to

lost EOS. In case of large EOS in the manufacturing and/or logistics processes some

speculation should be applied instead of manufacturing and full PM. Speculation, the op-

posite strategy to PM, rather leads to EOS: “Speculation permits goods to be ordered in

large quantities rather than in small frequent orders. This reduces the costs of sorting and

transportation”610.

(7) If (2) is “Yes”, (3) “High”, (4) “Yes”, (5) “High”, and (6) “Yes”, do you prefer re-

designing your products and/or processes611 to achieve leagility, both agility (respon-

siveness) and leanness (cost minimization), (PM)612 to a less expensive, fast implementa-

ble and changeable solution that keeps inventory closer to customers (CO)613? If yes, you

may implement PM (8), otherwise CO (9). Time and form PM are appropriate, if well-

timed product delivery to and differentiation for the customer are more important than

company-internal cost issues.614 On the one hand, CO may decrease responsiveness be-

cause of a lack of local knowledge about sales615 when ordering. On the other hand, it may

increase responsiveness because of allocating the joint order to the delivery warehouses,

retailers, or stores according to more recent demand information and because aggregate

forecasts usually are more accurate than disaggregate ones616. It is more likely that CO

leads to EOS in ordering than PM. While CO and speculation lead to consolidation of

goods in jointly used transfer and transformation processes and EOS617, PM tends to singu-

larize batches of goods in separate transfer and transformation processes618. To determine

which PM strategy might be most appropriate, you may turn to Zinn and Bowersox (1988),

Cooper (1993), Pagh and Cooper (1998), Yang et al. (2004), and Yeung et al. (2007).

(10) In case (6) is answered in the negative, and the less expensive, fast implementable

and changeable, less cross-functional solution is preferred to redesigning products

608 Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Christopher (1992), Feitzinger and Lee (1997),

Delfmann (1999: 195), Van Hoek (2001: 161). 609 Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994). 610 Bucklin (1965: 27). 611 Products and/or processes may have to be redesigned for PM (Lee and Tang 1997, Van Hoek 1998a, Kim

and Benjaafar 2002, Yang et al. 2005b: 994, Davila and Wouters 2007, Piontek 2007). PM might lead to higher manufacturing costs (Chopra and Meindl 2007: 365).

612 Feitzinger and Lee (1997), Fliedner and Vokurka (1997), Van Hoek et al. (1999a), Christopher (2000), Van Hoek (2000a), Christopher and Towill (2001), Herer et al. (2002), Graman and Sanders (2009: 206).

613 Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349). 614 Alderson (1957), Rabinovich and Evers (2003b: 34). 615 Ganeshan et al. (2007). 616 Cf. footnote 456. 617 Bucklin (1965: 27), Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157). 618 Cooper (1983: 71), Bowersox and Closs (1996: 475), Klaas (2002: 157).


63

and/or processes619 and there is no or no significant lead time (uncertainty) reduction

benefit in PM after all, TS and VP are considered. If in addition your supplier, wholesaler,

or warehouse locations have small-order drop-shipping or cross-filling capabilities620

(11), VP (12) may be appropriate. If not, TS (13) may do, especially if the TS cost is lower

than the VP cost. VP may reduce investment in inventory and fulfillment capabilities as

well as overall handling and warehousing costs621 more than TS. However, VP is only re-

commendable, if your company possesses the necessary IS capabilities and is powerful

within the supply chain, because it might lose product margin and control to the drop-

shipping party, which could negatively affect service quality. The drop-shipping party

might bypass the company and directly sell to customers as it possesses all the information

transparency it needs.622 “Virtual inventories provide little benefit in product categories,

such as grocery, where consolidation of orders is necessary but impossible to accomplish

from a few consolidated wholesalers”623.

TS and PM might be used in combination, as emergency TS, an important type of time

PM, support implementing form PM624.

If you do not mind redesigning products and/or processes and a more expensive mid-

to long-term cross-functional implementation and your PM strategy may reduce lead

time uncertainty (10), PM (14) might be the right method to reduce both demand and lead

time uncertainty. TS can increase leagility like PM625, but perhaps more inexpensively and

faster.

Returning to (5), if the fixed order cost is low, and (15) both demand uncertainty re-

duction and lead time (uncertainty) reduction and fewer order placements are pre-

ferred to only lead time uncertainty reduction, but avoiding premium transportation

and in-transit inventory costs, TS626, VP627, and PM628 come into question and the al-

619 Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001),

Swaminathan (2001: 129f.), Herer et al. (2002), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994), Davila and Wouters (2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 345f.).

620 Randall et al. (2002: 56), Cachon and Terwiesch (2009: 328f.). 621 Randall et al. (2002: 55). 622 Randall et al. (2002: 56). 623 Randall et al. (2002: 57). 624 Rabinovich and Evers (2003b: 41f.). 625 Herer et al. (2002: 201), Zhao et al. (2008). 626 Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Herer et al.

(2002), Çömez et al. (2006). 627 Randall et al. (2002: 56). 628 Jain and Paul (2001: 595ff.), Yang et al. (2004: 1054), Dilts (2005: 43), Anupindi et al. (2006: 193), Caux

et al. (2006: 3243), Chopra and Meindl (2007: 365), Pishchulov (2008: 24).


64

ready explained decision process (10) through (14) starts. If (15) is negated, OS629 (16)

may be implemented.

Moving upwards again, in case (3) is low and (17) inventory reduction is more impor-

tant than agility (customer responsiveness), IP630 and PS631 are considered. If (17) is ne-

gated, PM, PS, CO, and OS come into consideration. PM improves agility632 and flexibili-

ty633 and enables product variety634, but may not decrease inventory as much as IP or PS. PS

performs better than IP in terms of location accessibility and lost sales (customer responsive-

ness)635, but may not decrease inventory as much as IP. With PS the customer may get a

product right away, but not the originally desired one. CO performs worse than IP in terms of

inventory reduction, but keeps inventory near customers636. The allocation of the central or-

der to the delivery warehouses, retailers, or stores can be postponed and made more respon-

sively according to more recent demand information. Reducing lead time uncertainty OS

may lower (safety) stock for a given service level637, but not as much as IP, as the former

only pools lead times, not demands638. Simultaneously splitting an order among suppliers

can reduce cycle stock due to successive deliveries of smaller split orders639, but not the sum

of in-transit and cycle stock in the system640. OS may be more responsive than IP, because it

reduces lead time variability and keeps inventory close to customers. However, OS may in-

crease stockouts, if demand variability is high due to successive deliveries.641

In case (17) is confirmed, and (18) the fast implementable, changeable, less expensive

(especially in terms of transportation cost) solution with higher location accessibility and

629 Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188). 630 IP may reduce inventory more than PS, but creates distance between inventory and customers and there-

fore may reduce product availability and profits (Bowersox et al. 1986: 278f., McKinnon 1989: 104, Fawcett et al. 1992: 36ff., Evers 1999: 122f., Schulte 1999: 80, 377, Vahrenkamp 2000: 31f., Ballou 2004b: 573f., Schmitt et al. 2008a: 14, Cachon and Terwiesch 2009: 336).

631 PS might be seen as not as responsive as PM because the customer does not receive his original wish and is persuaded to buy a substitute, which may cause some customer dissatisfaction, but might reduce inven-tory more than PM.

632 Zinn and Bowersox (1988), Herer et al. (2002), Davila and Wouters (2007). 633 Lee and Tang (1997: 52), Feitzinger and Lee (1997: 117ff.), Van Hoek (2001: 162), Ma et al. (2002:

534), Graman and Magazine (2006: 1078), Piontek (2007: 86f.). 634 Cachon and Terwiesch (2009: 341). 635 Eynan and Fouque (2003, 2005). 636 Eppen and Schrage (1981), Cachon and Terwiesch (2009: 349), Pishchulov (2008: 22). 637 Evers (1999: 122, 132), Thomas and Tyworth (2006: 245). 638 Evers (1999: 122, 132). 639 Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et

al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Zhou and Lau (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003), Thomas and Tyworth (2006: 245).

640 Thomas and Tyworth (2006: 254). 641 Chiang and Chiang (1996) and Chiang (2001: 67, 73).


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fewer lost sales is preferred to product functionality and inventory reduction, PS (19)

may be suitable. If (18) is negated, IP (20) might be the right method. In contrast to PS, IP

entails aggregate and thus more accurate forecasts642. Individual demand forecasts for con-

trolling the previously separate inventories are replaced by a more accurate aggregate fore-

cast for managing the consolidated inventory. Of course, PS can only be applied, if prod-

ucts or parts are substitutable, which the preceding affirmation of question (2) suggested.

If (17) is negated and (21) lead times are highly variable/uncertain or long, PM, CO,

and OS are considered (cf. (4)). If then (22) the fixed order cost is high (CO and PM may

be appropriate (cf. (5))) and (23) a perhaps cheaper solution, that keeps inventory closer

to customers, is preferred to redesigning products and/or processes to offer customized

products more responsively and there are EOS in ordering643, CO (24) may be chosen. If

(23) is negated, PM (25) might be appropriate.

If (22) is low (OS and PM may be appropriate (cf. (5))) and product and/or process

redesign to reduce demand uncertainty and perhaps lead time (uncertainty) (cf. (4)) is

preferred to only lead time pooling and keeping inventory close to customers, but in-

curring higher ordering costs (26), then PM (25) might be suitable. Otherwise, OS (27)

may be worthwhile.

If (21) is negated and rather demand pooling is important, PM, PS, and CO are scruti-

nized (cf. (4)). If then (28) the less expensive, fast implementable, and changeable solu-

tion is preferred to giving the customer always the desired product (not a substitute), but

in a longer delivery time and with product and/or process redesign, PS (19) may be

appropriate, otherwise PM and CO are considered. If in this latter case (29) the cheaper

solution that keeps inventory closer to customers is preferred to product and/or

process redesign and leagility and there are EOS in ordering, then CO (24) may be ap-

propriate, otherwise PM (14) (cf. (23) to (25)).

If the importance of product variety is denied in (2) and lead times are highly varia-

ble/uncertain or long (30), TS, VP, OS, and CO are considered (cf. (4)). In case (30) is ne-

gated and rather demand uncertainty reduction is important, PP644, IP645, CP, and CO646 (cf.

(4)) are considered as they only pool demands and thus reduce demand variability, but not

lead time variability. According to Dilts (2005) CO may also reduce lead times (cf. (4)).

642 Cf. footnote 456. 643 CO may utilize EOS in procurement (Eppen and Schrage 1981: 67, Hu et al. 1997, 2005: 34, Gürbüz et

al. 2007: 293, Cachon and Terwiesch 2009: 341). 644 Cachon and Terwiesch (2009: 331f.). 645 Evers (1996: 115, 1997: 57, 60, 1999: 121). 646 Cf. Cachon and Terwiesch (2009: 336, 339, 341f., 349).


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If (30) is affirmed, (31) the fixed order cost is high (CO, TS, and VP are considered (cf.

(5))), (32) the transshipment or transportation cost is high and there are EOS in order-

ing, CO (33) may be reasonable (cf. (6)). If (32) is negated and (34) your supplier, wholesa-

ler, or warehouse locations have small-order drop-shipping or cross-filling capabilities647

(cf. (11)), VP (35) may be appropriate, especially if it is less expensive than TS. If not, TS

(36) may do (cf. (11) to (13)).

If (31) is low (OS, TS, and VP are considered (cf. (5))) and (37) both demand uncer-

tainty and lead time (uncertainty) reduction, fewer stockouts, and order placements are

preferred to only lead time pooling, but avoiding premium transportation and in-transit

inventory costs of stock transfers648, then TS and VP are considered further and the already

explained decision process (34) to (36) is triggered again. If (37) is answered in the negative,

OS (38) may be economically sensible.

If (30) is negated and (39) accommodating demand uncertainty649 is preferred to

reducing inventory and system utilization (arrival divided by service rate) is high, CP and

CO are considered. “While the relative benefit of inventory pooling tends to diminish with

utilization, the relative benefit of capacity pooling tends to increase with utilization” in a

production-inventory system with endogenous supply lead times.650 CP or manufacturing

flexibility is more valuable with approximately equal total capacity and expected demand.651

CO does not reduce inventory as much as IP, but keeps it near customers.652 The postponed

more responsive allocation of the central order to the delivery warehouses, retailers, or stores

according to more recent demand information enables better matching of supply and de-

mand653 (also cf. (17)). If afterwards EOS in ordering and a preference for a possibly less

expensive, fast implementable and changeable solution are affirmed in (40), CO (33) may

be appropriate. If (40) is negated and (41) CP/(manufacturing) flexibility is cheaper than

capacity, CP (42) might be applied654. Goyal and Netessine (2005) may help to choose a

type of manufacturing flexibility (volume and/or product flexibility)655. If capacity is cheap-

647 Randall et al. (2002: 56). 648 Evers (1997: 72, 1999: 123f.). 649 Cachon and Terwiesch (2009: 344, 348). 650 Benjaafar et al. (2005: 565). 651 Cachon and Terwiesch (2009: 348). 652 Eppen and Schrage (1981: 61), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349). 653 Cachon and Terwiesch (2009: 341). 654 Cachon and Terwiesch (2009: 348). 655 Volume flexibility is “[t]he ability to adjust the output volume of a product without incurring large costs“,

product flexibility “the ability to manufacture different products and to efficiently shift production from products with low demand to products with high demand” (Goyal and Netessine 2005: 2). For a monopol-ist, product flexibility reduces uncertainty in demand for individual products more and in aggregate de-


67

er than CP/flexibity, adding capacity (43) might be a better choice.656 CP may be more

appropriate for manufacturing, CO for trading companies (cf. (48)).

If (39) is negated, PP and IP (cf. (17)) are considered, as inventory reduction is given

priority. If then (44) product availability is preferred to product functionality, PP (45)

may lead to a higher product availability than IP (46): It does not increase the distance be-

tween products and customers and may enable EOS in production and procurement of a sin-

gle universal component or product, but might degrade product functionality, not achieve the

same total demand as a set of focused designs, and eliminate some brand/price segmentation

opportunities.657

Returning to (4), if lead times are not highly variable/uncertain or long, rather demand

pooling is important (PS, CP, CC, PM, and CO are considered), and (47) your products share

components or qualities to satisfy the same or similar needs or you are willing to create these

commonalities, then PS, CP, CC, PM, and CO may be applied.

Substitute goods satisfy the same or similar needs and therefore are seen as an alternative

or replacement by consumers. The reason for this replacement relationship is the functional

replaceability between two goods, if they correspond in price, quality, and utility or perfor-

mance so that they are able to meet the consumer's need. This thus enables substitution struc-

turally.658

CP is also based on commonalities: Common design, assembly processing, training in

common methods, suppliers capable of coping with common design and processing and

reacting to volume and complexity are needed.659 CC designs products that share compo-

nents.660

PM advantages partly arise from CC.661 CO does not require (component) commonality.

However, the centrally ordered products usually are needed by several requisitioners (deli-

very warehouses, stores, or departments). Therefore one could say the products are common

to two or more locations.

mand less than volume flexibility. Moreover, product flexibility copes better with substitutable and worse with complementary products than volume flexibility. Using both volume and product flexibility can lead to diseconomies of scope (Goyal and Netessine 2005: 1).

656 Cachon and Terwiesch (2009: 348). 657 Cachon and Terwiesch (2009: 335). 658 Wildemann (2008: 72). 659 Mayne et al. (2008). 660 Chopra and Meindl (2007: 326ff.). 661 Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al.

(1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al. (2008).


68

PM and CP perform better with similar demand. For PM that means that demand is of

comparable size662 or that the standard deviations of demand for items in the product line

are similar663, for CP approximately equal total capacity and expected demand664 and simi-

lar demand variability665. Capacity sharing among independent companies is more benefi-

cial, if they are similar in their characteristics (work content, demand rates, or delay

costs).666 PM may reduce EOS667 or increase the cycle/delivery lead time668.

If then (48) a less expensive, fast implementable and changeable solution is preferred

to product and/or process redesign and leagility and you run a trading or retail com-

pany rather than a pure manufacturing company, then PS and CO may be applied, other-

wise CP, CC, and PM.

PS can be implemented faster than CP, CC, and PM. It may only incur the costs of per-

suading a customer to buy a substitute669 and maybe cause customer dissatisfaction with

the substitute purchase670.

CO may be less responsive, but also less expensive, implemented within a shorter time

frame, and involve less departments (mainly purchasing and sales) than CP, CC, and PM.

It does not require a product redesign either. CP671, CC672, and PM673 may necessitate a

costly product and/or process redesign and therefore also involve at least manufacturing

and R&D in addition.

As products are only delivered after a customer order is received, in general PM leads to

a centralized logistics system674 and may increase the distance between inventory and cus-

tomers relative to CO675 and even more so compared to PS. With CP a product is produced,

662 Chopra and Meindl (2007: 363f.). 663 Zinn (1990: 14), Alfaro and Corbett (2003: 18f., 24), Cachon and Terwiesch (2009: 342). 664 Jordan and Graves (1995: 583), Cachon and Terwiesch (2009: 348). 665 Iyer and Jain (2004), Jain (2007). 666 Yu et al. (2008: 26). 667 Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994). 668 Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al.

(2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13), Mahar and Wright (2009: 3061).

669 Eynan and Fouque (2003, 2005). 670 Swaminathan (2001: 133). 671 Jordan and Graves (1995), Mayne et al. (2008), Cachon and Terwiesch (2009: 349). 672 Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129, 131), Ma et al. (2002: 536), Simchi-Levi et

al. (2008: 345f., 348). 673 Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001),

Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Davila and Wouters (2007: 2245), Yang et al. (2005b: 993f.), Piontek (2007), Shao and Ji (2008), Simchi-Levi et al. (2008: 346).

674 Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper (1998: 14), Van Hoek (1998a: 95).

675 Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349).


69

stored, or transported, or a customer served where there is capacity, so that the distance

between inventory and customers may increase.

PM research “is highly conceptual”676. Applications are mostly limited to manufactur-

ing677, e. g. in Zinn and Bowersox (1988: 121), Lee et al. (1993), Dröge et al. (1995), Feit-

zinger and Lee (1997), Garg and Tang (1997), Lee and Tang (1998: 172), Van Hoek

(1997), Dominguez and Lashkari (2004), Caux et al. (2006), Chopra and Meindl (2007:

365), Davila and Wouters (2007), Harrison and Skipworth (2008: 193), Kumar et al.

(2009), and Kumar and Wilson (2009). Bailey and Rabinovich (2005) exceptionally apply

PM in internet book retailing. “Currently, relatively simple postponement applications are

practiced in wholesale and logistics services as supplementary services. More complex,

high value adding manufacturing activities are still the primary domain of manufacturers

and these are not often outsourced to logistics service providers”678.

Our survey results in appendix A support that CC679, PM, and CP680 are predominantly

applied in manufacturing, CO or consolidated distribution681 and PS682 rather in trade, so

that their implementation might be more promising here. PS is more efficient than CC.683

In case (48) is answered in the affirmative (PS and CO are considered) and

(49) matching supply and demand and product functionality are preferred to a less

costly, fast implementable and changeable solution with higher (substitute) product

availability, but possible customer dissatisfaction because of substitution and there are

EOS in ordering, then CO (33) may be appropriate, otherwise PS (50). PS offers the cus-

tomer a product right away, however, not the originally desired one but a substitute, which

may lead to customer dissatisfaction. CO gives the customer the desired product maybe in

a longer lead time or the sale is lost. PS can be implemented and changed faster and less

expensively than CO. The latter may benefit from EOS in procurement though (cf. (23)).

676 Yang et al. (2005b: 994). 677 Boone et al. (2007: 594). 678 Van Hoek and Van Dierdonck (2000: 205). 679 Gerchak and Henig (1989), McDermott and Stock (1994), Tsubone et al. (1994), Sheu and Wacker

(1997), Swaminathan and Tayur (1998), Swaminathan (2001), Hillier (2002b), Ma et al. (2002), Labro (2004), Mohebbi and Choobineh (2005), Chew et al. (2006), Simchi-Levi et al. (2008: 345-348), Nonås (2009), Wazed et al. (2008, 2009: 76).

680 Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Plambeck and Taylor (2003), Pringle (2003), Iyer and Jain (2004), Benjaafar et al. (2005), Jain (2007), Goyal et al. (2006), Van Mieghem (2007), Mayne et al. (2008).

681 Eppen and Schrage (1981), Cachon and Terwiesch (2009: 336-341). 682 Anupindi et al. (1998), Smith and Agrawal (2000), Mahajan and Van Ryzin (2001a, 2001b), Rajaram and

Tang (2001), Eynan and Fouque (2003, 2005), Zhao and Atkins (2009). 683 Eynan and Fouque (2005).


70

If (48) is negated (CP, CC, and PM are considered), (51) the costs to have CP or

(manufacturing) flexibility are lower than the costs for CC (common components, product

redesign, and possible cannibalization) and PM (product and/or process redesign or rese-

quencing), then the already explained decision process (41) through (43) has to be com-

pleted.

If (51) is answered in the negative (CC and PM are considered) and the product684 (cf.

(47)) and (52) (manufacturing) process is modular685, “the firm maximizes its perfor-

mance by adopting”686 PM (53): It “will help to maximize effective forecast accuracy and

minimize inventory costs”687. In case the product is modular688 (cf. (47)) but the process

is not689, then differentiation cannot be delayed, but CC (54) “is the most effective ap-

proach”690. Simchi-Levi et al. (2008: 348) express this more cautiously: CC “is likely to be

effective”. However, we follow the primary source Swaminathan (2001: 132). To deter-

mine the optimal level of CC you may refer to Boysen and Scholl (2009).

Nevertheless, if the process (and the product) is modular, CC and PM may both be ap-

plied. To choose between them the CC691 cost (product redesign692 and possible cannibali-

zation of higher priced components693) has to be traded off against the PM cost (higher

production, transportation, and process and/or product redesign cost (cf. (7))). This be-

684 Feitzinger and Lee (1997), Lee (1998), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek

(1998a, 1998b, 2001: 173), Chiou et al. (2002: 113, 122), Yang et al. (2004: 1053), Simchi-Levi et al. (2008: 348), ElMaraghy and Mahmoudi (2009: 483).

685 Feitzinger and Lee (1997), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek (2001: 173), Simchi-Levi et al. (2008: 348). A modular product, e. g. a personal computer as opposed to a shirt, is as-sembled from a variety of modules such that there is a number of options the customer is interested in for each module. This is important for concurrent and parallel processing (Swaminathan 2001: 128, Simchi-Levi et al. 2008: 345). A modular (manufacturing) process, e. g. semiconductor wafer fabrication as opposed to oil refining, con-sists of discrete operations, so that inventory can be stored in semi-finished form between operations. Products are differentiated by undergoing a different subset of operations during the manufacturing process. Modular products are not necessarily made in modular processes (Swaminathan 2001: 128, Sim-chi-Levi et al. 2008: 345).

686 Swaminathan (2001: 131). 687 Simchi-Levi et al. (2008: 348). 688 Weng (1999), Swaminathan (2001: 131), Yang et al. (2005b: 993), Simchi-Levi et al. (2008: 348). 689 Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348). 690 Swaminathan (2001: 132). 691 The common component may be more expensive than the dedicated ones that it replaces (Hillier 2002a,

2002b, Van Mieghem 2004: 419, Zhou and Grubbström 2004, Mohebbi and Choobineh 2005: 473). Still component commonality may reduce total cost (Van Mieghem 2004: 419, Hillier 2002a, 2002b).

692 Sometimes, it is necessary to redesign products and/or processes to achieve commonality (Bagchi and Gutierrez 1992: 817, Swaminathan 2001: 129, 131, Ma et al. 2002: 536, Simchi-Levi et al. 2008: 345, 348), which may result in a smaller and more economical set of components though (Whybark 1989).

693 Excessive part commonality can reduce product differentiation, so that less expensive customization options might cannibalize sales of more expensive parts (Ulrich and Ellison 1999, Kim and Chhajed 2000, 2001: 219, Desai et al. 2001, Krishnan and Gupta 2001, Ramdas and Sawhney 2001, Simpson et al. 2001, Swaminathan 2001: 131, Heese and Swaminathan 2006, Simchi-Levi et al. 2008: 348).


71

comes important if not form, but place and time PM are considered. CC and PM often are

connected and can be applied together. Maybe applying both of them may be more eco-

nomical than applying only one. PM implementation may require CC694 (“postponement

through standardization”695). According to Caux et al. (2006: 3244), PM in the form of

delayed differentiation can be implemented by “process restructuring, component commo-

nality and product design”.

If (47) is negated, then CO and CP are considered, because they do not require CC, es-

pecially if transportation or storage capacity is pooled. Yet, we consider CP related to in-

ventories under IP. If then (55) the costs of CO are lower than both the ones of CP and

adding capacity and there are EOS in ordering, then CO (33) may be effective. Other-

wise CP and adding capacity are considered and the already explained decision process

(41) to (43) still has to be followed.

Frequently the risk pooling methods cannot be separated mutually exclusively, because

they are favorable under similar conditions as tables D.3 and D.4 already showed. If the de-

cisions in the RPDST are not selective and disjunctive, the respective risk pooling methods

are considered for both choices. The RPDST only shows tendencies and enables general

statements about the advantageousness of risk pooling design options, since the specific size

of the costs and benefits are unknown and the complex interdependencies are simplified. The

advantageousness of specific risk pooling methods in a specific situation for a specific

company depends on specific cost parameters and their interaction or ratios.696

In a particular company case risk pooling design recommendations might differ from

this RPDST. The identified conditions and recommendations for risk pooling methods de-

pend on the selected reference framework. Therefore a study with the same topic might

attain a different classification and thus different results. The framework gives general rec-

ommendations about the advantageousness of risk pooling methods. Afterwards a compa-

ny should weigh the costs and benefits of the different suitable options expressed in mone-

tary units to reach a decision about which risk pooling strategy to implement. Expenses for

implementing the risk pooling strategy might exceed the achievable savings.697

Some benefits besides decreased (inventory) cost such as increased flexibility, respon-

siveness, and customer service level are hard to quantify. Resequencing due to PM might

lower inventory levels, but increase the inventory value per unit. However, if customiza-

694 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347). 695 Ma et al. (2002: 534). 696 Cf. e. g. Wanke (2009) on IP. 697 Cf. Simchi-Levi et al. (2008: 349).


72

tion is postponed, the generic products may have a lower value than the customized ones.

Tariffs and duties for undifferentiated products might be lower. Still products and

processes might be more expensive under some risk pooling methods.698

Implementing risk pooling might lead to positive or negative effects not studied in detail

in this RPDST, such as human resistance or negative impacts on the whole supply chain.

It might be appropriate to apply risk pooling methods just to certain products (e. g.

the ones with uncertain demand).699

Combining several risk pooling methods might improve performance.700 Using, for

instance, time PM (e. g. emergency TS and inventory centralization), form PM (product

customization), and enterprise-wide information systems together improved “enterprise-

wide inventory management performance” more than using each of these methods sepa-

rately in an empirical model based on 216 large and established U.S. manufacturing

firms.701 (Logistics) PM might go hand in hand with IP (inventory centralization) or CO

(centralized distribution).702 A hybrid strategy of pooling demand by centralizing invento-

ries (IP) but splitting supply by multisourcing (OS) can be worthwhile.703 Substitutable

products support the implementation of variety PM.704 Demand substitution furthermore

facilitates flexible manufacturing without competition and may facilitate its adoption with

competition.705 CP may exploit CC.706

Kutanoglu (2008) considers both emergency lateral shipments from other local facilities

and direct shipments (VP in the sense of Netessine and Rudi 2006) from one central ware-

house of service parts to repair high-technology hardware systems such as computers and

telecommunication devices in case of a stockout at a local facility within the time window

necessary for the target service level. Alfredsson and Verrijdt (1999: 1430) find conjoint

use of lateral TS and direct deliveries can reduce costs significantly, particularly for slow

moving parts. Investing only in direct delivery flexibility may increase costs dramatically,

unless pipeline flexibility is applied. Pipeline flexibility means that a customer backorder is

satisfied by the part that arrives first either via normal replenishment or via direct delivery.

Similarly, Wong et al. (2007b: 1056) remark emergency direct deliveries from the central

698 Simchi-Levi et al. (2008: 349). 699 Cf. Chopra and Meindl (2007: 366). 700 Cf. e. g. Hong-Minh et al. (2000). 701 Rabinovich and Evers (2003b: 38, 42f.). 702 Shapiro (1984), Zinn and Bowersox (1988), Van Hoek (1998a, 2001), Nair (2005: 451). 703 Benjaafar et al. (2004a: 1442). 704 Heskett and Signorelli (1984), Kopczak and Lee (1994), Goyal and Netessine (2005: 22). 705 Goyal and Netessine (2006: 1). 706 Mayne et al. (2008).


73

warehouse and the plant in case of stockouts in a two-echelon system are only worthwhile,

if lateral TS between local warehouses are not possible.

The RPDST neglects the degree to which the different favorable risk pooling methods

should be applied and their opposite methods. Often two opposing methods are applied in

combination to a certain degree (e. g. centralization and decentralization, consolidation and

singularization, postponement and speculation). Speculative inventories, for instance,

should be held in the logistics channel wherever their costs do not exceed the savings

achievable by postponement.707 Furthermore, the certain part of the product line or the ge-

neric product can be made less expensively to stock, the uncertain products or product va-

riants to order.

An empirical verification of the derived results pertaining to the design recommenda-

tions appears worthwhile. The theoretical analysis revealed fundamental interdependencies

of risk pooling methods and facilitates the practical risk pooling design. Possible devia-

tions from business practice can be disclosed by empiricism. The analytic process can be

adapted accordingly. Therefore, we will apply the RPDST to a German paper wholesaler to

determine risk pooling methods that may reduce the demand and lead time uncertainty it

faces.

707 Bucklin (1965: 28).

74

5 Applying Risk Pooling at Papierco

In this chapter we will first introduce Papierco to you and some problems it faces. Afterwards

we will determine risk pooling methods with the help of the RPDST developed in the previous

chapter to solve these problems and consider their application at Papierco in more detail. Final-

ly we will summarize our results.

5.1 Papierco

A German paper wholesale company (to protect confidentiality we call it Papierco in the fol-

lowing) pursues the business strategy of a decentralized, differentiated full-line distributor and

system provider of paper, printing accessories, as well as screenprinting and advertising sys-

tems, which precludes central warehouses and minimal storage. This corporate strategy seems

to be Papierco's competitive advantage, as its competitors cannot offer such a ubiquitous and

fast delivery service as well as broad assortment. The decentralized warehouse network also

constitutes a competitive advantage in the light of increasing fuel costs, autobahn toll, climate

change, environmental legislation, and increased traffic volume. Papierco delivers its products

from its warehouses with its own truck fleet or has them drop-shipped from paper plants to its

customers.

According to its management, Papierco is a full-line wholesaler, as its 32,739 customers

(mainly printing offices) need all kinds of different product specifications mostly within 24

hours. If a product with a low turnover was eliminated from the assortment, some custom-

ers might not buy some other products either anymore due to product interdependencies.

The alliance Papierco of several legally independent paper wholesalers and exchange of

items between 21 regional warehouses in case of a stockout (emergency transshipments)

allow the individual companies and locations to offer a larger product assortment than they

could store on their own. Not every of the 7,000 product specifications Papierco offers is

stored at every location. Products with a low turnover share are only stocked at few loca-

tions due to cost considerations.708 This is called “selective stocking”709, selective stock

keeping710, or “specialization”711. The idea behind selective stock keeping is lowering in-

ventory holding costs by treating products differently without impairing the service level

708 Pfohl (2004a: 122f.), Simchi-Levi et al. (2008: 233). 709 Ross (1996: 310f.). 710 Pfohl (2004a: 118ff.). 711 Anupindi et al. (2006: 191f.).


75

considerably.712 Transshipments between Papierco's locations are necessary, so that every

location can offer the complete assortment. The shipping decision is postponed until a cus-

tomer order is received. Every warehouse thus functions as both a regional and central

warehouse and can access products in every other warehouse as if all warehouses were one

single warehouse (virtual inventory or warehouse). Hence Papierco takes advantage of

inventory pooling, but mitigates some of the disadvantages of a central warehouse

through the use of transshipments and information technology.713

5.2 Problems Papierco Faces

5.2.1 Fierce Competition in German Paper Wholesale

Paper wholesale in Germany is characterized by strong competition especially in office, illu-

stration printing, and offset paper: Sales stagnate, sales prices decrease, raw material, energy,

and logistics costs increase. A lot of customers go bankrupt and there is an ongoing concentra-

tion process in the printing industry.714 Paper manufacturers, the paper wholesale's suppliers,

suffer from bad profitability due to increasing costs, overcapacities, and price pressure715, as

well as competition pressure from Asia and Eastern Europe716, which they seek to improve by

mergers and markups. The current international economic downturn intensifies the cost and

competition pressure in all industrial sectors. Insufficient capacity utilization is a strain on the

paper wholesale, its customers, and suppliers. Increasing profit margin pressure is believed to

promote the consolidation tendency on all levels of the value chain.717 Thus paper wholesale

faces strong competition and economically stricken customers and suppliers, whose negotia-

tion power increases because of mergers. Competitiveness and economic success can be se-

cured on this market by efficient supply, storage, and distribution planning enabled by risk

pooling, particularly since logistics incurs the highest costs at Papierco.

5.2.2 Supplier Lead Time Uncertainty

The lead time of paper manufacturers fluctuates strongly, ranges from 14 to 154 days, and is

on average 28.49 days. It fluctuates subject to price increases, drop-shipping sales, (interna-

tional) demand, and production setup times. Supplier lead times are entered into the enterprise

712 Pfohl (2004a: 122). 713 Cf. Sussams (1986: 8f.), Simchi-Levi et al. (2008: 233). 714 BVdDP (2009). 715 Kibat (2007). 716 FPT (2007b: 7). 717 BVdDP (2009).


76

resource planning (ERP) system by a central master data maintenance in three German Papier-

co locations. The actual lead time of each supplier should rather be recorded for every delivery

to improve the purchasing policy.

Because of long and uncertain lead times for certain products paper merchants some-

times place so called “phantom orders” for product quantities they do not actually need as

a precaution, which intensifies the bullwhip effect718 and leads to even longer and more

variable lead times. This once resulted in all orders having to be cancelled and only enter-

ing real orders (with a corresponding real demand) again afterwards. Thus lead times nor-

malized again.

5.2.3 Customer Demand Uncertainty

Figure 5.1: Total Fine Paper Sales in Tons per Month in Germany (BVdDP 2010a: 8)

718 Lee et al. (1997a: 98).

Total Sales (t)

2009

2008

2007

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months

320,000

290,000

260,000

230,000

200,000


77

Figure 5.2: Papierco's Total Fine Paper Sales to Customers in Germany in Tons per Month

Total demand for fine paper in Germany is seasonal: It is higher in January, February, and

March, lower from April till July, and increases up to November in order to decrease again in

December as figures 5.1 and 5.2 show. Total customer demand depends on the overall eco-

nomic development, i. e. on the available financial means for e. g. new products and advertis-

ing budgets.

Warehouse sales made up 42 %, drop-shipping sales 58 % of all sales in 2007 and

2008,719 respectively 43 % and 57 % in 2009720. Warehouse sales of individual products

per week per warehouse are sporadic without a trend or seasonal pattern as figure 5.3

shows exemplarily.

719 BVdDP (2009). 720 BVdDP (2010b).

70000

75000

80000

85000

90000

95000

100000

105000

110000

115000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

To

tal S

ale

s (

t)

Months

2007

2008

2009


78

Figure 5.3: Papierco's 2007 Warehouse Sales to Customers per Week of Seven Standard

Paper Products from the Hemmingen Warehouse


79

“When demand for items is intermittent, because of low volume overall and a high degree of

uncertainty as to when and at what level demand will occur, the time series is said to be lumpy,

or irregular”721. Among others many products and stocking locations might explain the lumpi-

ness of demand for individual Papierco products.722 “The lumpy demand condition occurs

when two or three times the standard deviation of the historical data exceed the forecast of the

best model that can be fit to the time series”723. Ballou (2003a: 9) states in the PowerPoint

presentation to Ballou (2004b) a time series is lumpy, if the mean of the series is less than or

equal to three times the standard deviation of the series.

Although the items in figure 5.3 are considered standard, on average they did not sell

8.29 weeks or around 16 % of the year 2007 and their standard deviation of sales per week

per warehouse was on average 0.94 times their mean. Fast moving copy papers selling

nearly every week were the least lumpy with the standard deviation being only 0.37 times

the mean on average. Uncoated Cut-Size White Wood-Pulp Paper was the lumpiest with

no sale in 34 weeks or almost two thirds of the year 2007 and a lumpiness factor (standard

deviation of demand divided by mean demand) of 2.11, followed by the Folding Box

Board with no sale in 15 weeks and a lumpiness factor of 1.32.

On average the standard deviation of an item's sale per month per warehouse is 2.24

times the mean sale per month per warehouse in 2007. Nearly one third (31.45 %) of the

products show a standard deviation that is more than three times the arithmetic mean of

sales per month per warehouse. In these cases the standard deviation is on average

3.78 times the mean. Of a lot of articles no unit is sold for several months and then sudden-

ly some month a lot of units are sold. On average 7.83 months or nearly two thirds of the

year 2007 a specific product is not sold. We conclude that demand per product per month

is very random and lumpy or sporadic and therefore “difficult to predict accurately by ma-

thematical methods due to the wide variability in the time series”724. Risk pooling methods

might produce relief here.

Ballou (2004b: 311) suggests to use the reasons for the lumpiness in the forecast, sepa-

rate forecasting of lumpy and regular demand products, not react quickly to random de-

mand shifts without assignable cause and use slowly reacting forecast methods such as

exponential smoothing with a low smoothing constant or a regression model refit annually

721 Ballou (2004b: 288). For further definitions please refer to e. g. Ghobbar and Friend (2003: 2105), Kukre-

ja and Schmidt (2005: 2059), Bridgefield (2006), Gutierrez et al. (2008: 409, 412). 722 Cf. Ballou (2004b: 288, 310). 723 Ballou (2004b: 310). 724 Ballou (2004b: 310).


80

at the most, and maybe make up for forecast inaccuracy by a higher inventory level for low

demand items. Croston (1972) and Johnston and Boylan (1996) recommend an exponential

smoothing constant of 0.05 to 0.20 for lumpy demand. Silver et al. (1998: 127), however,

report pertaining to intermittent and erratic demand that “[t]he exponential smoothing fore-

cast methods […] have been found to be ineffective where transactions (not necessarily

unit-sized) occur on a somewhat infrequent basis. […] Infrequent in the sense that the av-

erage time between transactions is considerably larger than the unit period, the latter being

the interval of forecast updating”.

Lumpy or highly uncertain demand can be coped with by obtaining information directly

from customers, collaborating with other supply chain and channel members, collaborative

forecasting, forecasting total demand and apportioning it by regions, delaying supply re-

sponse, product differentiation, and forecasting as long as possible, supplying the more

certain products first, developing quick response and flexible supply systems, and applying

the forecasting methods with caution.725 Most of these suggested solutions rely on risk

pooling.

5.2.4 Distribution Requirements Planning (DRP)


Warehouse Hemmingen

725 Ballou (2003a: 39-42, 2004b: 310f., 314-317).

0

1000

2000

3000

4000

5000

6000

7000


Tons

Months

Inventory

Sales to Customers

Sales to Colleagues

Total Warehouse Sales

Goods Received from Suppliers

Goods Received from Colleagues

Total Goods Received


81


Warehouse Reinbek

Figures 5.4 and 5.5 illustrate Papierco's demand forecasting and inventory management prob-

lems using two standard Papierco warehouses. The inventory level is always around 1,000 to

2,000 tons higher than total warehouse sales. This may be partly explained by the large product

variety. The Total Goods Received and Total Warehouse Sales curves often are opposite in

phase or time-lagged, i. e. when total warehouse sales go up, often goods receipts go down or

vice versa.

Sales departments, product managers, and purchasing departments of the different

warehouse locations do not collaborate in planning demand and requirements. The sales

departments merely plan the customers' financial development, i. e. sales and contribution

margins per customer. On the basis of the product managers' aggregated sales planning on

the product group level for all German locations skeleton agreements are centrally nego-

tiated with the most important suppliers. The purchasing departments forecast demand on

the product level on the basis of the past six months' sales and order accordingly. These

three planning processes are unconnected. The sales departments do not report any ex-

pected exceptional demands to the purchasing departments either. The latter only plan

products sold via warehouses, without considering substitution effects between similar

0

1000

2000

3000

4000

5000

6000


Tons

Months

Inventory

Sales to Customers

Sales to Colleagues

Total Warehouse Sales

Goods Received from Suppliers

Goods Received from Colleagues

Total Goods Received


82

products or between warehouse and drop-shipping sales726. Drop-shipping sales are con-

ducted only by the sales departments.

Papierco should create a uniform cross-functional demand planning process, in which

sales, product managers, and purchasing collaborate, to contain extraordinary demands

through the sales assistants' and product managers' profound market knowledge and enable

a better demand forecast and thus order policy. Although Adam and Ebert (1976) show

that objective statistical forecasting models produce more accurate results than subjective

judgemental forecasts, Bunn and Wright (1991) remark expert forecasts had a higher quali-

ty than previous research claims. That is why Silver et al. (1998: 133) suggest combining

these two approaches.

The individual locations conduct their distribution requirements planning (DRP) with-

out any coordination, so that inventory reductions at one location strain the transshipment

flows and impair other locations' DRP. Thus, one location might deplete another one's

stock of a specific product via transshipments. In the following week the latter location

might have to obtain this product via transshipments from another warehouse due to a cus-

tomer demand and so on. Likewise a warehouse may receive a supplier's delivery, although

it has plenty of inventory left, while another one does not. This process seems to have tak-

en on a life of its own in a “vicious circle” with increasing transshipment volumes and in-

ventory variability at most warehouse locations.

The increased transshipments did not reduce the aggregate safety stock, although this

might be assumed because of the demand balancing effect thanks to the creation of a vir-

tual inventory through transshipments. Allegedly the customer service level increased,

which is difficult to verify, as Papierco does not record it in any way.

We will recommend a not necessarily geographically centralized procurement, which

forecasts and orders for all of Papierco's German locations on the product level and directs

the suppliers' deliveries to the warehouses according to current demand in section 5.3.3.

5.2.5 Demand Forecasting Methods

Increasing forecast accuracy decreases the need for risk pooling727 (e. g. emergency transship-

ments) and safety stock and increases customer service level (product availability).

726 Sometimes a drop-shipping sale is converted into a warehouse sale, if the drop-shipping lead times are

high. 727 Cf. Graman and Magazine (2006: 1081).


83

Today Papierco uses the forecast methods 4 (Moving Average) and 10 (Linear Smooth-

ing) of the twelve ones the ERP software JD Edwards OneWorld offers.

Method 1 (Percent Over Last Year), method 2 (Calculated Percent Over Last Year), me-

thod 3 (Last Year To This Year) and method 8 (Flexible Method or Percent Over Months

Prior) are so called “naïve estimates” and project sales of previous years into the future

either directly or after multiplying them with a factor.728 These methods are rather inade-

quate for Papierco, as sales of individual products differ significantly from year to year.

Method 12 (Exponential Smoothing with Trends and Seasonality) is not suitable either, as

demand for individual products does not follow a trend or seasonal pattern.

Method 4 (Moving Average), Method 7 (Second Degree Approximation), which ex-

presses sales in a curve, method 9 (Weighted Moving Average), method 10 (Linear

Smoothing), which assigns weights to the sales numbers linearly decreasingly with a for-

mula, and method 11 (Exponential Smoothing729) are similar. They are suitable for short-

term forecasts for mature products without trends or seasonal patterns.730 They could ena-

ble a good demand forecast for Papierco with an order cycle of two weeks.

Method 5 (Linear Approximation) establishes a trend on the basis of two data points.

Small changes influence long-term forecasts strongly. Method 6 (Least Squares Regres-

sion) also calculates a linear trend. Turning points and changes in the demand function are

recognized late with the Linear Regression. If the sales data form a curve or show strong

seasonal fluctuations, systematic forecast errors appear.731 Methods 5 and 6 may be suita-

ble for Papierco because of the short order cycle of two weeks, although demand for indi-

vidual products shows no or only a short-term trend.

Analyzing the forecast methods for the seven standard products, we discovered that a

forecast based on sales of the last twelve months leads to improved results compared to the

current one with six months. This comes as no surprise as Gibson and Horner (2005: 1f.)

state that JD Edwards OneWorld forecasting accuracy improves with the length of the used

sales history. The software is capable of using up to two years of sales history.

Method 11 (Exponential Smoothing) and method 6 (Least Squares Regression) led to

the best results most frequently. Ballou (2004b: 311) also recommends these methods for

forecasting lumpy demand.

728 Oracle (2009). 729 Exponential Smoothing automatically uses linearly decreasing weights and is a weighted average of ac-

tual sales and the previous period's forecast. 730 Oracle (2009). 731 Oracle (2009).


84

The results of method 11 (Exponential Smoothing) might be improved by letting JD

Edwards OneWorld determine the smoothing constant alpha based on past sales instead of

determining it arbitrarily.

Methods 9 (Weighted Moving Average), 4 (Moving Average), and 10 (Linear Smooth-

ing) also led to good results in order of descending quality. A naïve estimation (projection

of the previous year's sales into the current year) did not give good results. The results

could be improved by multiplying the previous year's sales with a growth factor.

We used the mean absolute deviation (MAD) of the forecast values from the actual

sales in 2006 and 2007 and the forecast error (the sum of the difference of the actual and

the forecast sale per week) to measure the quality of the respective forecast method. For

other forecast performance measures please refer to Gutierrez et al. (2008: 413f.).

Comparison of the forecast accuracy of forecast methods is difficult732, as the forecast

errors of the two methods may be correlated733. Besides “a linear combination of forecasts

from two or more [forecasting] procedures can outperform all of those individual proce-

dures”734. According to Kang (1986) a regular average of forecasts of several methods

leads to high-quality results.

Tiacci and Saetta (2009) evaluate the impact of usually neglected possible interactions

between demand forecasting methods and stock control systems on global system perfor-

mance. Accordingly, demand forecasting methods cannot be chosen only on the basis of

traditional measures of forecast errors. Total costs and service level of the global inventory

control system should also be considered. However, this is beyond the scope of this thesis

and remains for further research.

The products still have a lumpy demand pattern also according to Ballou's (2004b: 310)

definition: “[T]he forecast of the best model that” could “be fit to the time series” was 3.39

times “the standard deviation of the historical data”.

The MAD was on average half the size of the mean actual demand per week, i. e. even

with the best tested forecast method, we would have ordered half a week's average demand

too much or too little per product per week on average. The absolute forecast error was on

average four times the mean actual demand per week, i. e. even though the forecast errors

balance each other to a certain extent we would have had four week's average demand too

much or too little over the whole year per product on average.

732 Silver et al. (1998: 131). 733 Peterson (1969). 734 Silver et al. (1998: 131).


85

Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted

Moving Average) should be admitted to the DRP forecast run besides today's exclusively

used methods 4 (Moving Average) and 10 (Linear Smoothing), as they gave good results.

Gibson and Horner (2005: 4) recommend using as many forecast methods as possible “to

maximize the chances that the Best Fit forecast that is calculated is really close to what

reality will be”. Of course, this has to be traded off with calculation time and software per-

formance.

“The statistical forecast techniques discussed earlier may work well for stable, mature

products with significant demand history, whereas qualitative methods based largely on

human opinion and direct marketing intelligence (not a part of JD Edwards) usually make

more sense for new or unstable demand products. […] In fact, conventional wisdom is that

sales and marketing should ʻown the forecastʼ. Their input is especially important for new

products or products with unstable demand. Sales and marketing should participate in the

development of forecasts and they should also be formally ʻgradedʼ on their forecast accu-

racy performance results. […] And one final comment: always remember that there is far

more to be gained by people collaborating and communicating well than there is by using

all of the advanced formulas and algorithms yet developed”735.

Since our analysis is only based on seven standard products, as no further data were

provided, it should be extended to a larger, more representative number of products before

implementation.

Simple forecasting methods outperform statistically sophisticated procedures for indi-

vidual items. The reverse is true for macro-level data and medium and long-term forecast-

ing. Consequently, sophisticated forecasting methods do not outperform simpler ones in

terms of forecast accuracy in general.736 Nevertheless, one could check whether more so-

phisticated forecasting methods not available in JD Edwards OneWorld and developed for

products with lumpy demand lead to more accurate results.

The Croston (1972) method forecasts intermittent demand well737 and is available in fore-

casting software packages738. It “generates separate forecasts for the demand size and the

number of periods between demands, and uses the ratio as an estimate for the expected de-

mand per period. It also updates the mean absolute deviation of the forecast error for the de-

735 Gibson and Horner (2005: 9). 736 Makridakis et al. (1982). 737 Willemain et al. (1994), Johnston and Boylan (1996). 738 Syntetos et al. (2005).


86

mand size”739. Teunter and Sani (2009: 82) call Croston's method “the standard method for

forecasting intermittent demand” and use its forecasts to calculate order-up-to levels that lead

to close to target customer service levels. Gutierrez et al. (2008) apply neural network mod-

eling to forecasting lumpy demand. Neural network forecasts generally outperform single

exponential smoothing, Croston's method, and the Syntetos–Boylan approximation740. Synte-

tos and Boylan (2001, 2005) approximately correct an error in the mathematical derivation of

and the resulting bias in Croston's estimates of expected demand.

Gutierrez et al. (2008: 418) find neural network models generally perform better than

the traditional methods. The Syntetos–Boylan approximation performs better than Cros-

ton's and single exponential smoothing methods in lumpy demand forecasting. If the aver-

age nonzero demand is considerably smaller in the test than in the training sample, the tra-

ditional forecast methods perform better than the neural network forecasts with lower

smoothing constants. However, Gutierrez et al. (2008: 412) only consider 24 SKUs.

Analyzing other methods for lumpy demand forecasting not available in JD Edwards

OneWorld lies beyond the scope of this thesis. Furthermore, it would be difficult and ex-

pensive to integrate these forecasting methods into the current ERP system and DRP.

A better demand forecast leads to a higher product availability (customer service level)

at the primary warehouse and thus reduces transshipments. Customer service level can be

increased and at least safety stock can be reduced.

Of course it would be desirable to always have the desired product at the right time at

the right warehouse, so that no transshipments would be necessary at all. This however is

impossible741, as forecasts are generally incorrect742. The longer the forecast horizon, the

worse the forecast is743. Aggregate are more precise than individual forecasts.744

As the suggested forecast methods in JD Edwards OneWorld only lead to a limited

forecast improvement and the more sophisticated methods for lumpy demand are difficult

to implement at least in the short run and their benefit for Papierco is unknown, this com-

pany could resort to risk pooling methods that reduce demand uncertainty relying on ag-

gregate forecasting745, such as central ordering.

739 Teunter and Sani (2009: 82). 740 Syntetos and Boylan (2001, 2005, 2006), Syntetos et al. (2005). 741 Evers (2001: 316). 742 Anupindi et al. (2006: 168). 743 Anupindi et al. (2006: 169). 744 Cf. footnote 456. 745 Sheffi (2004: 95).


87

5.3 Solving Papierco's Problems

Papierco could cope with lead time and demand uncertainty and its related forecasting and

inventory problems and ensure its competitiveness and economic success by risk pooling.

5.3.1 Determining Suitable Risk Pooling Methods for Papierco

The RPDST developed in section 4.4 is used to determine appropriate risk pooling methods for

Papierco, which suffers from customer demand and supplier lead time uncertainty (1). Both

demand and lead times fluctuate strongly.

Product variety is important (2) for Papierco's competitive advantage and because its

customers, who are mostly printing offices, need all kinds of paper specifications.

Stockout penalty costs are high compared to inventory carrying costs and thus attainable

inventory cost savings (3) from e. g. inventory pooling: The stockout cost (209 €) is esti-

mated by the average contribution margin of one ton of warehouse sales to customers mi-

nus the sales assistant's premium. The average length of time a ton stays in inventory is

estimated by the average inventory level divided by average annual demand. Papierco has

an annual average turnover rate of 8, i. e. on average a ton of paper remains in storage for

one eighth of a year or one and a half months. Storing one ton of paper costs 22 € per

month, so that the cost of holding a ton of paper in storage is 33 € on average.

The supplier lead time means and variabilities are high and therefore their reduction is

important to Papierco (4). Papierco declared costs per order did not accrue. However, if all

2007 expenses of the purchasing departments are divided by the total amount of warehouse

purchases from suppliers, we arrive at an order cost of 3.31 € per ordered ton. This cost per

order is relatively low (5) compared to the average value per ton of 1,058 € in 2007. De-

mand uncertainty and lead time (uncertainty) reduction and fewer orders are preferred to

only lead time pooling, but lower premium transportation cost and in-transit inventory cost

(15), as Papierco suffers from both demand and lead time uncertainty, minimum order and

saltus quantities have to be observed, and the in-transit carrying cost per unit and emergen-

cy transfer cost per unit are low.

Order splitting (16) is not feasible because of among others the required minimum order

quantities and full truck load supplier deliveries. The cheaper, faster implementable and

changeable, and less cross-functional solution to cope with both demand and lead time un-

certainty is preferred to product and/or process redesign of a postponement (14) strategy

(10). Besides, manufacturing and assembly postponement can rather be applied by the paper

producer, not the paper wholesaler. Papierco could postpone the labeling, packaging (ream


88

wrapping paper), or delivery of products, e. g. by central ordering the allocation of ordered

products can be delayed and conducted according to more current demand information. Mix-

ing printer's ink from base colors can also be postponed to the delivery warehouses until a

customer order arrives instead of ordering already mixed colors from the supplier. Cutting

paper to the desired format could also be delayed until an order arrives. However, this can

only be applied to an insignificant part of the product line. The other postponement options

for Papierco will not reduce demand and lead time uncertainty much either.

The paper producers do not possess small-order drop-shipping capabilities (11). They

only drop-ship full truck loads to customers. However, there are endeavors of some paper

wholesalers to conduct drop-shipping sales via its warehouses to gain the higher profit

margin of warehouse sales and of paper producers to drop-ship less than truck load to pa-

per wholesale customers to increase their profit. This causes resentment on both sides.

Virtual pooling (12) by not holding any inventory, only arranging sales, and having all

products drop-shipped from the paper producers to the customers is no viable strategy for

the paper wholesaler, as it would make him dispensable and the paper producers do not

possess the necessary distribution infrastructure. Furthermore, the restriction to deliver to

customers usually within 24 hours could not be kept. Therefore lateral transshipments

(13) or cross-filling seem to be the risk pooling method of choice for Papierco to deal with

both demand and lead time uncertainty.

Order costs may also be considered high in (5), because minimum order and saltus

quantities make (placing) an order more expensive, as frequently more than forecast de-

mand minus on hand inventory has to be ordered by the individual locations to meet these

order restrictions, which results in unnecessary inventory costs. Increasing the needed or-

der quantity per order by postponement (8) or central ordering (9) for several locations

may better exhaust minimum order and saltus quantities and lead to economies of scale in

ordering (6) due to price discounts. As Papierco prefers the less expensive, fast implement-

able and changeable solution and the possibilities for postponement (8) are still limited as

described above, central ordering (9) might be a viable risk pooling method to achieve both

efficiency and responsiveness to customers. Some of the transportation cost otherwise in-

curred for emergency transshipments between warehouses may be shifted unto the suppli-

ers who deliver to Papierco's delivery warehouses. Therefore (9) central ordering might

make sense, especially against the background of increasing fuel prices.

Today Papierco's average transportation cost to deliver one ton of paper with its truck

fleet within Germany is 15.88 €. We arrived at this figure by dividing Papierco Germany's


89

total transportation cost (driver costs, capital commitment, depreciation, maintenance and

repair, motor vehicle tax, insurance, diesel, lubricant, tires, autobahn toll, parking, and

miscellaneous operating costs) by the total annual warehouse sales in 2008. The trans-

shipment cost per ton (transportation, shipment documentation, receiving, handling and

administration costs) amount to 69.48 € per transshipped ton of paper on average. This is

still relatively moderate (6), so that the decision process (10) through (13) can be followed

again, which reconfirms transshipments (13) as a favorable risk pooling method.

Papierco's management thinks that (2) product variety might be reduced in the office

paper segment and where product specifications just differ in their format in one or two

centimeters. The Paper Technology Research Association Forschungsvereinigung Papier-

technik e. V. (FPT) also denies the necessity of the current large product variety in German

paper wholesale.746 Affirming the importance of lead time (uncertainty) reduction (30)

afterwards leads to the same train of thoughts in (31) to (38) as in (5) to (16) without con-

sidering postponement (cf. 2), which favors transshipments (36) and perhaps central or-

dering (33).

If Papierco gives priority to reducing demand uncertainty, as demand variability is more

severe and lead times and their variability are not recorded accurately nowadays, and there-

fore (30) is denied and accommodating demand uncertainty is preferred to inventory reduc-

tion (39) due to the fierce competition for customers, then central ordering (33) is favored

again: It is less expensive, faster implementable and changeable than capacity pooling

(41f.) and permits to achieve economies of scale in ordering (40). Besides, capacity pool-

ing is rather suitable for manufacturing companies than for wholesalers. Papierco's loca-

tions cannot pool manufacturing capacity, as they do not produce paper. They could, how-

ever, pool or share printer's ink mixing, paper cutting, or ream wrapping capacity. This

might not be economically worthwhile, since the costs of shipping mixed paint or cut to fit

or ream wrapped paper between locations might destroy the capacity pooling benefits. Fur-

thermore, delivery time to the customer might suffer, and this can only be applied to an

insignificant part of the product line. Papierco's locations could pool transportation capaci-

ty, which is operationalized by transshipments, and inventory storage capacity, which cor-

responds to inventory pooling.

Papierco's management would also like to reduce inventory. One has to carefully check

whether this intention does not conflict with Papierco's business strategy and competitive

746 FTP (2007a, 2007b).


90

advantage of being a 24-hour delivery full-range paper wholesaler in Germany and inven-

tory savings outweigh possible lost sales. Remember that Papierco's inventory carrying

costs are moderate relative to stockout and transshipment costs per ton. If one concludes

that inventory reduction is more important than accommodating demand uncertainty (39),

product pooling (45) and inventory pooling (46) might be suitable. Product pooling

keeps inventory close to customers in the delivery warehouses, thus enables the nationwide

24-hour delivery service and product availability (44), pools demands, and improves fore-

cast accuracy, but perhaps degrades product functionality. Because of the mentioned short-

comings and because it only pools demands, product pooling should not be applied on its

own but together with another risk pooling method that reduces lead time uncertainty and

only within a product segment that can be rationalized without hurting customer service

level and product purchase interdependencies substantially. Rationalization in this context

means deleting products from the product line or replacing several product variants by a

universal product.

Physical inventory pooling in a single central warehouse would preclude the 24-hour de-

livery service. However, selective stock-keeping in several delivery warehouses may be feas-

ible, pool demands, enable to reduce at least safety stock and maintain the product variety

and delivery speed, but increase transportation costs. Fast movers could be stored at every

warehouse, while slow movers could be held at a limited number of warehouses only.

If Papierco disavows the importance of lead time (uncertainty) reduction in (30), it may

also do so in (4). Papierco's products share common qualities (47). The less expensive, fast

implementable and changeable solution is preferred to product and/or process redesign and

leagilty, and Papierco is a trading company (48). It does not produce its paper products

itself and its products neither are modular nor do they share common components besides

the raw materials, so that it cannot redesign the products and/or production processes.

Hence, component commonality (54) or manufacturing postponement (53) is not sensible

for Papierco. Postponing cutting paper to the right format, mixing printer's ink, and labe-

ling and ream wrapping paper are conceivable but not expected to reduce demand or lead

time uncertainty significantly.

Product substitution (50) can be implemented quickly and cheaply, but displease cus-

tomers as they do not receive the desired product in case of a stockout, but a substitute. In

contrast to product substitution, central ordering (33) might reduce lead time (uncertain-

ty) in addition to demand uncertainty and lead to economies of scale in ordering, but be

more expensive, particularly since transaction and coordination costs are higher.


91

On the whole, lateral emergency transshipments seem to be the most suitable risk pool-

ing method for Papierco, followed by central ordering, especially if fuel and transportation

costs continue to rise. Both methods may be applied in combination and enable to achieve

the seemingly conflicting aims of reducing demand and lead time uncertainty as well as

inventory investment and maintaining customer service level in terms of product variety,

inventory availability, and delivery speed. Product substitution, product pooling, inventory

pooling, and postponement may also be suitable in order of descending favorability, but

not as a sole method due to their mentioned drawbacks. They may not reduce lead times or

lead time uncertainty by themselves.

In the following we will deal with the suitable risk pooling methods determined for Pa-

pierco in more detail.

5.3.2 Emergency Transshipments between Papierco's German Locations

Papierco's German locations exchange products in case of a stockout, which supports the result

of the RPDST.

As the quantities exchanged by transshipments have risen over the last years, Papierco's

management asked whether these transshipments are economically sound and whether they

can be reduced or improved.

In our opinion this stock exchange must not be considered detachedly from sales747,

demand, demand forecast, order policy and storage policy, as it is influenced by these fac-

tors. Therefore the systemic approach of logistics should be accommodated and the inter-

dependencies between single components and the whole should be considered.748 It is de-

sired to contribute to a preferably spatially and temporally smooth, continuous, and aligned

sequence of activities and processes which target satisfying customer needs.749

5.3.2.1 Optimizing Catchment Areas

A business policy has evolved historically that if the sales department of one location attends to

a customer, the same location's logistics department also delivers products to this customer.

Therefore, today some of Papierco's customers in the same five-digit zip code areas are allo-

cated inefficiently to several of the current 21 German warehouse locations. Customers should,

however, be supplied standardly by the warehouse closest to them. There is a high potential for

747 The sales assistant triggers a transshipment order, i. e. he orders stock from another warehouse, if he

cannot satisfy a customer's demand from the primary warehouse. 748 Delfmann (2000: 322). 749 Delfmann (2000: 325).


92

transportation cost degression in switching from today's suboptimal to the determined optimal

customer allocation to Papierco's current 21 warehouses. Unfortunately, it cannot be numera-

lized exactly due to today's inefficient customer allocation to multiple locations, erroneous data

management, and ignorance of the number of delivery trips to each customer, delivery routes

and quantities, and truck utilization before and after optimization.

Optimizing the customer allocations can lead to cost reductions fast and without much

investment burden. The delivery route numbers merely have to be changed for some cus-

tomers in the customer master data of the ERP software. Furthermore, optimal customer

allocations may reduce transshipments.

The optimal customer allocation according to the shortest distance was found with the

software NCloc750 and Euclidean metric and visualized with the zip code diagram Das

Postleitzahlen-Diagramm 3.7751 in figure 5.6. The colored areas represent today's, the ones

outlined in black the optimal catchment areas.

750 ATL (2009). 751 Wessiepe (2009).


93

Figure 5.6: Comparison of Current and Optimal Catchment Areas of Papierco's Warehouses


94

5.3.2.2 Increase in Transshipments and Its Causes

Year Warehouse Sales

to Customers (t)

Transshipments (t) Transshipments

(% of Sales to Customers)

2005 381,694 53,636 14.05

2006 405,116 58,755 14.50

2007 428,491 71,967 16.80

Table 5.1: The Extent of Transshipments at Papierco

We can confirm that the transshipment quantities rose from 2005 to 2007 by 34.18 % (from

2005 to 2006 by 9.54 % and from 2006 to 2007 by 22.49 %). The warehouse sales to custom-

ers also increased from 2005 to 2007 by 12.26 % (from 2005 to 2006 by 6.14 % and from

2006 to 2007 by 5.77 %). However, this does not fully explain the increase in transshipments,

as the percentage of warehouse sales to customers enabled by transshipments increased as well

(cf. table 5.1).

In interviews with chief operating officers and directors of purchasing, sales, and logis-

tics at Papierco's different locations it became clear that the increase in transshipments is

caused by changing transshipment operations to direct invoicing in June of 2006752, some

locations decreasing their inventory levels, and including more and more products in the

product line753. According to one chief executive officer the “dramatic increase” in trans-

shipment volumes was “the manifestation of the sales department's service delusion”.

However, thanks to transshipments Papierco had also gained market share in warehouse

sales. Papierco's better development compared to its competitors was based on transship-

ments, as they enabled a higher product availability, broader product assortment, and faster

delivery. This confirms that transshipments can lead to a competitive advantage as Gug-

lielmo (1999), Kroll (2006), and Alvarez (2007) already insinuate.

The cost that locations are charged for using an emergency transshipment (transship-

ment cost rate) is based on quantity units (positions, pallets, and kilograms) and purchase

prices and does not reflect the actual logistical costs (picking, transportation, and reloading

costs). Within a company group only the costs really incurred by the transshipments should

752 Sales people do not search at the own warehouse for an alternative product to the one originally desired

by the customer in case of a stockout anymore. Today sales assistants order more via transshipments for reasons of simplicity than prior to the introduction of direct invoicing. This puts a strain on the product exchange flows between warehouses in terms of volume and costs.

753 These products tend to have small sales volumes and to steal sales from substitutes. Nonetheless, at least small quantities have to be stored at every location, which increases average stock, or the product has to be obtained via transshipments, which increases transshipment quantities.


95

be charged, so that there is no incentive to prefer or reject the use of transshipments due to

inadequate charges.

Although Rudi et al. (2001) find transshipment prices that are supposed to always in-

duce local deciders to make globally optimal inventory and transshipment decisions, Hu et

al. (2007) give a counterexample. There may exist coordinating prices for only a small

range of problem parameters, e. g. if the two locations are symmetric (both locations have

the same cost and revenue coefficients, demand distributions, and capacity constraints, and

changes in either demand or capacity distributions are simultaneously implemented in both

locations). The higher the capacity uncertainty is, the higher the coordinating prices are.

Increasing demand variability may increase or decrease coordinating prices depending on

the distribution. A linear transshipment price schedule often will not achieve coordination

of two locations' production and transshipment.

Apart from this the transshipment lead time tends to be shorter than the supplier lead

time. In Papierco's case the transshipment lead time ranges from a few hours to 4 work

days at the most. The supplier lead time for the various products ranges from 14 to 154

days and is 28.49 days on average. Therefore a transshipment from a sister location is pre-

ferred to a replenishment from a supplier in case of a stockout, as otherwise the sale is lost

due to the usual delivery time restriction of 24 hours.

Some managers remark that for some Papierco locations other ones were their “best

customers“, as they made profits by transshipping products. One director of logistics

claimed only locations obtaining a lot of products via transshipments criticized the trans-

shipment charge rate as too high. It would be even higher, if the really incurred logistical

costs were charged. This supports the call for fair transshipment charge rates.

The transshipment costs ought to be debited to the sales assistants (deducted from the

contribution margin which determines the sales assistants' premium) who release a trans-

shipment order or at least made transparent to them. The objection that one should not in-

hibit the sales assistants in their sales function can be countered that other wholesalers

commonly set up guidelines for the sales personnel.

Furthermore, if a sales assistant chooses, for instance, a paper with a one centimeter

larger format as an alternative to a stocked out product desired by a customer, the higher

purchase price cannot be charged. Therefore, the contribution margin that determines the

sales assistant's premium is lower and the sales assistant is enticed to obtain the originally

demanded product via transshipment from another warehouse location. This highlights that

the implementation of risk pooling methods is influenced by human resource and business


96

policy factors. Managers should formulate clear guidelines for the usage of transshipments

in case a desired item is not available at the primary stocking location.

A software tool should be created to help the sales assistant in deciding whether it is

more economical to obtain a stocked out item via transshipments from another warehouse,

search for a substitute at the own warehouse, cut paper to the right format, or ream wrap

paper at the own location if possible.

5.3.2.3 Transshipments Are Worthwhile for Papierco

A high customer service level at the warehouses can be achieved by either holding sufficient

inventory there, which entails high inventory investment and carrying costs, or by postpone-

ment through centralized inventory holding, which presumes fast and thus expensive delivery

of any amount of any product to any customer. A better alternative might be to hold some in-

ventory at the warehouses and let the warehouses transship products in case of a stockout.754

“A mathematical model of the exact implications [… of transshipments] is extremely

complicated”755. Evers (2001), Minner et al. (2003), and Minner and Silver (2005) consider

transshipments between two locations for a specific product in a specific situation only and

not whether transshipments might be worthwhile for a company with more locations and

products in general at all. Minner et al. (2003: 394) note that their model may be extended

to multiple locations with no fixed transshipment costs by successively determining which

location maximizes the savings for each transshipped unit. The problem becomes more

difficult with fixed costs, unless there are only a small number of warehouses as in Tagaras

(1999). The structures in all past transshipment research are much simpler than the practi-

cal ones.756

If the outlets use complete pooling, the exact form of the lateral transshipment policy

does not significantly affect total system performance.757 Deciding between never trans-

shipping or always transshipping as many units as disposable if one location faces a stock-

out while another one has stock on hand758 is almost as good as a more extensive investiga-

tion that considers the transshipment's prospective effect on the transshipping location's

cost759. Burton and Banerjee (2005: 169) also find that an ad hoc emergency transshipment

approach may lead to lower shortage (higher customer service) and transshipment cost

754 Cf. Evers (2001). 755 Minner et al. (2003: 385). 756 Chiou (2008: 442). 757 Tagaras (1999). 758 Cf. Olsson (2009). 759 Minner et al. (2003: 394f.), Minner and Silver (2005: 1).


97

(number of lateral transshipments) than a more systematic transshipment technique based

on stock level equalization760. Transshipping is better than not transshipping, but it increas-

es transportation activity.761 Backordered demand should not be partially fulfilled by trans-

shipments.762 In practice pull systems may offer simpler and more practical joint reple-

nishment/transshipment policies than the push systems mostly considered in the litera-

ture.763

At Papierco the charged transshipment costs (for transportation, shipment documenta-

tion, receiving, handling, and administration) amounted to 5 Mio. € in 2007, i. e. about

69.48 € per ton that was delivered via transshipments (5 Mio. €/71,967 t = 69.48 €/t). Ac-

cording to its inventory turnover curve (figure 5.7), Papierco needs around 10,291 t of av-

erage inventory for 71,967 t of warehouse sales to customers. This suggests that without

transshipments Papierco would have had to store at least 10,291 t of additional average

inventory.

This derivation might not be fully justified, as we derive inventory figures for the sys-

tem without transshipments from the figures for the existing system with transshipments

and while safety stocks will be lower in general, regular stocks may increase with cross-

filling of demand764.

Before transshipments were used, average inventory turnover in German paper whole-

sale was 5.4 from 1975 to 1984765. Therefore one might estimate that Papierco would have

needed 13,327 t (= 71,967 t/5.4) extra average inventory without transshipments. Conse-

quently, Papierco would have incurred approximately 3.5 Mio. € of additional inventory

carrying costs in order to sell 71,967 t without transshipments: 13,327 t × 1,058 €/t (av-

erage product purchase price in the warehouse sales business division) × 0.25 (average

inventory carrying cost rate) = 3,524,992 €. However, these additionally stored tons would

not necessarily have been the demanded ones in the right location. As the estimate of addi-

tional inventory carrying costs without transshipments is lower than the 2007 total trans-

shipment cost, the latter should be reduced, e. g. by storing fast-movers such as copy pa-

pers at all locations (cf. section 5.3.5), avoiding unnecessary and uneconomical transship-

ments, improving demand forecasts, and using less expensive alternative risk pooling me-

thods.

760 See, e.g., Jönsson and Silver (1987a). 761 Burton and Banerjee (2005: 169). 762 Wee and Dada (2005: 1529). 763 Bhaumik and Kataria (2006). 764 Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389). 765 Röttgen (1987: 109).


98

Centralizing all inventories in one or several central warehouses would decrease ware-

house fixed costs, safety stock and thus inventory holding costs as well as inbound trans-

portation costs to these central warehouses, but also the customer service level due to

greater delivery distances to the customers (the stockout costs would be higher and the

profit possibly lower) and increase outbound transportation costs to customers. Besides, a

central warehousing strategy would conflict with Papierco's corporate strategy of a decen-

tralized full-line 24-hour-delivery distributor.

As stockout costs could not be estimated in the aggregate consideration without trans-

shipments in general, we now consider the costs of transshipping versus not transshipping.

Transshipments entail transportation, shipment documentation, receiving, handling and

administration costs, the sending location's cost of reordering the transshipped product

from the supplier, as well as an increased probability of a stockout at the sending loca-

tion.766

Transportation, shipment documentation, receiving, handling, and administration costs

amount to 69.48 € per transshipped ton of paper on average. As derived in section 5.3.1 the

order cost per ton amounts to 3.31 €. Even though Papierco's locations order and receive

stock regularly about every two weeks and thus it is unlikely to place an order merely to

make up for transshipped items, we consider this value as an upper bound to the order cost

caused by transshipping.

The increased probability of a stockout at the sending location is difficult to quantify in

general and on average. In Papierco's case this cost is rather another transshipping cost

again, as the sending location would ask another location for a transshipment, if later it ran

out of stock of the product it had just transshipped. The increased stockout likelihood de-

pends on the transshipment quantity, the current on-hand inventory of the transshipped

product, customer demand for this item, and the stock receipts of this item (quantity on

order and its arrival time).

Transshipments made up 16.8 % of warehouse sales to customers in 2007, i. e. one could

assume that Papierco had an average overall stockout probability of 16.8 % and therefore an

inventory availability or fill rate before transshipments of 83.2 %. We assume that every

location faces a stockout probability of 16.8 % for an item, neglecting the different influen-

cing factors just mentioned, the derivation of this stockout probability from the situation with

transshipments, and the difference between alpha and beta service level. If two locations

766 Evers (2001: 312f.).


99

transship, they face a stockout with a probability of 0.168 100 2.82 %, three with a

probability of 0.168 100 0.47 %, four with 0.08 %, five with 0.013 %, six with

0.002 %, seven with 0.0004 %, and 21 with 5.3888354 10 %. This affirms that emer-

gency transshipments lead to a high effective fill rate for the customer (97.18 % for two,

99.53 % for three, and 99.92 % for four locations that transship), even if the item fill rate is

relatively low (83.2 %).767 The main benefit (reduced stockouts and safety stock levels) can

be reaped having just a few locations transship. It is neither necessary nor economical to

have all 21 locations transship due to diminishing marginal returns to transshipping768.

If we consider the worst but unlikely case that at every location one after another a

stockout occurs for the same item after having transshipped one ton of that item to the pre-

ceding location, then the reorder cost due to transshipment only accrues at the last (21st)

location. The cost of increased probability of a stockout can be estimated by another trans-

shipping cost of 69.48 €, since the likelihood that one transshipment triggers more than one

additional stockout and thus transshipment is negligible as the example above shows.

Therefore the average cost of transshipping can be estimated as: 142.27 €/t = 69.48 €/t

(transportation and related costs) + 3.31 €/t (reorder cost) + 69.48 €/t (increased transship-

ment usage/stockout probability).

Without transshipments Papierco incurs the cost of a stockout and the cost of holding a

ton in inventory until later at the not transshipping location. The stockout cost (209 €) is

estimated by the average contribution margin of one ton of warehouse sales to customers

minus the sales premium. The impact of stockouts on the future purchasing behavior of

customers is difficult to grasp and neglected here. Holding the ton of paper in storage until

later costs 33 € on average (cf. section 5.3.1). Therefore, the cost of not transshipping

amounts to approximately 242 €/t.

Transshipping is on average economically sensible for Papierco, as it generally is less

expensive (142.27 €) than not transshipping (242 €) a ton of paper in case of a stockout.

If only transportation-related costs evoked by transshipments and stockout costs due to

not transshipping are considered and the other costs are neglected, a sales assistant should

only make a transshipment order in case of a stockout, if the contribution margin is equal

to or larger than 69.48 €/t. Then at least the average transportation-related costs for the

transshipment are covered.

767 Cf. Ballou and Burnetas (2000, 2003), Ballou (2003b: 81, 2004b: 385-389). 768 Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389), Kranen-

burg and Van Houtum (2009).


100

In order to decide more accurately on emergency transshipments for a specific item in a

specific situation the methods proposed by Evers (2001), Minner et al. (2003), and Minner

and Silver (2005) can be used, provided that the necessary data are available. Minner et al.

(2003: 395) present a heuristic decision rule for the quantity and source of a transshipment.

In simulations, Minner et al.'s (2003: 390f., 393) method generally achieves lower average

annual costs than Evers' (2001) one. Since the cost parameters are likely to remain constant

in the short run, whether or not a particular transshipment is made depends principally on

the on-hand inventory level at the shipping location.769

However, before using transshipments, sales assistants should check their own ware-

house for substitutes for the customer wish and try to persuade the customer to buy another

product, which only incurs transaction costs (searching for substitutes in the information

system). This product substitution might cause a slight dissatisfaction on the customer's

part, but is certainly cheaper than a transshipment. If the alternative product is more expen-

sive than the original customer wish, a higher profit is gained. If only the sales price for the

originally desired product can be charged or the substitute is less expensive than the origi-

nal purchase wish, Papierco has to accept a lower contribution margin. Of course the prod-

uct should not be sold beneath cost price.

If no substitute can be found, it should be checked whether the paper can be cut to the

right size (form postponement770), which costs around 56.25 €/t (neglecting waste), or

ream wrapped (packaging postponement) for 33.50 €/t on average. Both options are

cheaper than and therefore should be preferred to a transshipment in general.

In order of increasing costs incurred by the considered risk pooling methods, Papierco's

sales assistants should first try to substitute an unavailable product, then to customize or

differentiate products, and then to resort to transshipments in case of a stockout. This

shows that risk pooling methods can be combined effectively.

Although this is a rather crude general average analysis, because exact data (especially

probabilities) were not available, and we advert to the perils of using averages as noted

e. g. by Savage et al. (2006), it shows some general relationships. Of course a decision for

a particular risk pooling method (product substitution, postponement, or transshipment) in

a certain situation depends on the specific cost parameters.

769 Evers (2001: 313). 770 See e. g. Chauhan et al. (2008).


101

5.3.3 Centralized Ordering

5.3.3.1 Papierco's Current Order Policy

At Papierco a replenishment order is placed with a supplier (the daily DRP run generates an

order message) whenever the reorder point is reached or in possibly short intervals (every two

weeks) within the suppliers' minimum order quantity restrictions. The reorder point is the sum

of safety stock, which is set by every Papierco member company independently, and average

lead time demand (average sales per day during the lead time times the lead time in days).

The purchase order planning code for a specific product is 1, if it is planned with DRP,

and 0, if it is not planned with DRP. The latter case applies to about 20 % of the warehouse

products, as for them the minimum order quantity is usually higher than the planned order

quantity, e. g. if they have fixed order dates or the minimum order quantity is a full truck

load. These products are planned manually with order lists.

Safety stock is calculated as the product of average sales per day during the lead time,

supplier lead time in days, and a safety factor. Thus double average demand during lead

time results in double safety stock. According to experience the safety factor is set to ¼ for

ream wrapped paper and 1/3 for not ream wrapped one. The safety factor is not entered

into the ERP system for every product, but for parts of the product line manually every

three months.

However, safety stock should not be set arbitrarily, but according to a target customer

service level (e. g. 90 % product availability for A items) and the statistical behavior of

demand during lead time or rather the forecast error in the case of Papierco, because de-

mand is forecast. The actual supplier lead time and whether and how often the safety stock

is touched is not recorded either. No cost optimal order quantities or times are determined.

Folding Box Board (cf. figure 5.3) has an average demand during one week lead time of

819.23 sheets, a current safety stock of 204.81 (= 819.23 × 1/4) sheets, and a reorder point of

1024.04 (= 819.23 + 204.81) sheets. According to the empirical distribution function this cor-

responds to a service level of approximately 76 % or a stockout probability during lead time of

24 %. A reorder point of 1.460 sheets or safety stock of 640.77 (= 1460 - 819.23) sheets would

be needed to reach an inventory availability of 80.8 % during lead time. According to the re-

spective empirical distribution functions, the Uncoated Cut-Size White Wood-Pulp Paper has an

inventory availability during lead time of 86 %, one continuous roll of approximately 84 %, the

other of 73.1 %, Woodfree Matte Coated Cut-Size Paper of 72 %, the Woodfree White Cut-

Size C-Quality Copy Paper of 76.9 %, and the Woodfree White Cut-Size A-Quality Copy Paper


102

of 86.5 % with today's calculation of safety stock. The safety stock can be determined more

definedly based on a target customer service level.

According to the nonparametric Kolmogorov–Smirnov test for the second continuous

roll (asymptotic significance (two-tailed) p = 0.700) and the copy papers (p = 0.741 and

0.616) the hypothesis H0 that the sample stems from a population with normally distributed

weekly demands cannot be rejected with a level of significance of 5 %. The Kolmogorov–

Smirnov test is also applicable to small samples, but might not be very definite if the un-

known distribution function is not continuous (as in this case) or the data are not metric.771

The hypothesis H0 that the sample stems from a population with uniformly, Poisson, or

exponentially distributed weekly demands is rejected with a level of significance of 5 %

for all products but the second continuous roll (for the exponential distribution p = 0.436).

However, there is one value outside the specified exponential distribution range that is

skipped. In the Kolmogorov–Smirnov test of exponential distribution for the other paper

grades (variables) there are also values outside the specified distribution range that are

skipped.

The used Order Policy Code 4 (Periods of supply) combines the order quantities (fore-

cast demands) for the time period defined in the Value Order Policy (for most Papierco

products 10 days). The JD Edwards OneWorld manual says “This order policy code was

designed to use with high-use/low cost items for which the user is not concerned about

carrying excess inventory”772. This partly explains why Papierco carries so much invento-

ry, although it mainly sells low-turnover and not necessarily low-cost products.

The other available Order Policy Codes are 0 (The DRP system will not plan this item.),

1 Lot-for-lot or as required (The system will create messages for purchase orders for the

exact amount needed.), 2 Fixed order quantity (The system will create messages for pur-

chase orders based on the value entered in the Value Order Policy in the Plant Manufactur-

ing Data. If demand exceeds the fixed order quantity, the system will generate purchase

orders in multiples of the fixed order quantity.), 3 Economic Order Quantity (EOQ), and 5

Rate scheduled item (The system will generate messages based on existing rates and rate

generation rules for parent rate-scheduled items only.).

The order quantity is the maximum of the ten day demand forecast and the minimum

order quantity, which is rounded to the next higher order quantity that is divisible by the

saltus quantity. For instance, if the minimum order and saltus quantity are 500 kg (only

771 Duller (2008: 108, 112). 772 Oracle (2009).


103

complete pallets must be ordered) and forecast demand for ten days is 1,150 kg, then

1,500 kg are ordered. Such a policy that determines and controls the inventory level at each

warehouse location in direct proportion to (forecast) demand is called stock-to-demand.773

Papierco's inventory turnover curve in grey in figure 5.7 confirms this. For all its

warehouses the average annual inventory in dependence of the annual throughput is plotted

with green squares. A linear regression line is adequate for these data as the coefficient of

determination R2 = 0.8362 shows. However, it also suggests that not all warehouses ex-

ecute this order policy consistently.774 Individual turnover rates range from 5 to 21 with an

average of 8.24. Deviations of the individual turnover rates might be explained by different

service levels or replenishment rules.775 Warehouses, whose data points lie above the turn-

over curve, might attain a higher turnover and lower inventory holding costs, if they fol-

lowed the stock-to-demand order policy more consistently. Warehouses, whose data points

are plotted beneath the turnover curve, exhibit a higher-than-average turnover rate than

attainable by this stock-to-demand policy.

An EOQ policy would lower the average turnover rate to 6.53 as the turnover curve in

black shows (a power function with the normative exponent suggested by Ballou (2000:

75) fitted to Papierco's data), probably because the stock-to-demand order policy is not

followed consistently today and some warehouses have an unusually high turnover rate of

11, 15, or 21.

Nevertheless, this paper distributor's average inventory levels appear rather high for the

annual throughputs. The annual average turnover rate of the German wholesale of paper,

cardboard, and office supplies from 1999 to 2006 was 17.3.776 However, this group con-

tains stationary wholesalers, which might raise the average turnover rate and make it un-

suitable as a benchmark for just paper wholesalers. The U.S. merchant wholesalers of pa-

per and paper products had an annual average turnover rate from 1992 to 2008 of 12.75.777

Papierco has a rather low average turnover rate of 8.24. This might be explained by the

large product variety it offers. Papierco sells at least 7,000 different product specifications.

Thus it is difficult to forecast demand for individual products. Furthermore, minimum or-

der and saltus quantities have to be met.

773 Ballou (2000: 74). 774 Cf. Ballou (2000: 76). 775 Cf. Ballou (2000: 78f.). 776 Statistisches Bundesamt Deutschland (2009a, 2009b, 2009c, 2009d, 2009e, 2009f, 2009g, 2009h), calcu-

lated by us. 777 U.S. Census Bureau (2009), calculated by us.


104

Figure 5.7: Inventory Turnover Curves for Papierco

EOQ = economic order quantity, Pot. = regression power function, Linear = linear regression line.

Papierco has 196 sum suppliers, but 83 % of the annual procurement quantity is sourced from

ten, 52 % from three, 40 % from two suppliers, and 20 % just from a single supplier. With big

suppliers a quantity structure is negotiated. There is a one-to-one product-supplier relationship,

i. e. every product is sourced from only exactly one supplier.

Therefore, Papierco should collaborate closer with its suppliers, conduct a better sup-

plier management, to enable shorter lead times, a better forecast, inventory policy and

product availability. One Papierco member company's director of purchasing had created

such a collaboration with Papierco's most important supplier that supplied the highest

quantity. A monthly demand forecasting for product groups and a guaranteed maximum

lead time of 14 days for fast and 28 days for slow movers was established. Previously this

supplier's lead time had been 4 to 6, sometimes 8 to 12 weeks. Inventories could be re-

duced considerably. Unfortunately, the business relationship to this supplier was broken

due to price policy reasons. This concept was neglected, and inventories rose again.

One director of purchasing is against a partner-like collaboration with suppliers for they

already took advantage of Papierco due to their big negotiation power. One director of

sales remarked, paper wholesalers and manufacturers did not cope with recurring demand

peaks correctly, such as in election times. When there were vacation close-downs, they

could not prevent supply bottlenecks. This shows again that a close collaboration with

y = 3.1756x0,7

y = 0.143xR² = 0.8362

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10000 20000 30000 40000 50000 60000 70000

Ave

rag

e In

ven

tory

(t)

Annual Warehouse Throughput (t)

EOQ Current Stock-to-Demand Policy Pot.(EOQ) Linear (Current Stock-to-Demand Policy)


105

suppliers is indispensable. Not least Weng and McClurg (2003) showed the value of sup-

plier–buyer coordination (in ordering) in coping with uncertain delivery time and demand.

5.3.3.2 Stock-to-Demand Order Policy with Centralized Ordering and Minimum

Order and Saltus Quantities

Risk pooling models are based on economic-order-quantity (trading off inventory holding

against order costs) or newsvendor models (trading off overage against underage costs).

In practice, however, a stock-to-demand order policy is followed frequently778 as we al-

so detected in interviews with logistics and purchasing managers and at Papierco. Orders

and therefore cycle inventories are proportional to demand at each warehouse.779 Expected

demand at each warehouse location is forecast. Order quantities result from the difference

of forecast demand and available inventory. Maister (1976: 132) and Evers (1995: 5) refer

to this order policy as the “replacement principle”, where orders are set equal to demand

during a certain time period. Such an order policy leads to a constant turnover. It is fre-

quently pursued, as it is simple and easily executable780 and because automated ordering

systems have very low ordering costs and thus the EOQ is not used781. The replacement

principle is followed e. g. in Zinn et al. (1990: 139), Evers (1996: 117, 1997: 59), and Ra-

binovich and Evers (2003a: 226).

If it is applied, centralization usually does not reduce cycle stocks:782 The system wide

order quantity of n warehouses and therefore average cycle stock in the decentralized sys-

tem are equal to the ones in the centralized system, if exactly the forecast demand is or-

dered.

Following a stock-to-demand order policy, safety stock is often calculated as the prod-

uct of a safety factor and average demand during lead time at each warehouse as our inter-

views with logistics and purchasing managers showed. Doubling demand results in double

safety stock. Safety stock is not determined by a desired target customer service level and

the statistical behavior of demand during lead time or the forecast error. Centralization

does not reduce system wide safety stock, if the safety factor is equal for all warehouses

778 Wanke (2009: 108). 779 Ballou (2000: 74). 780 Ballou (2000: 77f., 2004a: 20f.). 781 Herron (1987), Evers (1995: 14). Researchers disagree whether the EOQ model is rarely used (Herron

1987, Woolsey 1988, Zinn et al. 1990: 139, Evers 1995: 14) or often used (Osteryoung et al. 1986, Pan and Liao 1989, Lee and Nahmias 1993: 48, Dubelaar et al. 2001: 98, Slack et al. 2004). Of eleven com-panies that we surveyed (table D.1) five use a stock-to-demand, four an EOQ, one a dynamic order poli-cy, and one the newsvendor model.

782 Maister (1976: 132), Evers (1995: 2, 14f.).


106

and remains the same. The service level increases, however, due to the risk pooling effect.

Perhaps this service level is higher than necessary.

Often the stock-to-demand policy is subject to minimum order and saltus quantity con-

straints as in the case of Papierco. Then the order quantity qi for a specific product at ware-

house i = 1, …, n results from forecast demand minus available inventory di for a specific

period at warehouse i and a constant minimum order quantity m and saltus quantity s. The

saltus quantity demands that only certain multiples are ordered like in Köchel (2007), e. g.

only full pallets.

If a stock-to-demand order policy with minimum order and saltus quantities is followed,

centralization may lead to a reduction in average cycle stock. The order quantity and there-

fore average cycle stock in the decentralized system, where every location places orders for

itself, is more than or equal to the ones in the centralized system, where a common joint

order is placed for all locations783, since often more than forecast demand minus available

inventory is ordered in order to meet minimum order and saltus quantities. In the centra-

lized system the constant minimum order and saltus quantities may be exhausted more.

The order quantity qi for a specific product at warehouse i is

, . (5.1)

The total system wide order quantity in the decentralized system therefore is:

∑ ∑ , . (5.2)

The total system wide order quantity in the centralized system is:

∑, . (5.3)

The total system wide order quantity in the centralized system is less than or equal to

the one in the decentralized system, because the order quantity function (5.1) is subaddi-

tive:

∑, ∑ , . (5.4)

For the proof please refer to appendix E.

The centralized ordering effect (COE), the percent reduction of the order quantity by

centralized ordering, is:

783 For Özen et al. (2005: 1) inventory centralization also is a byword for joint ordering: “Groups of retailers

might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand”.


107

1 100 1

∑,

∑ ,100. (5.5)

Centralized ordering can reduce demand and supply uncertainty and thus inventory and

stockouts and increase customer service level by demand pooling, aggregate forecasting

across all locations, and postponement of order allocation to the delivery warehouses. This

will be shown in the following section.

5.3.3.3 Benefits of Centralized Ordering for Papierco

The example of a woodfree white cutsize A-quality copy paper in table 5.2 demonstrates that

the centralized ordering effect for a stock-to-demand order policy with minimum order and

saltus quantities can be significant. This copy paper has the highest annual sales and contribu-

tion margin in warehouse sales of all products at most Papierco locations.

Table 5.2 shows the actual warehouse sales for this copy paper for Papierco's 22 Ger-

man locations and one Dutch location per month in 2007. The sales forecasts were ob-

tained with exponential smoothing. The forecast method was initialized with the 2006 ac-

tual warehouse sales per month per location, i. e. data from 2006 were used to determine

starting values for the exponential smoothing model. The exponential smoothing constant

(column O) that minimized the forecast error (the standard error of the forecast (RMSE))

for the monthly forecasts of 2006 warehouse sales for every location was used for forecast-

ing 2007 sales.784

784 Cf. Ballou (2004b: 299).


108

1 A B C D E F G H I J K L M N O P Q R S2 Minimum order quantity 22,500 kg Value 0.93 €/kg All values in kg except for the exponential smoothing constant (sm. const.).3 Saltus order quantity 500 kg Contribution margin 0.23 €/kg Average monthly positive net stock (sum of the positive net stocks divided by twelve).45 Work days 22 20 22 19 20 21 22 23 20 22 22 196 Warehouse Location Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total/Average Sm. Const. MAD BIAS RMSE Safety Stock7 Aalen8 Actual sales 43,300 32,608 44,833 26,535 26,935 23,490 27,773 34,888 19,350 36,420 29,615 8,140 353,887 15,835

9 Forecast 27,465 27,624 27,674 27,845 27,832 27,823 27,780 27,780 27,851 27,766 27,852 27,870 333,162 0.01 7,523 1,727 9,92210 Forecast error 15,835 4,984 17,159 -1,310 -897 -4,333 -7 7,108 -8,501 8,654 1,763 -19,730 20,72511 Order quantity 27,500 43,500 33,000 45,000 26,500 27,000 23,000 28,000 35,000 22,500 33,000 30,000 374,00012 Net stock -15,800 -4,908 -16,741 1,724 1,289 4,799 26 -6,862 8,788 -5,132 -1,747 20,113 3,06213 Sales rate 1,968 1,630 2,038 1,397 1,347 1,119 1,262 1,517 968 1,655 1,346 42814 Average cycle stock (CS) 8,952 11,868 9,037 14,992 14,757 16,544 13,913 11,380 18,463 13,539 13,154 24,183 14,23215 Berlin16 Actual sales 40,165 44,888 37,418 39,375 33,300 41,138 34,318 39,308 41,488 40,243 42,313 8,241 442,195 6,862

17 Forecast 35,059 35,110 35,208 35,230 35,271 35,252 35,311 35,301 35,341 35,402 35,451 35,519 423,454 0.01 6,602 1,562 9,36218 Forecast error 5,106 9,778 2,210 4,145 -1,971 5,886 -993 4,007 6,147 4,841 6,862 -27,278 18,74119 Order quantity 35,500 40,000 45,000 37,500 39,500 33,000 41,500 34,000 39,500 41,500 40,500 42,000 469,50020 Net stock -4,665 -9,553 -1,971 -3,846 2,354 -5,784 1,398 -3,910 -5,898 -4,641 -6,454 27,305 2,58821 Sales rate 1,826 2,244 1,701 2,072 1,665 1,959 1,560 1,709 2,074 1,829 1,923 43422 Average cycle stock 15,788 14,097 16,835 16,122 19,004 15,307 18,557 16,019 15,392 15,847 15,323 31,426 17,47623 Bielefeld24 Actual sales 44,288 28,438 53,200 25,388 27,913 21,163 22,028 45,038 18,665 40,700 31,663 15,838 374,322 16,381

25 Forecast 28,440 28,599 28,597 28,843 28,809 28,800 28,723 28,657 28,820 28,719 28,839 28,867 344,713 0.01 9,472 2,467 11,78026 Forecast error 15,848 -161 24,603 -3,455 -896 -7,637 -6,695 16,381 -10,155 11,981 2,824 -13,029 29,60927 Order quantity 28,500 44,500 28,500 53,500 25,500 28,000 22,500 22,500 43,000 22,500 37,000 31,500 387,50028 Net stock -15,788 274 -24,426 3,686 1,273 8,110 8,582 -13,956 10,379 -7,821 -2,484 13,178 3,79029 Sales rate 2,013 1,422 2,418 1,336 1,396 1,008 1,001 1,958 933 1,850 1,439 83430 Average cycle stock 9,397 14,493 8,073 16,380 15,230 18,692 19,596 10,930 19,712 13,425 13,501 21,097 15,04431 Bremen32 Actual sales 22,150 17,000 22,450 12,913 13,988 17,938 12,663 24,038 11,238 14,188 24,013 16,825 209,404 4,968

33 Forecast 19,224 19,253 19,231 19,263 19,199 19,147 19,135 19,070 19,120 19,041 18,993 19,043 229,721 0.01 4,382 -1,693 4,79034 Forecast error 2,926 -2,253 3,219 -6,350 -5,211 -1,209 -6,472 4,968 -7,882 -4,853 5,020 -2,218 -20,31735 Order quantity 22,500 22,500 22,500 22,500 22,500 0 22,500 22,500 22,500 0 22,500 22,500 225,00036 Net stock 350 5,850 5,900 15,487 23,999 6,061 15,898 14,360 25,622 11,434 9,921 15,596 12,54037 Sales rate 1,007 850 1,020 680 699 854 576 1,045 562 645 1,092 88638 Average cycle stock 11,425 14,350 17,125 21,944 30,993 15,030 22,230 26,379 31,241 18,528 21,928 24,009 21,26539 Cologne40 Actual sales 127,123 114,645 241,830 96,180 123,998 111,878 105,668 176,203 84,720 139,303 113,465 97,890 1,532,903 58,566

41 Forecast 105,695 107,838 108,519 121,850 119,283 119,754 118,967 117,637 123,493 119,616 121,585 120,773 1,405,010 0.10 30,095 10,658 45,74242 Forecast error 21,428 6,807 133,311 -25,670 4,715 -7,876 -13,299 58,566 -38,773 19,687 -8,120 -22,883 127,89343 Order quantity 106,000 129,000 115,500 255,000 94,000 124,500 111,000 104,000 182,500 80,500 141,500 112,500 1,556,00044 Net stock -21,123 -6,768 -133,098 25,722 -4,276 8,346 13,678 -58,525 39,255 -19,548 8,487 23,097 9,88245 Sales rate 5,778 5,732 10,992 5,062 6,200 5,328 4,803 7,661 4,236 6,332 5,158 5,15246 Average cycle stock 44,605 50,926 25,768 73,812 57,927 64,285 66,512 40,147 81,615 51,851 65,220 72,042 57,89347 Dietzenbach (Frankfurt)48 Actual sales 37,325 44,800 36,765 35,105 28,875 58,725 26,413 82,000 23,588 37,725 34,888 39,073 485,282 22,120

49 Forecast 36,609 36,616 36,698 36,699 36,683 36,605 36,826 36,722 37,174 37,039 37,045 37,024 441,738 0.01 9,555 3,629 15,73950 Forecast error 716 8,184 67 -1,594 -7,808 22,120 -10,413 45,278 -13,586 686 -2,157 2,049 43,54451 Order quantity 37,000 37,000 45,000 37,000 35,000 28,500 59,000 26,500 82,500 23,500 37,500 35,000 483,50052 Net stock -325 -8,125 110 2,005 8,130 -22,095 10,492 -45,008 13,904 -321 2,291 -1,782 3,07853 Sales rate 1,697 2,240 1,671 1,848 1,444 2,796 1,201 3,565 1,179 1,715 1,586 2,05654 Average cycle stock 18,352 15,183 18,493 19,558 22,568 11,743 23,699 8,784 25,698 18,555 19,735 17,844 18,35155 Dortmund56 Actual sales 2,238 2,775 8,503 3,800 4,050 6,040 4,225 3,300 3,440 5,190 2,813 2,690 49,064 2,383

57 Forecast 3,625 3,611 3,603 3,652 3,653 3,657 3,681 3,686 3,682 3,680 3,695 3,686 43,911 0.01 1,218 429 1,75758 Forecast error -1,387 -836 4,900 148 397 2,383 544 -386 -242 1,510 -882 -996 5,15359 Order quantity 22,500 0 0 0 0 22,500 0 0 0 0 22,500 0 67,50060 Net stock 20,262 17,487 8,984 5,184 1,134 17,594 13,369 10,069 6,629 1,439 21,126 18,436 11,80961 Sales rate 102 139 387 200 203 288 192 143 172 236 128 14262 Average cycle stock 21,381 18,875 13,236 7,084 3,159 20,614 15,482 11,719 8,349 4,034 22,533 19,781 13,85463 Ernstroda (Erfurt)64 Actual sales 6,900 4,888 15,125 7,213 11,788 10,650 14,313 16,263 27,225 18,238 18,525 19,263 170,39165 Forecast 18,712 12,806 8,847 11,986 9,599 10,694 10,672 12,492 14,378 20,801 19,520 19,022 169,529 0.50 4,756 72 6,254 6,278

66 Forecast error -11,812 -7,918 6,278 -4,773 2,189 -44 3,641 3,771 12,847 -2,563 -995 241 86267 Order quantity 22,500 0 0 22,500 0 22,500 0 22,500 22,500 23,000 22,500 22,500 180,50068 Net stock 15,600 10,712 -4,413 10,874 -914 10,936 -3,377 2,860 -1,865 2,897 6,872 10,109 5,90569 Sales rate 314 244 688 380 589 507 651 707 1,361 829 842 1,01470 Average cycle stock 19,050 13,156 3,865 14,481 5,039 16,261 4,236 10,992 11,860 12,016 16,135 19,741 12,23671 Fellbach (Stuttgart)72 Actual sales 32,800 37,603 41,795 39,615 39,400 30,535 45,043 49,350 42,663 49,505 52,850 14,850 476,009 11,905

73 Forecast 36,395 36,035 36,192 36,752 37,039 37,275 36,601 37,445 38,636 39,038 40,085 41,361 452,854 0.10 8,071 1,930 10,45074 Forecast error -3,595 1,568 5,603 2,863 2,361 -6,740 8,442 11,905 4,027 10,467 12,765 -26,511 23,15575 Order quantity 36,500 32,500 38,000 42,000 40,000 39,500 30,000 46,000 50,500 43,000 50,500 54,500 503,00076 Net stock 3,700 -1,403 -5,198 -2,813 -2,213 6,752 -8,291 -11,641 -3,804 -10,309 -12,659 26,991 3,12077 Sales rate 1,491 1,880 1,900 2,085 1,970 1,454 2,047 2,146 2,133 2,250 2,402 78278 Average cycle stock 20,100 17,465 16,130 17,172 17,604 22,020 15,143 14,603 17,788 15,706 15,502 34,416 18,63779 Garching (Munich)80 Actual sales 56,395 51,943 69,108 46,790 53,673 53,540 56,500 47,680 50,575 59,443 41,563 37,363 624,573 15,463

81 Forecast 40,932 48,664 50,303 59,706 53,248 53,460 53,500 55,000 51,340 50,958 55,200 48,382 620,693 0.50 7,933 323 10,05482 Forecast error 15,463 3,279 18,805 -12,916 425 80 3,000 -7,320 -765 8,485 -13,637 -11,019 3,88083 Order quantity 41,000 64,500 53,500 78,500 40,000 54,000 53,500 58,000 44,000 50,500 63,500 35,000 636,00084 Net stock -15,395 -2,838 -18,446 13,264 -409 51 -2,949 7,371 796 -8,147 13,790 11,427 3,89285 Sales rate 2,563 2,597 3,141 2,463 2,684 2,550 2,568 2,073 2,529 2,702 1,889 1,96686 Average cycle stock 15,147 23,280 18,871 36,659 26,447 26,821 25,446 31,211 26,084 22,287 34,572 30,109 26,41187 Hemmingen (Hanover)88 Actual sales 60,453 62,338 75,190 42,813 52,063 47,125 59,500 76,913 41,063 45,175 56,228 36,325 655,186 24,282

89 Forecast 41,620 45,386 48,777 54,059 51,810 51,861 50,914 52,631 57,487 54,202 52,397 53,163 614,307 0.20 13,119 3,407 15,27990 Forecast error 18,833 16,952 26,413 -11,246 253 -4,736 8,586 24,282 -16,424 -9,027 3,831 -16,838 40,87991 Order quantity 42,000 64,000 66,000 80,500 40,500 52,000 46,000 61,500 81,500 38,000 43,500 57,000 672,50092 Net stock -18,453 -16,791 -25,981 11,706 143 5,018 -8,482 -23,895 16,542 9,367 -3,361 17,314 5,00893 Sales rate 2,748 3,117 3,418 2,253 2,603 2,244 2,705 3,344 2,053 2,053 2,556 1,91294 Average cycle stock 14,881 16,949 16,490 33,113 26,175 28,581 22,038 18,625 37,074 31,955 24,934 35,477 25,52495 Kiel96 Actual sales 17,728 19,563 26,308 21,080 17,575 24,715 27,015 29,045 21,305 18,883 29,563 14,013 266,793 5,483

97 Forecast 23,673 23,614 23,573 23,601 23,575 23,515 23,527 23,562 23,617 23,594 23,547 23,607 283,006 0.01 4,505 -1,351 5,00998 Forecast error -5,945 -4,051 2,735 -2,521 -6,000 1,200 3,488 5,483 -2,312 -4,711 6,016 -9,594 -16,21399 Order quantity 24,000 22,500 22,500 22,500 22,500 22,500 22,500 22,500 25,500 22,500 22,500 24,500 276,500

100 Net stock 6,272 9,209 5,401 6,821 11,746 9,531 5,016 -1,529 2,666 6,283 -780 9,707 6,054101 Sales rate 806 978 1,196 1,109 879 1,177 1,228 1,263 1,065 858 1,344 738102 Average cycle stock 15,136 18,991 18,555 17,361 20,534 21,889 18,524 13,068 13,319 15,725 14,035 16,714 16,988103 Leizen104 Actual sales 2,488 2,388 6,025 5,100 4,075 3,700 3,238 4,375 5,613 8,563 7,550 3,125 56,240 2,662

105 Forecast 4,920 4,896 4,871 4,882 4,885 4,876 4,865 4,848 4,844 4,851 4,888 4,915 58,542 0.01 1,611 -192 1,896106 Forecast error -2,432 -2,508 1,154 218 -810 -1,176 -1,627 -473 769 3,712 2,662 -1,790 -2,302107 Order quantity 22,500 0 0 0 0 22,500 0 0 0 0 22,500 0 67,500108 Net stock 20,012 17,624 11,599 6,499 2,424 21,224 17,986 13,611 7,998 -565 14,385 11,260 12,052109 Sales rate 113 119 274 268 204 176 147 190 281 389 343 164110 Average cycle stock 21,256 18,818 14,612 9,049 4,462 23,074 19,605 15,799 10,805 3,749 18,160 12,823 14,351111 Lohfelden (Kassel)112 Actual sales 4,650 1,288 4,700 2,763 1,950 388 2,013 2,775 1,963 2,200 2,900 2,400 29,990 2,398

113 Forecast 2,252 2,276 2,266 2,290 2,295 2,292 2,273 2,270 2,275 2,272 2,271 2,277 27,309 0.01 870 223 1,206114 Forecast error 2,398 -988 2,434 473 -345 -1,904 -260 505 -312 -72 629 123 2,681115 Order quantity 22,500 0 0 0 0 0 0 0 22,500 0 0 0 45,000116 Net stock 17,850 16,562 11,862 9,099 7,149 6,761 4,748 1,973 22,510 20,310 17,410 15,010 12,604117 Sales rate 211 64 214 145 98 18 92 121 98 100 132 126118 Average cycle stock 20,175 17,206 14,212 10,481 8,124 6,955 5,755 3,361 23,492 21,410 18,860 16,210 13,853119 Lunteren (NL)120 Actual sales 1,513 100 2,625 100 0 1,163 2,150 513 963 2,138 1,863 1,075 14,203 1,414

121 Forecast 437 652 542 959 787 629 736 1,019 918 927 1,169 1,308 10,083 0.20 833 343 988122 Forecast error 1,076 -552 2,083 -859 -787 534 1,414 -506 45 1,211 694 -233 4,120123 Order quantity 22,500 0 0 0 0 0 0 0 0 0 0 0 22,500124 Net stock 20,987 20,887 18,262 18,162 18,162 16,999 14,849 14,336 13,373 11,235 9,372 8,297 15,410125 Sales rate 69 5 119 5 0 55 98 22 48 97 85 57126 Average cycle stock 21,744 20,937 19,575 18,212 18,162 17,581 15,924 14,593 13,855 12,304 10,304 8,834 16,002


109

Table 5.2: Effects of Centralized Ordering at Papierco

The order quantity for every month is the demand forecast for that month minus the

net stock (at the end of the period after demand has been satisfied but before the order ar-

rives at the beginning of the new period) left from the previous period plus the quantity to

meet the minimum order and saltus quantity. Supplier lead time is neglected785. If net cycle

stock is negative (the actual sales exceeded the order quantity and the cycle stock on hand),

this demand is either satisfied via transshipments, covered by safety stock786, or backor-

785 Actually a location might run out of stock before the end of the period and have to wait until the begin-

ning of the next period to place and receive a new order. This time might be seen as a replenishment order lead time.

786 Safety stock is neglected here at first. However, safety stock may also be “defined as the average level of the net stock just before a replenishment arrives” (Silver et al. 1998: 234, cf. Chopra and Meindl 2007: 305). Here we adhere to the definition “Safety inventory is inventory carried to satisfy demand that ex-ceeds the amount forecasted for a given period” (Chopra and Meindl 2007: 304).

1 A B C D E F G H I J K L M N O P Q R S6 Warehouse Location Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total/Average Sm. Const. MAD BIAS RMSE Safety Stock

127 Mannheim128 Actual sales 14,475 8,225 21,500 23,625 18,025 18,463 17,050 22,575 12,025 16,913 23,900 11,188 207,964 7,061

129 Forecast 16,620 16,598 16,514 16,564 16,635 16,649 16,667 16,671 16,730 16,683 16,685 16,757 199,773 0.01 4,148 683 4,957130 Forecast error -2,145 -8,373 4,986 7,061 1,390 1,814 383 5,904 -4,705 230 7,215 -5,569 8,191131 Order quantity 22,500 22,500 0 22,500 22,500 22,500 22,500 22,500 22,500 0 22,500 22,500 225,000132 Net stock 8,025 22,300 800 -325 4,150 8,187 13,637 13,562 24,037 7,124 5,724 17,036 10,382133 Sales rate 658 411 977 1,243 901 879 775 982 601 769 1,086 589134 Average cycle stock 15,263 26,413 11,550 11,504 13,163 17,419 22,162 24,850 30,050 15,581 17,674 22,630 19,022135 Nuremberg136 Actual sales 2,540 4,488 8,425 9,135 9,488 8,668 10,638 6,400 10,188 7,843 11,113 7,675 96,601 1,598

137 Forecast 10,388 9,603 9,092 9,025 9,036 9,081 9,040 9,200 8,920 9,047 8,926 9,145 110,503 0.10 2,094 -1,158 3,014138 Forecast error -7,848 -5,115 -667 110 452 -413 1,598 -2,800 1,268 -1,204 2,187 -1,470 -13,902139 Order quantity 22,500 0 0 22,500 0 0 22,500 0 22,500 0 0 22,500 112,500140 Net stock 19,960 15,472 7,047 20,412 10,924 2,256 14,118 7,718 20,030 12,187 1,074 15,899 12,258141 Sales rate 115 224 383 481 474 413 484 278 509 357 505 404142 Average cycle stock 21,230 17,716 11,260 24,980 15,668 6,590 19,437 10,918 25,124 16,109 6,631 19,737 16,283143 Ottendorf-Okrilla (Dresden)144 Actual sales 1,613 200 650 1,188 625 500 1,200 63 1,188 2,463 963 500 11,153 803

145 Forecast 810 818 812 810 814 812 809 813 805 809 826 827 9,765 0.01 509 116 649146 Forecast error 803 -618 -162 378 -189 -312 391 -750 383 1,654 137 -327 1,388147 Order quantity 22,500 0 0 0 0 0 0 0 0 0 0 0 22,500148 Net stock 20,887 20,687 20,037 18,849 18,224 17,724 16,524 16,461 15,273 12,810 11,847 11,347 16,723149 Sales rate 73 10 30 63 31 24 55 3 59 112 44 26150 Average cycle stock 21,694 20,787 20,362 19,443 18,537 17,974 17,124 16,493 15,867 14,042 12,329 11,597 17,187151 Queis (Halle)152 Actual sales 34,400 33,738 34,800 40,538 24,025 28,750 30,938 36,663 25,863 29,650 39,575 23,238 382,178 9,117

153 Forecast 28,771 29,334 29,774 30,277 31,303 30,575 30,393 30,447 31,069 30,548 30,458 31,370 364,321 0.10 5,378 1,488 6,151154 Forecast error 5,629 4,404 5,026 10,261 -7,278 -1,825 545 6,216 -5,206 -898 9,117 -8,132 17,857155 Order quantity 29,000 35,000 34,000 35,500 41,500 23,500 28,500 31,000 37,000 25,500 29,500 40,500 390,500156 Net stock -5,400 -4,138 -4,938 -9,976 7,499 2,249 -189 -5,852 5,285 1,135 -8,940 8,322 2,041157 Sales rate 1,564 1,687 1,582 2,134 1,201 1,369 1,406 1,594 1,293 1,348 1,799 1,223158 Average cycle stock 12,331 13,081 12,908 11,720 19,512 16,624 15,288 13,056 18,217 15,960 12,009 19,941 15,054159 Reinbek (Hamburg)160 Actual sales 60,375 50,345 55,478 48,475 64,020 62,413 70,720 81,763 41,658 61,405 62,938 42,615 702,205 16,611

161 Forecast 43,764 48,748 49,227 51,102 50,314 54,426 56,822 60,991 67,223 59,553 60,109 60,958 663,237 0.30 11,003 3,247 13,547162 Forecast error 16,611 1,597 6,251 -2,627 13,706 7,987 13,898 20,772 -25,565 1,852 2,829 -18,343 38,968163 Order quantity 44,000 65,500 50,500 57,500 47,500 68,500 64,500 75,000 88,000 34,000 62,000 64,000 721,000164 Net stock -16,375 -1,220 -6,198 2,827 -13,693 -7,606 -13,826 -20,589 25,753 -1,652 -2,590 18,795 3,948165 Sales rate 2,744 2,517 2,522 2,551 3,201 2,972 3,215 3,555 2,083 2,791 2,861 2,243166 Average cycle stock 16,294 24,011 22,021 27,065 20,053 24,232 23,142 23,218 46,582 29,122 28,992 40,103 27,070167 Sasbach (Strasbourg)168 Actual sales 16,790 16,953 18,805 18,165 14,225 15,950 15,005 12,015 7,950 10,223 13,553 12,723 172,357 2,273

169 Forecast 15,090 16,790 16,953 18,805 18,165 14,225 15,950 15,005 12,015 7,950 10,223 13,553 174,724 1.00 2,038 -197 2,390170 Forecast error 1,700 163 1,852 -640 -3,940 1,725 -945 -2,990 -4,065 2,273 3,330 -830 -2,367171 Order quantity 22,500 22,500 22,500 22,500 0 22,500 22,500 0 22,500 0 0 22,500 180,000172 Net stock 5,710 11,257 14,952 19,287 5,062 11,612 19,107 7,092 21,642 11,419 -2,134 7,643 11,232173 Sales rate 763 848 855 956 711 760 682 522 398 465 616 670174 Average cycle stock 14,105 10,734 24,355 28,370 12,175 19,587 26,610 13,100 25,617 16,531 4,643 14,005 17,486175 Tettnang (Lake Constance)176 Actual sales 5,238 4,900 6,425 2,238 3,513 4,968 4,235 4,313 4,300 4,988 3,200 3,163 51,481 1,932

177 Forecast 3,306 3,692 3,934 4,432 3,993 3,897 4,111 4,136 4,171 4,197 4,355 4,124 48,349 0.20 1,059 261 1,308178 Forecast error 1,932 1,208 2,491 -2,194 -480 1,071 124 177 129 791 -1,155 -961 3,132179 Order quantity 22,500 0 0 0 22,500 0 0 0 0 0 22,500 0 67,500180 Net stock 17,262 12,362 5,937 3,699 22,686 17,718 13,483 9,170 4,870 -118 19,182 16,019 11,866181 Sales rate 238 245 292 118 176 237 193 188 215 227 145 166182 Average cycle stock 19,881 14,812 9,150 4,818 24,443 20,202 15,601 11,327 7,020 2,381 20,782 17,601 14,002183 Trierweiler (Trier)184 Actual sales 19,150 19,728 41,668 19,038 21,400 22,665 27,153 27,925 8,113 30,838 18,025 23,425 279,128 9,166

185 Forecast 21,553 21,529 21,511 21,713 21,686 21,683 21,693 21,748 21,809 21,672 21,764 21,727 260,088 0.01 5,687 1,587 8,062186 Forecast error -2,403 -1,801 20,157 -2,675 -286 982 5,460 6,177 -13,696 9,166 -3,739 1,698 19,040187 Order quantity 22,500 22,500 22,500 35,000 22,500 22,500 22,500 23,000 28,000 22,500 22,500 22,500 288,500 SUM(S7:S184) =188 Net stock 3,350 6,122 -13,046 2,916 4,016 3,851 -802 -5,727 14,160 5,822 10,297 9,372 4,992 245,561189 Sales rate 870 986 1,894 1,002 1,070 1,079 1,234 1,214 406 1,402 819 1,233190 Average cycle stock 12,925 15,986 10,029 12,435 14,716 15,184 12,809 8,923 18,217 21,241 19,310 21,085 15,238191 Total demand 654,097 603,842 873,626 567,172 594,904 614,565 619,799 823,406 505,144 682,237 663,079 441,638 7,643,509 201,579192 Aggregate forecast 571,613 588,110 591,256 647,730 631,619 624,276 622,334 621,827 662,143 630,743 641,042 645,449 7,478,140 0.2 95,502 13,781 130,602193 Forecast error 82,484 15,732 282,370 -80,558 -36,715 -9,711 -2,535 201,579 -156,999 51,494 22,037 -203,811 165,369 43,982194 Pooled order quantity 572,000 670,500 607,000 930,000 551,000 587,500 613,000 619,000 864,000 473,500 692,500 667,500 7,847,500195 Non-pooled order quantity 721,000 668,000 599,000 892,000 542,500 636,000 614,500 599,500 872,000 449,500 718,500 661,500 7,974,000196 Net stock -82,097 -15,439 -282,065 80,763 36,859 9,794 2,995 -201,411 157,445 -51,292 -21,871 203,991 40,987197 Sales rate 29,732 30,192 39,710 29,851 29,745 29,265 28,173 35,800 25,257 31,011 30,140 23,244198 Average CS central ordering 251,782 287,217 204,515 364,349 334,311 317,077 312,895 238,270 410,017 292,938 310,619 424,810 312,400199 Average CS decentral ordering 411,112 430,134 352,512 466,755 428,452 463,209 458,833 369,495 541,441 401,898 446,266 551,405 443,459200201 Negative net stock202 Pooled system 654,175 kg203 Non-pooled system 845,636 kg


110

dered. In any case this quantity has to be ordered in addition for the next period to reple-

nish the stock of the location that has transshipped this item or the safety stock or satisfy

the backordered demand. It is assumed that there are no available inventories or backorders

of the copy paper at the beginning of the year 2007. The net stock of the respective period

is the order quantity minus the actual sales plus the previous period's net stock. If the fore-

cast of next period's sales can be met with net stock no order is placed with the supplier

(the order quantity is zero). This occurs at the locations Bremen, Dortmund, Ernstroda,

Leizen, Lohfelden, Lunteren, Mannheim, Nuremberg, Ottendorf, Sasbach, and Tettnang,

where the monthly forecasts and actual sales are lower than the minimum order quantity

(except in Bremen in August and November and Ernstroda in September).

For central ordering (total demand) the monthly actual sales are the sum of the individ-

ual locations' monthly sales (row 191). The total 2007 order quantity of this copy paper

with central ordering for all locations (pooled order quantity) 7,847,500 kg (cell N194) is

lower than the sum of the total order quantities of the individual locations ordering sepa-

rately (non-pooled order quantity) 7,974,000 kg (cell N195). The centralized ordering

effect (equation (5.5)) amounts to 1.59 %. With central ordering Papierco could have saved

ordering 126,500 kg, 117,645 € (= 126,500 kg × 0.93 €/kg) purchasing costs, as well as

average cycle inventory and the associated inventory carrying cost just for this one product

by improved exhausting of the minimum order and saltus quantity.

For some months the non-pooled order quantity is lower than the pooled one. This is

evoked by some locations not placing an order in some months and serving demand from a

minimum order quantity and net stock, as the forecasts and actual sales are much lower

than the minimum order quantity. However, in these cases higher inventory carrying costs

have to be borne, as the ordered minimum order quantity minus sales remains in stock for

several periods. Negative net stock also postpones order quantities to later periods. Be-

sides, a higher order quantity than the forecast to meet minimum order and saltus quantities

works as a buffer for positive forecast errors (if the actual demand exceeds the forecast):

The absolute value of the negative net stock is always less than the forecast error in these

cases. Nevertheless, on the whole a lower total order quantity is needed to serve the same

total annual demand with central than with decentral ordering.

We approximated the average cycle stock per warehouse location as follows: We calculated

the sales rate (actual sales divided by work days). Sales can only occur on work days. We de-

termined the work days per month for the year 2007 (row 5). In case the work days in the dif-

ferent German federal states differed, we took the maximum. We then determined the inventory


111

level at the end of each working day after sales, deducting the sales rate from the previous end

of day inventory. Whenever the end of day inventory was negative we replaced it with zero

physical inventory. The inventory level at the beginning of the month is the order quantity plus

the previous month's end inventory level. We thus assumed that backordered demand (negative

end of month net stock) is satisfied instantaneously at the beginning of the new month when

the order quantity arrives. Finally we determined the arithmetic mean of the end of work

day inventory levels as the average cycle inventory. This also confirms that today average

inventory at Papierco is so high relative to actual sales partly due to minimum order and

saltus quantities.

The total average cycle stock with central ordering (row 198) is lower than with decen-

tral ordering (row 199) in every month and for the whole year 2007, because of improved

exhausting of minimum order and saltus quantities. For this copy paper Papierco could

have saved 131,059 kg of average cycle stock and the corresponding inventory carrying

costs of 30,471 € (= 131,059 kg × 0.93 €/kg × 0.25) in 2007.

The sum of the average monthly positive net stock of the individual locations

(184,234 kg) in column N is larger than the average monthly positive net stock with central

ordering in cell N196 (40,987 kg).

The sum of the forecast error statistics mean absolute deviation (MAD 142,459), bias

(BIAS 29,560), and root mean square error (RMSE 190,306) for the individual locations in

columns P, Q, and R is higher than the error statistics for the central order (95,502, 13,781,

and 130,602 respectively) in cells P, Q, and R192.787

This confirms788 that the aggregate forecast of monthly sales of this copy paper for all

23 considered locations is more accurate than the disaggregate forecast for the individual

locations. This leads to a higher inventory availability, i. e. a smaller total stockout or

backorder quantity (negative net stock) and thus smaller stockout or backorder costs in the

system with central ordering (654,175 kg) than in the system with decentral ordering

(845,636 kg), if safety stock is neglected.

According to the One-Sample Kolmogorov-Smirnov Test, the H0-hypothesis that the

forecast error at the locations Aalen, Berlin, Bielefeld, Bremen, Cologne, Dietzenbach,

Dortmund, Ernstroda, Fellbach, Garching, Hemmingen, Kiel, Leizen, Lohfelden, Lunteren,

Mannheim, Nuremberg, Ottendorf, Queis, Reinbek, Sasbach, Tettnang, and Trierweiler

787 “MAD is […] the average of the absolute differences between the actual […] and the forecast” sales.

“BIAS is the average of the differences between actual and forecast” sales. “RMSE is [the] square root of the average of the squared differences between the actual and the forecast” sales (Ballou 2004c: 5f.).

788 Cf. footnote 456.


112

and of total demand is normally distributed cannot be rejected with an asymptotic signific-

ance (two-tailed) p of 0.984, 0.317, 0.879, 0.872, 0.485, 0.268, 0.582, 0.996, 0.513, 0.974,

0.970, 0.922, 0.973, 0.695, 0.966, 0.984, 0.681, 0.864, 0.832, 0.711, 0.758, 0.991, 0.851,

and 0.968 respectively. The One-Sample Kolmogorov-Smirnov Test for the exponential

distribution shows a higher asymptotic significance (two-tailed) for Cologne (p = 0.820),

Dortmund (p = 0.936), Fellbach (p = 0.824), Leizen (p = 0.993), Lohfelden (p = 0.911),

Nuremberg (p = 0.839), Reinbek (p = 0.830), Trierweiler (p = 0.977), and total demand

(p = 0.993). However, for Fellbach and Reinbek there are 3, for Cologne, Dortmund, Loh-

felden, Trierweiler, and total demand 6, for Leizen and Nuremberg 7 values outside the

specified distribution range. These values are skipped. Kiel shows a higher asymptotic sig-

nificance (two-tailed) of 0.958 in the One-Sample Kolmogorov-Smirnov Test for the uni-

form distribution. As Poisson variables are non-negative integers and negative values occur

in the data, the One-Sample Kolmogorov-Smirnov Test cannot be performed for the Pois-

son distribution. In conclusion, the forecast error can be assumed to be rather normally

distributed at the different locations. According to Thonemann (2005: 258) most applica-

tions assumed a normally-distributed forecast error.

Nevertheless, we use the empirical distribution function of the forecast error to deter-

mine the safety stock. The empirical distribution function F(y) gives the probability that

the forecast error is less than or equal to y, i. e. F(y) = P (forecast error Y ≤ y). In order to

have an inventory availability of 91.7 %, we determine the y for P = 91.7 %. If we carry y

as safety stock, this will cover demand that exceeds the forecast with a probability of

91.7 %, as the forecast error is less than or equal to this safety stock with the probability of

91.7 %. The safety stock that ensures a service level of 91.7 % is shown in column S for

every location. The sum of the individual locations' safety stocks (245,561 kg) in cell S188

is larger than the safety stock with central forecasting and ordering for all locations

(201,579 kg) in cell S191, as the aggregate forecast is more accurate than the disaggregate

one. Papierco could have saved 43,982 kg of safety stock and the associated inventory

holding cost of 10,226 € (= 43,982 kg × 0.93 €/kg × 0.25) just for this copy paper in 2007.

Although Papierco forecasts demand and therefore should use safety stock as protection

against the forecast error and not demand uncertainty789, it uses the average past demand

for the copy paper to determine safety stock.

789 Cf. Thonemann (2005: 255f.).


113

With decentralized ordering there would have been 123,215 kg negative net stock that

could not have been absorbed by the safety stock for all locations in 2007. We arrived at

this figure by adding the negative net (cycle) stock and safety stock for every location for

every month, whenever the absolute value of the former was greater than the one of the

latter, and then adding up all the negative sums. With centralized ordering 80,486 kg of

demand would have exceeded available inventory (cycle stock and safety stock). In the

decentralized system the 123,215 kg of demand could have been satisfied by transship-

ments from other warehouses, backordered, or lost. In the centralized system, transship-

ments would not have been possible, as demand would have exceeded the order quantity

and safety stock for all locations, and demand could have been only backordered or lost.

Therefore one could argue that in this regard the service level in the decentralized system

would have been higher. Transshipping 123,215 kg of this copy paper in the decentralized

system would have cost at least 8,561 € = 123.215 t × 69.48 €/t (cf. section 5.3.2.3). Losing

the contribution margin of selling the 80,486 kg of this copy paper would have cost

80,486 kg × 0.23 €/kg = 18,512 € in the centralized system. Thus the net stockout costs

(lost contribution margin in the centralized system minus the transshipment cost in the de-

centralized one) amount to 9,951 € = 18,512 € - 8,561 € at the most. If all the unsatisfied

demand had been backordered in both systems, backorder costs would have been higher in

the decentralized than in the centralized system because of the backordered volume.

Overall, Papierco could have saved at least 30,746 € in inventory holding costs just

for this one copy paper in 2007, if it had used centralized planning and ordering instead of

the current decentralized one: 30,746 € = 30,471 (saved inventory holding costs for aver-

age cycle stock) + 10,226 € (saved inventory holding costs for safety stock) - 9,951 € (net

stockout costs).

This example highlights that centralized ordering enables to reduce order quantities and

thus average cycle inventory and inventory carrying costs by exhausting minimum order

and saltus quantities better as well as to reduce safety stock and improve overall customer

service level (inventory availability) or reduce negative net stock as the aggregate forecast

is more accurate than the disaggregate one.

Therefore, we propose a central distribution requirements planning with aggregate

forecasting and central ordering for all Papierco locations. After placing a joint order, cen-

tral planning would receive a notification of dispatch from the producer when the ordered

products are produced and the trucks are ready to deliver them. Then Papierco tells the

supplier which warehouses to deliver to according to current demand. Full truck loads can


114

be delivered to single warehouses or one truck can deliver to several warehouses on a deli-

very route. The delivery destination decision is postponed until the ordered products are

produced and ready to be delivered from the production facility to the delivery warehouses

(geographic or logistics postponement).

Today each warehouse location forecasts its warehouse sales and places orders with the

suppliers individually. The warehouse receives a dispatch notification from the supplier

before the delivery truck leaves the production facility to deliver the ordered products to

the warehouse. The delivery destination is determined at the time of placing the order.

With today's decentralized release orders within the centrally negotiated framework

contracts every Papierco location orders all products for itself.

With centralized ordering each location or company of the eight ones comprising Pa-

pierco could process the orders for one part of the product line, e. g. a main product group,

for all considered 23 locations. This would lead to the following advantages:

Fewer orders at the suppliers (1/23 of today's decentralized orders), lower order

costs, improved utilization of minimum order and saltus quantities, lower average

inventory, higher turnover, lower capital commitment, lower inventory holding

costs.

Only one procurement manager per product line part or product, higher specialist

knowledge about this part of the assortment, improved forecasting, improved

matching of supply and demand, improved potential utilization (negotiation power),

closer collaboration with suppliers, long-term planning with suppliers, cost degres-

sion potentials for Papierco and its suppliers, reduced lead times.

Directing supplier deliveries to certain warehouse locations at short notice (higher

flexibility, product availability, and customer service level, reduced transshipments

and inventories).

This approach would maintain the importance of the legally independent companies

forming Papierco and their decentral locations. The employees of the purchasing depart-

ments do not have to relocate to a physically central ordering department, but can remain at

their locations. They may become more motivated by their increased responsibility, as they

do not place replenishment orders for their own location only anymore, but for all Papierco

locations albeit just for a certain part of the product line. Thus possible disadvantages of

centralized ordering such as decreased responsiveness and sales due to lacking local know-


115

ledge790 can be mitigated as well. Procurement employees may have more time for im-

proved forecasting and collaboration with suppliers and other departments or their number

may be reduced.

The number of the suppliers' trips to the warehouses would probably remain unchanged.

Perhaps the supplier would charge a fee for delivery routes, if a truck load is to be trans-

ported to more than one Papierco location. This charge is unlikely to outweigh all the other

stated benefits. The products, however, have to be managed more intensively by procure-

ment managers. Operations and rules in all locations have to be standardized. Necessary

data have to be available and correct.

Orders would still be placed according to order suggestions generated by DRP consis-

tent with customer orders, demand forecasts, inventory levels, and supplier lead time. Of

course the ERP software has to be adapted to plan across all Papierco locations.

The paper industry shows long production lead times, expensive holding costs for in-

ventory surplus, and highly random demand at the retailers. Orders can be backlogged only

for a few days at the most in case of a stockout or the sale is lost. These conditions favor

centralized ordering according to Eppen and Schrage (1981: 51) and Schoenmeyr (2005:

5). Total demand is less variable than demand at the individual stores, which makes con-

solidated distribution most effective according to Cachon and Terwiesch (2009: 340). The

time from placing an order with the supplier until production of the order is finished is

longer than the delivery time from the production facility to the delivery warehouses. This

corresponds to Cachon and Terwiesch's (2009: 340) observation that consolidated distribu-

tion “is most effective […] if the lead time before the distribution center is much longer

than the lead time after the distribution center”. Replenishment coordination is most bene-

ficial for high fixed order/transportation cost, large truck capacities, and many retailers.791

The minimum order and saltus quantity restrictions Papierco has to observe can be sub-

sumed under large fixed order or transportation cost and truck capacities, and Papierco has

many delivery warehouses in Germany.

In contrast to Eppen and Schrage (1981), Gürbüz et al. (2007: 305), and Cachon and Ter-

wiesch (2009) our considerations do not contain a distribution center (here we follow

Schonmeyr's (2005: 4) proposition), Papierco uses a stock-to-demand order policy with min-

imum order and saltus quantities and transshipments between regional warehouses, weekly

demand often does not follow a theoretical distribution (cf. section 5.3.3.1), demand at the

790 Ganeshan et al. (2007: 341). 791 Gürbüz et al. (2007: 305).


116

different warehouses is correlated, and supplier lead time is largely neglected. Our centra-

lized ordering model does not increase the distance a unit must travel from the supplier to the

delivery warehouses, unless it is delivered on a delivery route with several stops.

Eppen and Schrage (1981) consider centralized ordering policies in a periodic-review

base-stock multi-echelon, multi-period system in the conglomerate for steel industry with

independent normally distributed stationary random demands and identical proportional

costs of holding and backordering at N warehouses, and no transshipments between the

warehouses. In Eppen and Schrage (1981) products are ordered and quantity discounts are

possible. Papierco just calls quantities of products from the supplier within the bounds of

previously centrally negotiated skeleton agreements. Possible quantity discounts have been

granted before.

Diruf (2005, 2007) and Heil (2006: 169) examine only the demand-pooling savings of

postponement, centralized ordering, and lateral transshipments between cooperating possi-

bly independent fashion retailers with normal and lognormal792 demand, equally big sales

areas793, and a newsboy structure. In their model the central ordering system leads to lower

costs than the local ordering system with transshipments unless over- and underage costs

are equal. In this case both systems achieve the same improvements compared to a system

without risk pooling.794

Hu et al. (2005) deal with the impact of emergency transshipments on (s, S) (order-up-

to) ordering policies and centralized ordering.

Gürbüz et al. (2007: 296, 305) consider only one outside supplier, but inventory and

transportation costs and four order-up-to policies.

Cachon and Terwiesch (2009) consider consolidated distribution in retail with 100

stores, an order-up-to-model, Poisson demand at the retail stores per week795, normally-

distributed demand at the retail distribution center796, lead times, and backordering797.

One could still determine an optimal delivery allocation procedure and order policy for

Papierco, but this would go beyond the scope of this thesis. The reader is referred to e. g.

Silver et al. (1998) for a detailed treatment of inventory control policies.

792 Heil (2006: 145f.). 793 Heil (2006: 169). 794 Diruf (2005: 59f.), Heil (2006: 110). 795 Cachon and Terwiesch (2009: 336). 796 Cachon and Terwiesch (2009: 338). 797 Cachon and Terwiesch (2009: 336f.).


117

Alfaro and Corbett (2006: 24) find that within certain quite wide ranges of suboptimali-

ty of inventory control policies, risk pooling is better than optimizing the policy. This

range expands with the number of SKUs. Papierco carries thousands of SKUs.

Harrison and Skipworth (2008: 193) also find that form postponement in three companies

improved responsiveness of manufacturing, although it had not been implemented theoreti-

cally ideally.

Finally, risk pooling reduces decision errors, biases, and local suboptimization of boun-

dedly rational decision makers and thus total costs “by pooling decision errors across loca-

tions”, even if demands are perfectly positively correlated or deterministic (behavioral

benefits of inventory pooling)798.

Therefore, introducing risk pooling methods at Papierco at first, does not hurt.

5.3.4 Product Pooling

For the last years more and more products have been added to Papierco's product line without

dropping any other ones. The product range meanwhile comprises around 20,000 current

products, some with few sales, and is planned to be diversified further especially in the busi-

ness units printing accessories and screens and signs. This diversification leads to higher in-

ventories, as every warehouse has to store at least some units of every product in order to be

able to deliver every product specification, or more transshipments. Product availability de-

creases as forecasts for more and more individual items are less accurate.

“Every firm wishes to be ʻcustomer focusedʼ or ʻcustomer oriented,ʼ which suggests

that a firm should develop products to meet all of the needs of its potential customers. Tru-

ly innovative new products that add to a firm's customer base should be incorporated into a

firm's product assortment. But if extra product variety merely divides a fixed customer

base into smaller pieces, then the demand–supply mismatch cost for each product will in-

crease. Given that some of the demand–supply mismatch costs are indirect (e.g., loss of

goodwill due to poor service), a firm might not even realize the additional costs it bears

due to product proliferation”799.

Already in 1987 Röttgen remarked due to the cut-throat competition fine paper whole-

salers are forced to distinguish themselves from their competitors. This is possible by in-

tensifying some selected distribution functions rather than accepting additional ones. Thus

paper wholesalers seek to diversify their product line more and more to exhaust the cus-

798 Su (2008: 33). 799 Cachon and Terwiesch (2009: 335f.).


118

tomer potential as much as possible.800 Fine paper wholesale has to abandon the idea to be

a specialist for all paper grades. This implies prioritizing within the product range instead

of a sprawling product line diversification. An escalating diversification will lead to dis-

proportionately high costs and continue to keep the return low.801

According to the FPT-Workshop No. 4 in Munich on October 24, 2007 the variety of

paper grades is narrower in the U.S. and is not demanded by customers (printing offices) in

Germany either. The majority of printing offices deny the necessity of the present variety

of grades. For them operativeness, color consumption, quality consistency, and mixability

of paper grades are decisive and not a new brand or grade.802

A FPT study supports this: A change in demand behavior for paper grades seems to gain

momentum away from the unclear vast variety of grades towards a homogenization. The

printing industry foremost demands good operability and printability of the paper in the

printing machine. Paper grades with standard functionality (reproducible operability and

printability) and multifunctionality are the focus of the forthcoming development.803

Furthermore a too large product variety might backfire, as customers might not like to

choose from many alternatives.804 Toyota's and Nissan's fast introduction of a series of

products, for instance, was counterproductive as it confused customers.805

For all these reasons Papierco should rationalize its product line by product pooling

taking into account its business strategy, demand and buying interdependencies between

products, customer needs, and cooperation with suppliers806 also in order to simplify its

procurement planning. Serving “demand with fewer products” reduces “demand variabili-

ty, which leads to better performance in terms of matching supply and demand (e.g., higher

profit or lower inventory for a targeted service level)”807.

5.3.5 Inventory Pooling

Nowadays there are bilateral agreements between some Papierco member companies to store

slow-moving items for one another. However, there is no transparency, which articles are

stored at which location, and the partly sought selective stock keeping is not pursued strategi-

cally and economically.

800 Röttgen (1987: 83). 801 Röttgen (1987: 124). 802 FPT (2007b). 803 FPT (2007a). 804 Chain Drug Review (2009a), Hamstra (2009), Ryan (2009). 805 Pine II et al. (1993), Lau (1995). 806 Kulpa (2001), Hamstra (2009), MMR (2009), Pinto (2009a, 2009b), Thayer (2009: 23). 807 Cachon and Terwiesch (2009: 330, 335).


119

If a new product is launched, it is stored at only three locations first. If it has been sell-

ing well for half a year, further locations start inventorying it and it may be stocked at

every Papierco location in the end.

Papierco's uniform price list suggests immediate availability of all paper grades at every

warehouse location. Due to the increasing range of products, however, availability of every

product at every location cannot be assured anymore. Some products are only available at

one warehouse in Germany. Thus demands for transshipments rise and the 24-hour delivery

service cannot be guaranteed anymore. Transshipment errors increase, especially if a product

is transshipped via other warehouses. Often truck capacity is exceeded. Papierco's competi-

tive advantage of delivering any paper grade mostly within 24 hours is fading.

The product master record contains 61,132 different products. Thereof merely 23,740

ones show stock on hand at at least one warehouse. Of these only 9,868, of the 61,132 only

14,565 ones, are planned automatically with DRP. The product master record should be rid

of inactive products with no sales.

Product purchase planning and storing is distributed unequally between the eight Pa-

pierco member companies as figures 5.8 and 5.9 show. If it was distributed more evenly

at least for fast movers, product availability could be increased and transshipments de-

creased (cf. section 5.3.2.3).

Along the same line, Pasin et al. (2002) simulate pooling of equipment for homecare

service for a group of local community service centers (CLSCs) in the Montreal, Canada

region. Overall pooling reduces shortages (rental costs) with the same inventory level, but

the larger CLSCs with considerable equipment overcapacity may lose, because they almost

never need to borrow equipment from other CLSCs, but have to bear the disadvantages

(wear-and-tear costs). A more even distribution of over-capacity reached by inter-CLSC

sales or an equivalent financial compensation is much more effective than minimum stock,

maximum contribution or maximum debt rules in producing an overall reduction in costs

without penalizing any of the partners in the pooling process.

We would have liked to design an optimal policy of strategic stock-keeping (inventory

pooling through selective stock keeping). However, the necessary data such as the turnover

or (average) inventory per SKU were not available.


120

Figure 5.8a: Product Purchase Planning at Papierco's Member Companies

Figure 5.8b: Product Purchase Planning at Papierco's Member Companies

3003

4261

3872

6057

3936

48794624

4197

296

703

2651

3124

926 959 939

1668

0

1000

2000

3000

4000

5000

6000

7000

100 200 300 400 500 600 700 800

Nu

mb

er o

f P

rod

uct

s

Papierco Member Company (Code)

Number of products planned with DRP (planning code = 1)

Number of products not planned with DRP (planning code = 0), but with stock on hand

7537

2229

1487

992735 639 656

288

0

1000

2000

3000

4000

5000

6000

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8000

1 2 3 4 5 6 7 8

Nu

mb

er o

f P

lan

ned

Id

enti

cal

Pro

du

cts

Number of Papierco Member Companies


121

Figure 5.9: Stockkeeping at Papierco's Warehouses in February 2008

5.3.6 Challenges in IT and Organization

Today too little process-oriented information exchange between departments inhibits business

processes. Data are not transparent enough. If they are recorded at all, often they can only be

obtained from the diverse, little integrated electronic data processing (EDP) systems with great

effort. Too many subsystems and interfaces result in data transfer problems, too much data

maintenance, and high costs. A lot of workarounds were programmed in the standard ERP

system for Papierco, as many locations wanted to keep some unique business processes. How-

ever, the standard ERP system should standardize the business processes or one does not de-

rive the full benefit from the standard software.808 CLM (1995: 6) also concludes that “the vast

majority of available technology capable of facilitating process integration is underutilized”.

Papierco's different data analysis tools often show different numerical results for the

same data query specifications. Data are often not available on a disaggregate individual

product basis, but only for product groups. Analyses are hampered by different product

codes for the same product for drop-shipping and warehouse sales, different periods (days,

weeks, and months), units (sheets and kilograms), and product groupings and levels in dif-

808 Fleisch et al. (2004), Laudon and Laudon (2010: 369).

2982

2972

2972

4974

4970

4970

4459

4464

6152

6144

4029

4025

4033

4835

4835

4831

4853

5021

50

5029

5960

3567

418

96

3274

3036

492

6447

11

8664

1687

3915

443

1983

5407

295

1131

5077

0 0 0

7303

8446

840

322

5339

3791

782

1108

3

1

1214

5

3223

6555

1357

3424

7309

848

2367

6208

0 0 0

8596

0

2000

4000

6000

8000

10000

12000

14000

101 102 103 201 202 203 301 302 401 402 501 502 503 601 602 603 701 702 703 704 801

Nu

mb

er o

f S

KU

sIn

ven

tory

(t)

Warehouse

Number of routinely stocked SKUs (product code P = purchase including raw materials) Number of SKUs with stock on hand Inventory (t)


122

ferent parts of the EDP system, too little knowledge about the analysis tools at Papierco's

locations, as well as a bad data structure and maintenance. The delivery situation is not

transparent enough: There are customer and delivery addresses. The delivery addresses are

not assigned to customers uniquely. Sales can only be attributed to customer and not to

delivery addresses. Some data are not recorded at all, such as cycle, safety, and average

stock, as well as turnover per product, utilization of safety stock, cycle time, actual supplier

lead times, and actual transshipment costs. Some computerized reports give wrong (calcu-

lated, not actual) safety stock levels for product groups, so that often the shown safety

stock is higher than the actual total inventory on hand. Certain costs can only be obtained

by checking every single cost unit. Higher cost awareness might lead to higher return. Set-

ting up a systematic controlling might be worthwhile.

Data and information are passed on by employees only hesitantly and after direct re-

quest. Important extra information to get a complete idea often is omitted. This might be

interpreted as a defense strategy to secure the job and power position by exclusive know-

ledge. Any criticism can be invalidated by pointing out that certain information had not

been considered. Similar “micropolitical games” were observed e. g. by Reihlen (1997: 3)

in a heating technology company. Change in logistical practices often faces resistance.809

This can be remedied with a company culture that promotes transparency.

Papierco consists of eight different and legally independent companies, but is and

wants to be seen as a single uniform company. However, employees rather feel obliged to

their individual member companies that pay their salaries. This sometimes leads a member

company to transship products for its own warehouse locations first and leave the goods

bound for other member companies' locations behind. Products ought to be transshipped

according to urgency and not company affiliation. Papierco should not optimize locally but

globally.

Logistics is seen very restrictively within Papierco as storing, handling, and transport-

ing goods. Taking on its interdepartmental function, logistics should collaborate closely

with and support management, sales, purchasing, finance, accounting, and controlling.

During this study differences in managing Papierco's different locations became obvious.

Papierco should standardize its operational policy, measure performance uniformly, and re-

structure its distribution system cautiously. For this a consistent and faultless data mainten-

ance and accessibility is essential. Some data are deficient for logistical management.

809 CLM (1995: v, 6), Ballou et al. (2004b: 550), Graman and Magazine (2006: 1077).


123

Most of these challenges are common in a lot of companies. Papierco is addressing

them successfully and is a profitable company.

5.4 Summary

The paper wholesale company Papierco can increase its competitiveness and reduce customer

demand and supplier lead time uncertainty by the risk pooling methods transshipments, prod-

uct substitution, postponement, centralized ordering, product pooling, and inventory pooling.

The proposed optimization of the customer allocation to the individual warehouses can

lead to considerable transportation cost savings near-term and without much investment

burden. Customers should be served by the warehouse nearest to them.

The following suggestions can be made to reduce inventory and transshipments, which

have increased for the last years, and maintain or improve the customer service level and

profitability:

(1) The organizational structure and logistics should support the business

processes as well as possible.

(2) The company culture should promote transparency and a process view.

(3) Improve the fragmented, little integrated, little standardized, not process- but

function-oriented system landscape. This would also lower the disproportio-

nately high IT costs.

(4) Necessary data should be collectable faultlessly.

(5) The demand planning810 and purchasing policy should be improved, as this

will result in higher product availability (customer service level) and less

transshipments and inventory.

(6) Create a uniform cross-functional demand planning process, in which sales,

product managers, and purchasing collaborate to contain extraordinary de-

mands through the sales assistants' and product managers' profound market

knowledge and enable a better demand forecast and thus order policy.

(7) Communicate and coordinate inventory reductions at the different member

companies and warehouses. If a company is member of a purchasing group, it

cannot act autonomously anymore.

810 Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted Moving Average)

should be admitted to the DRP forecast run besides today's exclusively used methods 4 (Moving Aver-age) and 10 (Linear Smoothing), as they gave good results. The forecast should be based on the last 12 to 24 months of sales history, if system performance permits this.


124

(8) Establish (not necessarily physically) centralized procurement, which fore-

casts and orders for all of Papierco's German locations on the product level

and directs the suppliers' deliveries to the warehouses according to current

demand (consolidated distribution with pooling over the outside-supplier lead

time).

(9) Foster a close, reliable, long-term collaboration and exchange of information

between suppliers, Papierco, customers, and individual departments.

(10) Safety stock and transshipments can be reduced without hurting product avail-

ability by decreasing lead time (uncertainty) through improved collaboration

with suppliers and reducing demand uncertainty by better forecasts and infor-

mation gathering and usage.

(11) Determine safety stocks more definedly according to the target customer ser-

vice level, forecast error, supplier lead time, and lead time variability.

(12) Enable determining the correct inventory levels per product and utilization of

safety stock.

(13) Rationalize the product line considering the business strategy, customer needs,

product interdependencies, and cooperation with suppliers (product pooling).

(14) Establish transparency regarding the storage locations of products.

(15) Pursue selective stock keeping (inventory pooling) strategically economically.

(16) Use alternatives to transshipments (product substitution and form postpone-

ment).

(17) Papierco's emergency transshipments are economically worthwhile on aver-

age.

(18) However, they should only be used, if the contribution margin of a sale is at

least 69.48 €/t.

(19) Establish transshipment cost rates that reflect the true costs.

(20) Set up clear rules for the sales assistants for using transshipments.

(21) Transshipment costs should be made transparent to the sales assistants and

perhaps be deducted from the premium-determining contribution margin.

We would have liked to always evaluate the cost savings attainable by these suggestions for

improvement in money units, but necessary cost data and information were not provided. A

consultancy described similar problems of obtaining data at Papierco.


125

Human resource factors, transaction costs, and local suboptimization seem to be impor-

tant in risk pooling and transshipments. These factors are commonly neglected in the risk

pooling literature.

This application shows that risk pooling can be used effectively as a guiding umbrella

principle in systematically restructuring a distribution system to cope with supplier lead

time, customer demand, and forecast uncertainty, as well as product variety and reduce

costs and inventory, increase customer service, and make a company more competitive.

Risk pooling methods can be used side by side to take advantage of their benefits, while

making up for disadvantages of other ones.

Our Risk Pooling Decision Support Tool is suitable to determine appropriate risk pool-

ing methods for a company that faces lead time and demand uncertainty. Some of the me-

thods determined with the help of this tool are already applied by Papierco nowadays

(transshipments, product substitution, inventory pooling, and postponement), but can and

should be improved. The other ones still make sense after a more thorough investigation

(centralized ordering and product pooling).

Centralized ordering can reduce average cycle inventory, even if a stock-to-demand or-

der policy is followed and minimum order and saltus quantities have to be observed. It also

enables to decrease safety stock and improve inventory availability, as the aggregate fore-

cast for the central order is more accurate than the disaggregate one for the decentral or-

ders.

126

6 Conclusion

Our main novel contributions lie in the (1) comprehensive and concise definition of risk pool-

ing distinguishing between variability, uncertainty, and risk, (2) holistic review and value-

chain-oriented structuring of the plethora of research on risk pooling methods in business lo-

gistics, especially on inventory pooling, according to their uncertainty reduction abilities,

(3) developing tools to help in comparing and choosing appropriate risk pooling methods and

models for different economic conditions based on a contingency approach, (4) applying these

tools to German paper wholesale, and (5) conducting a survey on the recognition and usage of

the various risk pooling concepts and their associations in 102 German trading and manufac-

turing companies.

Risk pooling in business logistics can reduce total variability of demand and/or lead

time and thus uncertainty and the possibility of not achieving business objectives (risk) by

consolidating individual variabilities (measured with the standard deviation) of demand

and/or lead time. These individual variabilities are consolidated by aggregating demands

(demand pooling) and/or lead times (lead time pooling).

This reduction in uncertainty allows to reduce inventory without reducing the custom-

er service level (product availability) or to increase the service level without increasing the

inventory or a combination of both and to cope with product variety. Risk pooling is ex-

plained by the Minkowski-inequality, the subadditivity property of the square root of non-

negative real numbers, and the balancing effect of higher-than-average and lower-than-

average values of a random variable.

Risk pooling usually shows increasing returns, but diminishing marginal returns. Its

benefit generally increases with decreasing correlation of pooled demands and/or lead

times and concentration of uncertainty as well as increasing variability.

Risk pooling in business logistics comprises well over 600 publications mostly contain-

ing modeling research. After the concept borrowed from modern portfolio and insurance

theory has been mainly applied to inventory pooling, meanwhile research focuses on post-

ponement, transshipments, and the coordination of risk pooling arrangements and cost and

profit allocation through contracts. The researchers are of different backgrounds, orienta-

tion, and prominence, so that they use inconsistent terms, frameworks, and structures and

make our thorough literature review, structuring, and definitions essential.

We identified ten risk pooling methods: (1) inventory pooling, (2) virtual pooling,

(3) transshipments, (4) centralized ordering, (5) order splitting, (6) component commonali-

6 Conclusion

127

ty, (7) postponement, (8) capacity pooling, (9) product pooling, and (10) product substitu-

tion.

These methods can be implemented everywhere along the supply chain and mainly per-

tain to the value activities storage (inventory pooling), transportation (virtual pooling and

transshipments), procurement (centralized ordering and order splitting), production of

goods and services (component commonality, postponement, and capacity pooling), and

sales (product pooling and product substitution). We presented a classification of risk

pooling methods according to their ability to pool demands and/or lead times.

They all but order splitting can reduce demand uncertainty, order splitting only lead

time uncertainty, capacity pooling, component commonality, inventory pooling, product

pooling, and product substitution only demand uncertainty. Transshipments, virtual pool-

ing, postponement, and central ordering may dampen both uncertainties.

(1) Inventory pooling is the consolidation of inventories, e. g. by inventory or ware-

house system centralization or selective stock keeping, in order to reduce inventory hold-

ing and shortage costs through risk pooling. Its risk pooling effect in terms of inventory

savings can be quantified with the square root law (SRL), portfolio effect (PE), and in-

ventory turnover curve.

The SRL states that the total system wide stock of n decentralized warehouses is equal

to that of a single centralized one multiplied with the square root of the number of ware-

houses n. Despite confusion in the literature it applies to regular stock, if an economic

order quantity (EOQ) order policy is followed, the fixed cost per order and the per unit

stock holding cost, demand at every decentralized location, and total system demand is the

same both before and after centralization. It is valid for safety stock, if demands at the

decentralized locations are uncorrelated, the variability (standard deviation) of demand at

each decentralized location, the safety factor, and average lead time are the same at all lo-

cations both before and after consolidation, average total system demand remains the same

after consolidation, no transshipments occur, lead times and demands are independent and

identically distributed random variables and independent of each other, the lead time va-

riance is zero, and the safety-factor approach is used to set safety stock for all facilities

both before and after consolidation. It applies to total stock (the sum of regular and safety

stock), if the assumptions stated above of the SRL both as applied to regular and safety

stock hold (cf. appendix B). It does not hold, if its assumptions are not fulfilled.

If an EOQ policy is followed and constant fixed costs per order, holding costs, and total

demand are assumed for all locations before and after centralization, the total order fixed

6 Conclusion

128

cost usually is lower because of less orders and the inventory holding cost is lower due to

a smaller total EOQ in the centralized than in the decentralized system (cf. appendix C).

Savings in safety stock through inventory pooling stem from balancing demand variabili-

ties (risk pooling).

Although some researchers811 claim the SRL estimated real savings well, in 13 of 14

practical cases we reviewed it overestimated actual inventory savings often significantly.

This means its assumptions are not fulfilled in these cases or there were other inventory- or

service-related changes. In a survey that we conducted with eleven companies from differ-

ent countries and industries (see table D.1) only one fulfilled all, two fulfilled none of the

five assumptions necessary for applying the SRL to regular stock. The participants fulfilled

at least two and at the most seven of the eleven assumptions of the SRL when applied to

safety stock.

It seems that seldom is it appropriate to apply the SRL, because mostly not all its as-

sumptions are fulfilled. Nonetheless, the other SRL- and PE-models that we synoptically

compared in terms of their assumptions in table D.2 might be applied as their assumptions

are fulfilled.

Researchers questioning the SRL either question its assumptions or do make other as-

sumptions and therefore arrive at different results.

Zinn et al.'s (1989) PE shows the reduction in aggregate safety stock by centralizing

several warehouses' inventories in one warehouse in percent, if lateral transshipments are

not usual, there is no lead time uncertainty, customer service level is not affected by a

change in the warehouse number, demand at each warehouse is normally distributed, and

the order quantity equals demand during lead time.

The inventory turnover curve shows average inventory in dependence of the inventory

throughput for a specific company. It can be constructed from a company's stock status

reports and be used to estimate the average inventory (not only safety stock as with the PE)

for any (planned) warehouse throughput without the limitations of the SRL.

(2) Virtual pooling extends a company's warehouse or warehouses beyond its or their

physical inventory to the inventory of other own or other companies' locations by means of

information and communication technologies, drop-shipping, and cross-filling.

(3) Transshipments are inventory transfers among locations (e. g. between warehouses

or stores) for example in case of a stockout.

811 For example Sussams (1986: 10), Pfohl (1994: 141).

6 Conclusion

129

(4) Centralized ordering places joint orders for several locations and later allocates the

orders (perhaps by a depot) to the requisitioners or distribution points in consolidated dis-

tribution according to current demand information.

(5) Order splitting is partitioning a replenishment order into multiple orders with mul-

tiple suppliers or into multiple deliveries.

(6) Component commonality designs products sharing parts or components. This re-

duces the variability of demand for these components.

(7) Postponement delays decisions in production, logistics, or distribution as long as

possible, e. g. developing, purchasing, ordering, fulfillment assignment, production, manu-

facturing, assembly, packaging, labeling, pricing, and shipping. Because of a shorter fore-

cast period and an aggregate forecast more accurate information can be used.

(8) Capacity pooling is consolidating production, service, or inventory capacities of

several facilities. Without pooling every facility fulfills demand just with its own capacity.

With pooling demand is aggregated and fulfilled by a single (perhaps virtually) joint facili-

ty. A higher service level can be attained with the same capacity or the same service level

can be offered with less capacity.

(9) Product pooling is unifying several product designs to a single generic or universal

design or reducing the number of products thereby serving demands that were served by

their own product variant before with fewer products.

In (10) product substitution one tries to make customers buy another alternative prod-

uct, because the original customer wish is out of stock or although it is available (demand

reshape).

Using contingency theory, we explored conditions that favor these individual risk

pooling methods, their advantages and disadvantages, and basic trade-offs in detail. Based

on this synopsis the Risk Pooling Decision Support Tool (RPDST) was developed for

choosing an appropriate risk pooling strategy for a specific situation.

This tool was effectively utilized to choose suitable risk pooling methods for a large

German paper distributor. This application showed that risk pooling can be used effec-

tively as a guiding umbrella principle in systematically restructuring a distribution system

to cope with supplier lead time, customer demand, and forecast uncertainty, as well as

product variety and reduce costs and inventory, increase customer service, and make a

company more competitive. Human resource factors, transaction costs, and local subopti-

mization seem to be important in risk pooling and transshipments. These factors are com-

monly neglected in the risk pooling literature. Risk pooling methods can be and are used

6 Conclusion

130

side by side to take advantage of their benefits, while making up for disadvantages of other

ones. This is in line with our survey findings.

Centralized ordering can reduce average cycle inventory even if a stock-to-demand

order policy is followed and minimum order and saltus quantities have to be observed. It

also enables to decrease safety stock and improve inventory availability as the aggregate

forecast for the central order is more accurate than the disaggregate one for the decentral

orders.

The literature review and this application showed the theoretical benefits risk pooling

can bring. However, survey research on the knowledge and application of risk pooling is

scarce. Therefore, we explored whether the different risk pooling concepts are known, ap-

plied, and associated in a survey of 102 German manufacturing and trading companies:

A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It

appears that mainly transshipments and postponement are associated with risk pooling.

Although at least in our sample the risk pooling concepts are known fairly well (central

ordering, product substitution, and selective stocking the most), only selective stocking,

transshipments, and central ordering are widely applied. Transshipments are more, post-

ponement and product pooling less applied than suggested by some publications mostly for

other regions.

Less sample companies have centralized their warehouse system than European ones.

For our sample we cannot confirm a major decentralization trend as one may expect due to

increasing fuel costs. Companies seem to be consistent in their strategy of centralization,

decentralization, or no change in warehouse number over time.

The utilization and knowledge of a risk pooling concept are correlated. This suggests

that improving the knowledge of risk pooling may increase its application. Research needs

to convey under what conditions and how the different risk pooling concepts can be ap-

plied successfully. This research constitutes one step in this direction.

Prominently associated is past decentralization with future decentralization, the utiliza-

tion of product substitution and demand reshape, past centralization and decentralization

(the only negative correlation), the application of the inventory turnover curve and trans-

shipments, commonality and product pooling, risk pooling and transshipments, turnover

curve and order splitting, selective stocking and virtual pooling, transshipments and virtual

pooling, risk pooling and postponement, product substitution and transshipments, product

substitution and virtual pooling, as well as postponement and commonality and vice versa.

6 Conclusion

131

We can support Rabinovich and Evers' (2003b) finding that time postponement (emer-

gency transshipments and inventory centralization) contributes to the implementation of

form postponement at best only weakly for our sample.

Trading companies seem to apply product substitution and transshipments more than

manufacturing companies. The opposite is true for commonality and postponement. This

was considered in the RPDST. In contrast to Van Hoek (1998b) our sample shows no sig-

nificant difference in the application of postponement by electronics, automotive, food, and

clothing manufacturers.

More large companies appear to use risk pooling and postponement than smaller ones,

perhaps because they can better afford to invest in expensive risk pooling methods as sug-

gested by Huang and Li (2008b: 12). More small companies have centralized their ware-

house or logistics system in the past than large ones in our sample.

The survey is of limited representativeness and generalizability, as a genuine simple

random sample of the relevant population of German manufacturing and trading compa-

nies could not be drawn. Survey research is very laborious and prone to many biases and

errors and has low response rates that disappoint the researcher and impair the results. Our

experience supports that face-to-face methods tend to achieve higher response rates.

As this treatise constitutes a first attempt to structure the vast risk pooling research in

business logistics, develop tools to choose between the various risk pooling methods, and

get an idea about their recognition and application in German companies, we make the

following suggestions for further research:

Our RPDST and its underlying contingency factors should be empirically validated

with additional companies in different industries. Conditions and implementation modali-

ties favoring the different risk pooling methods should be further explored, especially for

product pooling, central ordering, (particularly non-manufacturing) capacity pooling, vir-

tual pooling, and substitution/demand reshape, as our considerations are not exhaustive.

The effectiveness and efficiency of the different methods should be compared. Evers

(1999), Swaminathan (2001), Eynan and Fouque (2005), and Wanke and Saliby (2009)

made a good start here.

Perhaps a normative model could be developed that integrates and compares the ten

identified methods in terms of their costs and benefits in order to choose an optimal one.

However, such a model might be either too complex or simple. Perhaps combining simula-

tion and analytic frameworks may better account for the complicated interaction effects

6 Conclusion

132

among various factors.812 Centralized ordering and transshipments at Papierco could be

simulated as well.

In general, risk pooling models should become more realistic in terms of their assump-

tions, accessibility for practitioners, and allowing (practitioners) to quantify the benefits of

risk pooling.813

We considered choosing suitable risk pooling methods for individual companies for cer-

tain economic conditions and sometimes their relation to their immediate supply chain

members at the most. However, a risk pooling strategy that is beneficial for an individual

supply chain member might not be profitable for others or the whole supply chain.814

Therefore, it should not be implemented by one company unilaterally and further re-

search should focus on the supply chain as a whole: Which conditions render a risk pool-

ing method or a combination of risk pooling methods beneficial for all members of a

supply chain? How do you get independent parties to agree on or join a risk pooling strate-

gy? If some supply chain members are better and other ones worse off after risk pooling,

how do you distribute the gains to encourage risk pooling and make it beneficial for every-

body? The contracting side of risk pooling still leaves room for further research.

Another interesting question to explore would be whether the risk pooling methods

make individual companies and the whole supply chain more resilient to external uncer-

tainties other than demand and lead time uncertainty. Sheffi (2006, 2007) explores this

question for several risk pooling methods and individual companies815. Snyder and Shen

(2006: 42) conclude that “[s]upply chain resilience [to supply disruptions and demand un-

certainty] can be improved significantly without large increases in cost” by centralization

(risk pooling) and decentralization (risk diversification). How should supply chains or lo-

gistics systems be designed, so that risk pooling is exploited optimally and uncertainties

are minimized?

812 Cf. Hwarng et al. (2005). 813 Cf. Heil (2006: 81, 169). 814 Some or all supply chain members may be hurt by centralized ordering (Gürbüz et al. 2007: 305), inven-

tory pooling (Anupindi and Bassok 1999, Pasin et al. 2002, Simchi-Levi et al. 2008: 234-238), postpone-ment (García-Dastugue and Lambert 2007), transshipments (Grahovac and Chakravarty 2001, Dong and Rudi 2002, 2004, Zhang 2005, Shao et al. 2009), and virtual pooling (Randall et al. 2002: 56).

815 He examines how an enterprise can be made more resilient to disruptions (supply shortages, production disruptions, energy price increases, exchange rate fluctuations, strikes, and natural disasters) especially by risk pooling (Sheffi 2006: 117f., 210, 212, 248, 303, 317), flexibility (Sheffi 2006: 117ff., 199ff.), post-ponement (Sheffi 2006: 297), commonality (Sheffi 2007: 184-186), standardization (Sheffi 2007: 186-193), interchangeability (Sheffi 2006: 210), multiple suppliers (Sheffi 2007: 99f., 215-222), invento-ry/forecast aggregation (Sheffi 2006: 117f.), exchange of parts (Sheffi 2006: 248), and reduction of prod-uct variants (Sheffi 2006: 119).

6 Conclusion

133

An empirical analysis of risk pooling in the German auto industry might be interesting,

because of the current changes in model mix (high gas prices), production volume (reces-

sion), and steel prices. How can you prepare your production system for something like

this?

How does the current economic downturn affect risk pooling? We already noted that

this might have contributed to increased research and implementation of risk pooling.

How do increased transportation costs affect risk pooling? If they are lasting and

warehouse networks are therefore decentralized, how is this decision affected by risk pool-

ing and how does network redesign affect risk pooling?

Another more representative survey with a higher response rate could also shed light

onto the companies' reasons for and against as well as the manner, degree, benefits, and

costs of applying the risk pooling concepts, as we intended in the six-page version of our

survey that yielded a uselessly low response rate. As risk pooling can affect the whole

supply chain, another survey could consider a supply chain wide perspective rather than

single companies.

Risk pooling is usually shown or proved with the standard deviation. For other meas-

ures of dispersion, such as the variance of independent random variables or the range,

there might be no risk pooling effect. Therefore one could consider risk pooling with

measures of dispersion other than the standard deviation. Risk pooling should also be fur-

ther explored with different order policies.

Finally, the SRL- and PE-models can be extended to include further assumptions. One

should also check whether the conditions or assumptions necessary for the SRL to hold

(necessary conditions) are also sufficient conditions, i. e. if the SRL holds, these conditions

also automatically apply.

134

Appendix A: A Survey on Risk Pooling Knowledge and

Application in 102 German Manufacturing and Trading

Companies

135

1 Introduction

After reviewing the limited recent survey research in OR, business logistics, SCM, and particu-

larly risk pooling mostly with low response rates, we describe our findings from a survey on

risk pooling knowledge and application we conducted among 102 German manufacturing and

trading companies. Such a survey has been demanded by some researchers and – to our know-

ledge – has not been conducted before.

1.1 Motivation: Scarce Survey Research on Risk Pooling

There is little empirical and especially survey research in OR816, business logistics817, and risk

pooling818. The samples and response rates are usually small or not mentioned819.

No surveys have been conducted on risk pooling in business logistics in general yet.

Only few surveys touch types of risk pooling. Most of these surveys deal with postpone-

ment, although the majority of empirical research on postponement relies on case stu-

816 Cachon (2004), Netessine (2005). 817 Griffis et al. (2003: 237). 818 Labro (2004: 358). 819 The following researchers conducted surveys on logistics topics with the following returns: Jackson

(1985, 53 usable responses), Dubelaar et al. (2001, 72 usable of 101 surveys), Griffis et al. (2003: 241f., response rate: 13.25 %), Kisperska-Moroñ (2003: 130, 538 questionnaires, on average three respondents in one company), Bagchi and Skjoett-Larsen (2005, 149 responses, response rate: 5.7 %), White (2005, 429 answers, response rate: 10.93 %), Hilmola and Szekely (2006, 67 usable responses, response rate: 8.9 %). Johnson et al. (2006, 297 usable responses, response rate: 55 %, 305 usable responses, response rate: 51 %, 284 usable responses, response rate: 44 %), Shao and Ji (2006, 321 surveys, response rate: 89.2 %), Böhnlein and Lünemann (2008, 51 responses), Chikán (2009, 51 responses, response rate: 20.82 %). Surveys on postponement received 65 (Kisperska-Moroñ 2003: 130), 76 (Yang et al. 2005b), 80 (Van Hoek 1998b), 102 (Chiou et al. 2002), 106 (Huang and Li 2008b), 111 (completed 24-page workbooks in interviews with world class companies, CLM 1995: 8, 384), 129 (McKinnon and Forster 2000: 5, Delphi survey with logistics experts), 256 (Rabinovich and Evers 2003b), 306 (Nair 2005), 322 (in the base-line survey in Germany, CLM 1995: 381f.), 358 (Oracle 2004, response rate: 2.24 %), 782 (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000, response rate: 53 %), and 3,693 (altogether in the base-line survey, CLM 1995: 381f.) usable responses. The surveys with high returns were conducted via logistics associa-tions (CLM 1995, Rabinovich and Evers 2003b, Oracle 2004, Nair 2005) or via phone with very few questions (Van Hoek 2000b). They were administered in Europe (McKinnon and Forster 2000: 5), Greater China (Mainland China, Hong Kong, and Taiwan) (Huang and Li 2008b), Taiwan (Chiou et al. 2002), the U. S. (an expert study by Morehouse and Bowersox 1995, Van Hoek 1998b, Rabinovich and Evers 2003b, Nair 2005), the UK (Yang et al. 2005b), the Netherlands (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000), and Upper Silesia, Southern Poland (Kisperska-Moroñ 2003) among manufactur-ing (Van Hoek 1998b, Van Hoek and Van Dierdonck 2000, Chiou et al. 2002, Kisperska-Moroñ 2003, Rabinovich and Evers 2003b, Nair 2005, Yang et al. 2005b, Huang and Li 2008b), trading (Van Hoek and Van Dierdonck 2000, Nair 2005), and transport and logistics services companies (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000). Graman and Magazine (2006: 1068, 1070f., 1075) conducted depth in-terviews with five managers of a small U.S. manufacturer of mops and brooms on issues influencing suc-cessful postponement implementation.

Appendix A

136

dies820, such as Dapiran (1992), Cooper (1993, examples), Feitzinger and Lee (1997), Garg

and Tang (1997), Van Hoek (1997, 1998a, 1998b), Van Hoek et al. (1998), Magretta

(1998), Brown et al. (2000), Waller et al. (2000), Ghemawat and Nueno (2003), Huang and

Lo (2003), and Huang and Li (2008a).

Whereas some researchers find postponement application has increased, will increase,

or postponement is widely applied821, others state it is not applied as much (as expected)822

and will be even less used in the future823. This is explained by “a general lack of under-

standing of postponement” regarding its conception, gains, and costs824, perceived technol-

ogy limitations, ineffective organization alignment825, as well as difficulties in managing

the relations to suppliers and customers826 and in estimating the costs and benefits of post-

ponement827.

Van Hoek (1998b: 513) finds that “[d]ownstream activities such as distribution and

packaging are largely postponed (56.93 per cent of the flow of goods and 53.95 per cent).

Upstream activities such as engineering and purchasing are postponed to a lesser extent

(37.49 per cent of the flow of goods and 37.42 per cent). Overall however, the findings

indicate that postponement is applied at multiple points in the chain and to a significantly

high share of the flow of goods”. Yang et al. (2005b: 1000) remark that postponement is

mostly applied as make to order and ship to order.

820 Van Hoek (2001). 821 CLM (1995: 213), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), Van Hoek and Van

Dierdonck (2000), McKinnon and Forster (2000: 7f.), Chiou et al. (2002), Huang and Li (2008b). CLM (1995: 213) finds “Research clearly supports the generalization that firms are rapidly adopting both form and time postponement”, although 10.3 % of North American and 85 % of non-North American world class companies have decreased or substantially decreased the use of postponement and 31 % of North American and 0 % of non-North American (European/Pacific Basin) world class companies have in-creased or substantially increased the use of postponement (Workbook Section 4: Organization, Question 31, “Electronic Appendix” Disk to CLM 1995). Yet, only few non-North American companies completed the workbook (CLM 1995: 384).

822 Van Hoek et al. (1998: 34, 51), Bowersox et al. (1999), Battezzati and Magnani (2000: 423), Brown et al. (2000: 78), Van Hoek (2000b, in third party logistics or TPL), Van Hoek and Van Dierdonck (2000, in TPL), Oracle (2004), Yang et al. (2004, 2005a, 2005b: 991), Boone et al. (2007: 594), Yang et al. (2007: 972). Van Hoek et al. (1998: 51, 34) observe that although “the theoretical benefits of postponement [were] introduced [already] in the 1950s and 60s”, this “highly attractive principle has hardly been ap-plied to date”. “[P]ostponement applications are still in the infancy stage” (Van Hoek et al. 1998: 51). It “has an enormous potential, still largely under-exploited, in Italy” (Battezzati and Magnani 2000: 423). Boone et al. (2007: 594) remark “the slow rate of postponement adoption among practitioners”. „[P]ostponement is an underutilized concept“ (Yang et al. 2007: 972).

823 “Postponement applications are still not as widespread as expected. […] The respondents also expected postponement to be less used in three years” (Yang et al. 2005b: 991).

824 Oracle (2004: 2, 7). 825 Capgemini (2003), Matthews and Syed (2004: 30). 826 Yang et al. (2005b: 991), Waller et al. (2000), Van Hoek et al. (1998). 827 Van Hoek et al. (1998).

Appendix A

137

Rabinovich and Evers (2003b: 41f.) find that time postponement (emergency trans-

shipments) contributes to the implementation of form postponement.

Huang and Li (2008b: 5, 16f.) discover that the degree of postponement application is

higher in China than CLM (1995), Yang et al. (2005a), and Van Hoek (1998b) remarked in

Western countries and increases. Chiou et al. (2002: 122) also conclude “that form post-

ponement strategies are practiced widely by IT firms in Taiwan”. Huang and Li (2008b:

12) sent their questionnaires only to 411 companies that had confirmed on the phone that

they applied postponement. They, Chiou et al. (2002), and Yang et al. (2005b) do not state

how many companies in their research countries actually apply postponement. In a person-

al correspondence on September 4, 2009 Dr. Biao Yang, The York Management School,

University of York, UK, explained that speaking from their experience, given the working

definitions of different postponement strategies they provided828, very few companies

would claim that they are not using any postponement.

The Council of Logistics Management (CLM) conducted a base-line survey in North

America (Canada and the U.S.), Europe (France, Germany, the Netherlands, Norway,

Sweden, and the UK), and the Pacific Basin (Australia, Japan, and Korea) from May to

September 1993. Of the 21,592 mainly manufacturing companies contacted, 3,693 an-

swered (response rate: 17.1 %). In Germany 3,000 surveys were mailed and 322 returned

(response rate: 10.7 %).829

It also did interviews with 111 companies from 17 countries in North America, Europe,

and the Pacific Basin from early 1994 until spring 1995 that were believed “by a group of

logistics experts to have a high potential to possess world class logistical capabilities” and

asked them to complete a 24-page workbook.830

35.3 % of North American and 29.1 % of non-North American world class companies

consider location flexibility (“[t]he ability to service customers from alternative ware-

house locations”, i. e. in our opinion transshipments or virtual pooling) less or least impor-

828 In their survey Yang et al. (2005b: 1002f.) ask for “the percentages of goods related to” engineer, pur-

chase, make, final manufacturing/assembling, package/label, and ship to order to elicit the extent of post-ponement application in the respondents' companies. Thus they equate make-to-order with postponement or delayed differentiation, while Cachon and Terwiesch (2009: 344) distinguish these strategies: Al-though “they are conceptually quite similar”, “[d]elayed differentiation is thought of as a strategy that stores nearly finished product and completes the remaining few production steps with essentially no de-lay. Make-to-order is generally thought to apply to a situation in which the remaining production steps from components to a finished unit are more substantial, therefore involving more than a trivial delay. Hence, delayed differentiation and make-to-order occupy two ends of the same spectrum with no clear boundary between them”.

829 CLM (1995: 381f.). CLM was named Council of Supply Chain Management Professionals (CSCMP) in 2005.

830 CLM (1995: 8f., 384).

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138

tant, 35.3 % or 37.5 % respectively more or most important. The North American and non-

North American world class companies see mostly the logistics department as responsible

for location flexibility (77.19 and 74.76 % responsibility). Fifty-one percent of North

American and 58.3 % of non-North American world-class companies believe they perform

better or much better than their competitors in terms of location flexibility.831

According to McKinnon and Forster (2000: 17), “the proportion of retail sales bypass-

ing conventional shops and being delivered directly to the home is likely to increase signif-

icantly” until 2005. “Direct distribution to the home from nationally based suppliers is like-

ly to experience the fastest growth”832. That means that virtual pooling in the form of

drop-shipping is expected to increase.

In a small phone survey by Randall et al. (2006) of 64 (56 responses, 54 usable re-

sponses, response rate: 84.4 %) publicly held e-tailers that made up 60 % to 70 % of U.S.-

wide e-tailing revenue, 36 companies (67.7 %) chose to hold inventory. That means 33.3 %

of the surveyed e-tailers conducted virtual pooling.

In the CLM base-line survey, 62.81 % of North American, 68.31 % of European, and

47.26 % of Pacific Rim companies agree or strongly agree that on an equal volume basis

they had inventory located at fewer sites in 1993 (today) than in 1988 (five years ago).833

That means that 68.31 % of the surveyed European companies conducted inventory pool-

ing.

The world class companies' “[l]ogistics strategy includes a priority to reduce […] [t]he

number of logistics facilities” more so in Europe and the Pacific Basin, where the mean

answer was 3.55 than in North America, where the mean answer was 3.23 on a scale from

1 (Strongly Disagree) to 5 (Strongly Agree).834

McKinnon and Forster (2000: 6f.) find “The centralisation of inventory is likely to out-

strip that of production. At a European level, the degree of inventory concentration is fore-

cast to increase by a third, twice as much as at a national level. A significant minority of

the panel (around 15 %) indicated that within countries there would be net decentralisation

of inventory, with firms increasing their number of stockholding points. The prevailing

view, however, was that inventory centralisation, which has been one of the main logistical

trends over the past 30 years, would continue apace for at least the next 5 years”.

831 Workbook Section 3: Relative Performance Competencies, Question 20, “Electronic Appendix” Disk to

CLM (1995). 832 McKinnon and Forster (2000: 9). 833 Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995). 834 CLM (1995: 387).

Appendix A

139

A Warehousing Education and Research Council survey with 139 U.S. participants in

manufacturing, retail, wholesale, public utilities and government showed that the number

of warehouses continues to shrink, although there are a few new large facilities in West or

Mid Atlantic regions.835

Contrarily, according to a survey by Lemoine and Skjoett-Larsen (2004) among logis-

tics managers of mechanical, electronic, and medical equipment companies in Denmark in

2001 (46 usable questionnaires, response rate: 10 %) the number of suppliers, production

facilities and warehouses has not been changed in the last three to five years in Europe, but

has been increased or will be increased outside Europe.

Bandy (2005) conducts an anonymous survey among 24 students that shows that a sim-

ple spreadsheet in-class simulation helps students understand the impact of pooling safety

stock.

Reviewing literature and interviewing Belgian companies, Naesens et al. (2007) find

that companies are reluctant to implement inventory pooling in a horizontal collaboration.

Nonetheless, companies seem to have conducted inventory pooling within companies to

a broad extent.

Twenty-seven percent of North American and 29.1 % of non-North American world-

class companies consider substitution flexibility (“[t]he ability to substitute product or

service offerings in the event of a delay or stockout versus backorder or line cancellation”)

less or least important, 46.2 % or 25 % respectively more or most important. Responsibili-

ty for substitution flexibility rests 49.9 % with logistics, 35.63 % with marketing according

to North American, or 48.41 % or 42.95 % respectively according to non-North American

world-class companies. 44.2 % of North American and 37.5 % of non-North American

world-class companies believe they perform better or much better than their competitors in

terms of substitution flexibility.836

Only few surveys provide information on how many companies apply the respective

risk pooling method.

Nearly 50 % of more than 350 companies from all over the world have not implemented

postponement strategies.837 Hence, about half of these companies use postponement.

More than 40 % of the companies surveyed by Kisperska-Moroñ (2003: 131) gear total

production towards customer orders. Surveyed companies manufacture on average 16 % to

835 Modern Materials Handling (2002). 836 Workbook Section 3: Relative Performance Competencies, Question 29, “Electronic Appendix” Disk to

CLM (1995). 837 Oracle (2004).

Appendix A

140

stock and 84 % to order, engineering 97 %, metal 74 %, plastic products 83 %, and electro-

technical companies 77 % to order. Thus one could infer that about 40 % of the surveyed

companies in Upper Silesia, Poland apply manufacturing postponement.

From 1988 to 1993 inventory was centralized or pooled by 68.31 % of the European

companies surveyed by the CLM.838

Virtual pooling is applied by 33.3 % of the U.S. e-tailers that Randall et al. (2006) in-

terviewed.

None of the surveys gives detailed information on Germany, although Germany is the

fourth largest economy in the world according to its nominal GDP in USD in 2008839 and

is very progressive, advanced, and sophisticated in logistics, especially in “operating effi-

ciency and cost” and customer service, and, like other European countries, in the “func-

tional integration of logistics work within the firm” and “environmental issues” like “re-

verse logistics”840. European countries have opportunities for improvement in “the external

integration of logistics systems and development of supply chain relationships throughout

Europe”841.

1.2 Objective

We would like to determine to what extent the different risk pooling concepts are known and

applied by 102 German manufacturing and trading companies and examine for our sample the

following remarks, suggestions, and demands:

Van Hoek (1998b) finds that postponement is extensively applied in electronics and au-

tomotive and less extensively applied in food and clothing. We would like to find out

whether this applies to our sample as well.

Alfaro and Corbett (2003: 12f., 15) observe that “several approaches to the widely rec-

ognized challenge of managing product variety rely on the pooling effect. Pooling can be

accomplished through the reduction of the number of products or stock-keeping units

(SKUs), through postponement of differentiation, or in other ways [component commo-

nality and inventory pooling]. These approaches are well known and becoming widely

applied in practice”. However, there are no studies yet whether product pooling and com-

ponent commonality really are widely applied in practice.

838 Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995). 839 IMF (2009). 840 CLM (1995: 365). 841 CLM (1995: 366).

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141

Herer et al. (2006) remark “Transshipments are not widely adopted in practice because

the IT infrastructure is inadequate and there are no realistic models to take advantage of

transshipment benefits”. However, there are no studies yet whether transshipments really

are not widely used in practice.

Thomas and Tyworth (2006) demand a survey to determine whether order splitting is

employed in practice842.

Boone et al. (2007) review postponement literature published from 1999 to 2006 and

conclude research should be extended to non-manufacturing postponement and investigate

the slow rate of postponement adoption among practitioners.

Huang and Li (2008b: 12) only surveyed large electronic/information technology, cloth-

ing, and electric appliances companies. They remark large companies may apply post-

ponement more than small ones, since they may be better able to afford the redesign of

products and/or processes usually required by postponement843. “Hence, further studies

could compare the differences of postponement application between large-scale and small

and medium companies”844.

842 “Yet, despite the impressive amount of past and present work on pooling lead-time risk by order splitting,

it is difficult to find any substantive evidence of successful applications in academic or practitioner litera-ture” (Thomas and Tyworth 2006: 246). “Although studies in both tracks provide hypothetical evidence that pooling lead-time risk by splitting orders simultaneously may be worthwhile, it is difficult, if not im-possible, to find substantive empirical validation of the proposition” (Thomas and Tyworth 2006: 254). “Collectively, these limitations make the value proposition rather dubious. Thus future research in this area should include case studies, simulations, and surveys to determine whether companies use such order splitting methods and the business setting where successful applications appear” (Thomas and Tyworth 2006: 254f.).

843 Ernst and Kamrad (2000), Aviv and Federgruen (2001b). 844 Huang and Li (2008b: 19).

142

2 The Survey

There has not been a survey on how many companies know and apply the various risk pooling

methods yet, especially not in Germany. In order to respond to the aforementioned demands

and remarks, we conducted a survey among German manufacturing and trading companies

from September 2008 to August 2009 and obtained 102 completed questionnaires (response

rate: 21.3 %) from logistics or supply chain management professionals. Since an earlier six-

page survey that was e-mailed to 3,600 companies had a response rate of only 0.3 %, we asked

478 manufacturing and trading company representatives in person to complete the one-page

questionnaire in figure A.4 or forward it to the appropriate person mainly on company and job

fairs in various German cities.

Respondents were promised a summary of the survey results as an incentive.845 Our ex-

perience supports that face-to-face methods usually achieve higher response rates846.

2.1 Research Design

The respondents worked for companies from the following branches of economic activity ac-

cording to the German Classification of Economic Activities Edition 2003 of the German Fed-

eral Statistical Office (Statistisches Bundesamt Deutschland):

845 Cf. Yang et al. (2005b: 996). 846 Kisperska-Moroñ (2003: 130), Groves et al. (2004: 165).

Appendix A

143

Table A.1: Comparing Respondents with the Total Population of Manufacturing and Trading

Companies in Germany

a Source: Statistisches Bundesamt Deutschland (2009i: 371, 408f.). Companies with in general 20

employees and more. Status of 09/30/2006 (trade), 09/30/2007 (manufacturing).

Classification Description Number % Number % Variance (%)

11Extraction of crude petroleum and natural gas; service activities incidental to oil and gas extraction, excluding surveying

17 0.01 1 0.98 0.97

15 Manufacture of food products and beverages 5,189 4.46 4 3.92 -0.54

16 Manufacture of tobacco products 24 0.02 1 0.98 0.96

18Manufacture of wearing apparel; dressing and dyeing of fur

378 0.32 1 0.98 0.66

21 Manufacture of pulp, paper and paper products 817 0.70 2 1.96 1.26

22Publishing, printing and reproduction of recorded media

2,456 2.11 2 1.96 -0.15

24 Manufacture of chemicals and chemical products 1,405 1.21 3 2.94 1.73

25 Manufacture of rubber and plastic products 2,635 2.26 2 1.96 -0.30

26 Manufacture of other non-metallic mineral products 1,677 1.44 1 0.98 -0.46

27 Manufacture of basic metals 897 0.77 1 0.98 0.21

28Manufacture of fabricated metal products, except machinery and equipment

6,175 5.31 4 3.92 -1.38

29 Manufacture of machinery and equipment n.e.c. 5,990 5.15 13 12.75 7.60

30 Manufacture of office machinery and computers 164 0.14 1 0.98 0.84

31Manufacture of electrical machinery and apparatus n.e.c.

1,922 1.65 7 6.86 5.21

32Manufacture of radio, television and communication equipment and apparatus

542 0.47 5 4.90 4.44

33Manufacture of medical, precision and optical instruments, watches and clocks

2,067 1.78 2 1.96 0.18

34Manufacture of motor vehicles, trailers and semi-trailers

1,001 0.86 14 13.73 12.87

35 Manufacture of other transport equipment 314 0.27 3 2.94 2.67

36 Manufacture of furniture; manufacturing n.e.c. 1,484 1.27 2 1.96 0.69

37 Recycling 168 0.14 3 2.94 2.80

40 Electricity, gas, steam and hot water supply 1,196 1.03 2 1.96 0.93

45.2Building of complete constructions or parts thereof; civil engineering

6,352 5.46 1 0.98 -4.48

51.46 Wholesale of pharmaceutical goods 3,148 2.70 2 1.96 -0.74

51.47.8Wholesale of paper and paperboard, stationery, books, newspapers, journals and periodicals

2,259 1.94 3 2.94 1.00

51.53.1Non-specialized wholesale of wood, construction materials and sanitary equipment

1,254 1.08 2 1.96 0.88

51.88Wholesale of agricultural machinery and accessories and implements, including tractors

1,333 1.15 1 0.98 -0.16

52.11 Retail sale in non-specialized stores with food, beverages or tobacco predominating

24,790 21.30 7 6.86 -14.44

52.42 Retail sale of clothing 25,896 22.25 10 9.80 -12.44

52.46 Retail sale of hardware, paints and glass 11,279 9.69 1 0.98 -8.71

52.48.6 Retail sale of games and toys 3,564 3.06 1 0.98 -2.08

Total 116,393 100 102 100

Responding companies

The whole

populationa

Appendix A

144

As 78.7 % of the sampling frame population did not respond and the sample is small, it is not

too representative of neither the whole population in the different branches of economic ac-

tivity the respondents' companies belong to in table A.1 nor of the target population of German

manufacturing and trading companies.847 Not all areas of domestic production and trade are

covered. Our sample consists of too many manufacturing companies, especially from vehicle

construction (34, 35), although this is an important industry in Germany, manufacture of ma-

chinery (29, 31, 32), and recycling (37) and too few trading companies, particularly in food

(52.11), clothing (52.42), and hardware retail (52.46) as the variance in the last column shows.

Deviations of responding companies from the whole population in Huang and Li

(2008b: 13) are of similar magnitude. In contrast, the responding companies in Yang et al.

(2005b: 997) closely reflect the whole population. Of the 28 mentioned surveys in this sec-

tion848 only Huang and Li (2008b) and Yang et al. (2005b) (7.14 %) compare the respond-

ing companies' characteristics to the whole population (retrospective quota sampling).

We have to highlight that the whole population in table A.1 only consists of companies

with 20 or more employees, while our sample encompasses three companies (respondents

2, 65, and 100 from industrial sectors 52.42, 27, and 51.47.8) with less than 20 employees.

If we omitted them, the variance would increase and the representativeness decrease even

more. A detailed classification of the branches of economic activity with all German com-

panies with any number of employees is not publicly available. The German Federal Statis-

tical Office told us we could apply for a special query with charges. A retrospective quota

sampling with more detailed subgroups of industrial economic activity than in table A.1

and all German companies, which cannot be conducted due to lacking data, might reveal

that our sample is more representative of these subgroups.

The size of the responding companies ranges from 5 to 182,739 employees. 2 % have

less than 10, 9 % less than 50, 31 % less than 250, 32 % less than 500, and 68 % have 500

847 There were 52,362 manufacturing (9.94 % of manufacturing and trading companies) and 474,065

(90.06 %) trading companies with in general 20 or more employees in Germany in 2007 or 2006 respec-tively (Statistisches Bundesamt Deutschland 2009i: 409, 371). In our sample there are 75 (73.53 %) man-ufacturers and 27 (26.47 %) trading companies.

848 Jackson (1985), CLM (1995), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), McKinnon and Forster (2000), Van Hoek and Van Dierdonck (2000), Dubelaar (2001), Chiou et al. (2002), Griffis et al. (2003), Kisperska-Moroñ (2003, two surveys), Rabinovich and Evers (2003b), Lemoine and Skjoett-Larsen (2004), Oracle (2004), Bagchi and Skjoett-Larsen (2005), Nair (2005), White (2005), Yang et al. (2005a, 2005b), Himola and Szekely (2006), Johnson (2006), Randall et al. (2006), Shao and Ji (2006), Naesens et al. (2007), Böhnlein and Lünemann (2008), Huang and Li (2008b), and Chikán (2009).

Appendix A

145

or more employees. The majority of the sample consists of larger companies, while the

majority of the whole population comprises small ones.849

Nevertheless our survey can at least show the risk pooling knowledge and activities of

the surveyed companies for a given moment in time. They are relatively heterogeneous in

terms of industry membership and number of employees (size), so that risk pooling know-

ledge and activities of a wide company spectrum and size specific specialties can be de-

tected.850 Besides, the respondents do not deviate from the overall population extremely

regarding the branches of activity. Therefore, the absence of data from the nonrespon-

dents may not contaminate the conclusions drawn from the sample too much.851

The questionnaire was scrutinized by three academics and three logistics managers,

pretested among eleven companies, and adjusted according to the suggestions and de-

tected problems before the final distribution to insure content validity.852 Validity meas-

ures whether the questions capture what they are intended to capture.853 Of the 28 surveys

mentioned previously 28.57 % deal with their validity. Reliability measures “whether res-

pondents are consistent or stable in their answers”854. Only 17.86 % of the 28 surveys men-

tioned address their reliability. We did not measure reliability as respondents usually are

not willing to be interviewed twice or to answer a questionnaire enlarged by asking for the

same construct twice.855 We could not check for “systematic reporting errors”856 (response

bias), as external data, which the survey responses could be compared to, are not availa-

ble857. None of the 28 surveys mentioned refers to their response bias.

We did not check for non-response bias, because we could not collect the nonrespon-

dents' characteristics858. Non-response bias is the distortion of the sample and therefore the

basic population because some people do not respond or do not answer certain questions.

The answers of respondents may differ from the ones of nonrespondents. There is no con-

sensus on when nonresponse reduces survey quality and therefore on appropriate response

849 In 2006 there were 4,307 (0.63 %) active industrial and 1,362 (0.18 %) trading companies with 250 and

more, 680,561 (99.37 %) or 735,820 (99.81 %) ones respectively with less than 250 employees subject to social security (Statistisches Bundesamt Deutschland 2009i: 493). In our sample 74.67 % of the industrial and 51.85 % of the trading companies have 250 and more employees.

850 Cf. Böhnlein and Lünemann (2008: 6). 851 Cf. Vockell and Asher (1995: ch. 8). 852 Cf. Yang et al. (2005b: 995, 998), Huang and Li (2008b: 13). 853 Groves et al. (2004: 254). 854 Groves et al. (2004: 261). 855 Groves et al. (2004: 266), Yang et al. (2005b: 998). 856 Groves et al. (2004: 259). 857 Cf. Groves et al. (2004: 266). 858 Cf. Groves et al. (2004: 169-196), Schneekloth and Leven (2003).

Appendix A

146

rates.859 Nevertheless, our response rate is above the unfavorable response rates below

20 %860, within the 10 % to 30 % of the past mean861 and the 4 % to 32.7 % of large sam-

ples in the Journal of Business Logistics from 1997 to 2001862, and higher than a lot of the

mentioned surveys' ones863.

Nonresponse rates often are ignored, because it is assumed that the reason for the non-

response is not associated with the measured statistical values and therefore it does not

affect the quality of the survey's results.864 Of the 28 surveys we mentioned ten (35.71 %)

deal with their non-response bias. Most of these determine the nonresponse bias, checking

whether the answers of first respondents and late respondents differ, although late respon-

dents may not be an appropriate estimate for nonrespondents.

Nonetheless, the answers of our 51 first and 51 last respondents are independent (the

null hypothesis that there is no significant relationship between the answers cannot be re-

jected) in Pearson's and Yates' chi-square and Fisher's exact test at the 5 % level, except for

the question about their risk pooling knowledge865 and centralization in the past866. In all

other cases the distribution of the answers within the two groups does not differ signifi-

cantly: The two-sided asymptotic significance of the respective test statistic is greater than

0.05 in each case, so that it is safe to say that any differences are due to chance variation,

which implies that the two groups answered equally.

With our sample size of 102 the confidence interval or margin of error is 9.7 on the

95 % confidence level for an estimated percentage of 50 %, i. e. one can be 95 % certain

that if 50 % of the sample picks an answer between 40.3 % (50-9.7) and 59.7 % (50+9.7)

of the whole population would have also picked that answer. However, the true percentage

of the population only is the sample's percentage plus/minus the confidence interval, if a

genuine simple random sample of the relevant population was drawn. This cannot be con-

firmed for our sample, so that this confidence interval is an underestimate. No errors and

“biases of coverage, sampling, nonresponse, or measurement […] are included in the mar-

gin of error”867. When random sampling is not used, one has to depend on logic apart from

859 Fowler (1993), Schneekloth and Leven (2003), Groves et al. (2004: 169-196). 860 Yu and Cooper (1983). 861 Flynn et al. (1990). 862 Griffis et al. (2003: 242). 863 Cf. Yang et al. (2005b: 998). 864 Groves et al. (2004: 169-196), Schneekloth and Leven (2003). 865 In this case Pearson's chi-square test gives χ2 = 9.046 with df = 1 and p = 0.00263, Yates' correction for

continuity χY = 7.880 with df = 1 and p = 0.004998, and Fisher's exact test p (two-tailed) = 0.004728. 866 In this case χ2 = 4.752 with df = 1 and p = 0.029264, χY = 3.928 with df = 1 and p = 0.047432, and

p = 0.046973 in Fisher's exact test. 867 Groves et al (2004: 382).

Appendix A

147

mathematical probability to assess to what extent the sample deviates from the population

it was drawn from.868

2.2 Data Analysis and Findings

2.2.1 Risk Pooling Knowledge and Utilization in the German Sample

Companies

Figure A.1: Risk Pooling Knowledge and Utilization in the German Sample Companies

The most known concepts related to risk pooling in the whole sample are central ordering,

product substitution, selective stocking, transshipments, and order splitting, followed by prod-

uct pooling, commonality, virtual pooling, capacity pooling, “risk pooling”, postponement,

demand reshape, the portfolio effect (PE), inventory turnover curve, and square root law (SRL)

in order of descending percentage of respondents that know these concepts.

Surprisingly, the SRL (28 %) is less known than the PE (54 %), although it is the sim-

pler concept and there are more and earlier publications on it in business logistics. Perhaps

the PE is more popular, as it is a generalization of the SRL and originated in finance.

868 Vockell and Asher (1995: ch. 8).

58

28

54

84

70

45

76

88

54

79

55

64 64

91

79

34

16

28

66

49

25

40

47

22

66

35

4641

66

35

48

6

17

7

0

10

20

30

40

50

60

70

80

90

100

Percent of Responding Compan

ies

Knowledge Utilization

Appendix A

148

A lot of respondents obviously did not realize that risk pooling may comprise all these

different concepts. Otherwise they would have noted that they know and apply risk pool-

ing, whenever they checked to know or apply any of these concepts. Risk pooling is a

hypernym and not a risk pooling concept itself.

The most applied risk pooling concepts in the whole sample are selective stocking,

transshipments, central ordering, commonality869, and centralization, followed by product

substitution, virtual pooling, capacity pooling, product pooling, postponement, order split-

ting, “risk pooling”, the PE, inventory turnover curve, demand reshape, decentralization,

and the SRL in order of descending percentage of surveyed companies applying these con-

cepts.

While the knowledge of the different risk pooling concepts is fairly good870 (only the

SRL and the inventory turnover curve are known by less than 50 %), they are not widely

applied. Only the well established concepts selective stocking, transshipments, and central

ordering show application rates over 50 %, namely 66 %. This disagrees with Herer et al.

(2006), who remark “Transshipments are not widely adopted in practice because the IT

infrastructure is inadequate and there are no realistic models to take advantage of trans-

shipment benefits”. Some companies which do not employ central ordering remarked it

increased transportation and delivery costs too much. This could be counteracted with a

centralized ordering system like the one we designed for Papierco earlier. Transportation

costs do not increase (substantially) or the supplier incurs them.

Postponement is only applied by 35 % of the companies. Thus we cannot conclude

“that firms are rapidly adopting both form and time postponement”871 and widely apply

it872 in Germany as CLM (1995: 209) reports for North America and Europe, McKinnon

and Forster (2000: 5) for Europe, and Chiou et al. (2002) and Huang and Li (2008b) for

China. More sample companies in Germany (65 %) have not implemented postponement

strategies than suggested by Oracle (2004) (nearly half of 358 mainly manufacturing com-

panies from all over the world). We agree with Van Hoek et al. (1998), Bowersox et al.

(1999), Battezzati and Magnani (2000), Brown et al. (2000: 78), Oracle (2004), Yang et al.

869 Wazed et al. (2009: 70) find “Although the benefits of commonality are widely known, many companies

are still not taking full advantage of it when developing new products or re-designing the existing ones”. We can agree with them for our sample.

870 Alfaro and Corbett (2003: 12f., 15) already remark that risk pooling approaches such as product pooling, postponement, component commonality, and inventory pooling “are well known […] in practice”.

871 CLM (1995: 213). 872 Alfaro and Corbett (2003: 12).

Appendix A

149

(2004, 2005a, 2005b, 2007), and Boone et al. (2007) that postponement is not applied as

much (as expected).

Some respondents told us they did not use postponement as it entailed completely dif-

ferent production and storage concepts and therefore usually was uneconomical. Research

has to determine more clearly the changes necessary for postponement, methods for calcu-

lating the costs of postponement, and conditions that render postponement economical.

Practice seems to lack the knowledge to implement postponement economically. Perhaps

more concepts have to be developed that may make postponement less expensive, such as

operations reversal. This is in line with Oracle (2004: 7f.). Our survey suggests that the

reason for the low application may not lie in the basic knowledge of this concept (55 %

know it), but it is less known than most of the other concepts except for demand reshape,

the PE, inventory turnover curve, and SRL.

Component commonality is well known and applied by nearly every second surveyed

company. Thus, we can support Kim and Chhajed (2001: 219), who remark “The use of

commonality in product line extensions is a growing practice in many industries”, and Al-

faro and Corbett (2003: 12, 15), who observe it is “becoming widely applied in practice”.

Nevertheless some companies who do not use it pointed out it was too expensive. This

confirms that the cost of common components can be high873.

Location flexibility achieved by transshipments and virtual pooling seems to be more

important in the sample companies in Germany than suggested by CLM874 for North

American and non-North American world class companies. McKinnon and Forster (2000:

9, 17) predicted virtual pooling in the form of drop-shipping to increase. Randall et al.

(2006) found that 33.3 % of the 56 interviewed U.S. e-tailers relied on virtual pooling.

More generally we find that 46 % of the surveyed manufacturers and traders apply virtual

pooling in Germany. Our sample only contains a single toy e-tailer.

Fewer German sample companies (48 %) have centralized their stockholding than Eu-

ropean ones overall (68.31 %)875. Our findings agree with McKinnon and Forster (2000:

6f.), Modern Materials Handling (2002), and Alfaro and Corbett (2003: 12f.) that inventory

centralization is an important trend. However, we can also confirm the minority opinion

of 15 % of the panelists in McKinnon and Forster (2000: 6f.) that there will be a slight net

decentralization of inventory in Germany in the future. Thirty-five percent of the German

873 Van Mieghem (2004: 419). 874 Workbook Section 3: Relative Performance Competencies, Question 20, “Electronic Appendix” Disk to

CLM (1995). 875 Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995).

Appendix A

150

sample companies have not changed the number of warehouses or production facilities in

the past. Lemoine and Skjoett-Larsen (2004) reached a similar result in Denmark. Some of

the companies that did not or will not centralize declared it increased transportation costs

too much.

Most companies have already centralized or to a lesser extent decentralized their ware-

house or logistics system in the past. Only six percent intend to centralize their logistics

system in the future. Merely seven percent plan to increase the number of warehouse or

production locations in the future. This is in opposition to the expectation that the increas-

ing fuel and transportation costs induce companies to decentralize their warehouse or logis-

tics systems. The risk pooling advantages derived from physical inventory pooling may

outweigh the increased transportation costs.

Product substitution flexibility seems to be more important in Germany than suggested

by CLM876 for North American and non-North American world class companies. Compa-

nies applying demand reshape mostly indicated they persuaded customers to buy another

substitute product even though the original customer wish was available to increase the

profit margin and not for risk pooling reasons as intended by Eynan and Fouque (2003,

2005).

We have to disagree with Alfaro and Corbett (2003: 12) who observe “the reduction of

the number of products or stock-keeping units (SKUs)”, also known as product pool-

ing877, and “postponement of differentiation” are “becoming widely applied in practice”.

Product pooling is applied by 40 % and postponement by 35 % of the companies in our

sample.

We can answer the call of Thomas and Tyworth (2006: 254f.) for empirical research “to

determine whether companies use such order splitting methods”, pointing out that only

35 % of German companies in our sample do apply them. However, our survey does not

inform about the conditions and success of these order splitting applications.

Some interviewees said they did not know when and how it was favorable to apply the

various risk pooling concepts. Research needs to address these issues further. More re-

search is needed to convey to practice when and how the different risk pooling concepts

may be implemented successfully. Our research constitutes one step in this direction.

876 Workbook Section 3: Relative Performance Competencies, Question 29, “Electronic Appendix” Disk to

CLM (1995) 877 Cachon and Terwiesch (2009: 330, 467).

Appendix A

151

2.2.2 Association between the Knowledge of Different Risk Pooling

Concepts

The knowledge of risk pooling is significantly associated with the knowledge of postponement

(Goodman and Kruskal's Tau (τ) = 0.147, approximative significance based on chi-square ap-

proximation (p) = 0.000), product pooling (τ = 0.104, p = 0.001), transshipments (τ = 0.091,

p = 0.002), the turnover curve (τ = 0.087, p = 0.003), commonality (τ = 0.066, p = 0.010), de-

mand reshape (τ = 0.061, p = 0.013), and virtual pooling (τ = 0.050, p = 0.025) in order of de-

scending significance.

Goodman and Kruskal's Tau was chosen, as it offers advantages over all other meas-

ures of association for nominal variables. It can be interpreted easily, its maximum is one,

it takes the value 0, if the variables are independent, and it is suitable, if the number k of

the independent variable x's categories is not equal to the number m of the dependent vari-

able y's categories. Its only disadvantage is its complicated calculation, which is remedied

with modern statistics software.878 Goodman and Kruskal's Tau measures the association

of two categorical variables in terms of an improvement of prediction relative to a random

distribution of people (or responding companies in this case) based on the marginal distri-

bution.879 It is a measure of proportional reduction of error (PRE).880

The above Tau of 0.147, for instance, means that the postponement knowledge of

14.7 % more of responding companies is predicted correctly, if we predict the postpone-

ment knowledge of a company not only according to the general distribution of postpone-

ment knowledge, but according to the conditional distribution of postponement knowledge

that is distinguished by the risk pooling knowledge.881 Postponement might be the most

popular type of risk pooling, as its recognition shows the highest correlation with the

knowledge of risk pooling. Forty-two of the 59 responding companies who know risk pool-

ing also know postponement. Twenty-nine of the 43 logistics professionals not knowing

risk pooling do not know postponement either. The knowledge of risk pooling is also high-

ly significantly associated with knowing product pooling (τ = 0.104, p = 0.001) and trans-

shipments (τ = 0.091, p = 0.002).

Further significant correlations at least at the 5 % level between the knowledge of the

different risk pooling concepts can be read from table A.2 at the end of this section.

878 Müller-Benedict (2007: 203, 206). 879 Müller-Benedict (2007: 203). 880 Müller-Benedict (2007: 200). 881 Cf. Müller-Benedict (2007: 204).

Appendix A

152

Most significantly correlated is the knowledge of product pooling and transshipments

(τ = 0.163, p = 0.000), risk pooling and postponement (τ = 0.147, p = 0.000), transshipments

and capacity pooling (τ = 0.139, p = 0.000), as well as transshipments and postponement

(τ = 0.135, p = 0.000) and vice versa in order of descending strength of correlation.

In this sample the knowledge of postponement and capacity pooling (τ = 0.116,

p = 0.001), product substitution and demand reshape (τ = 0.112, p = 0.001), product pool-

ing and demand reshape (τ = 0.104, p = 0.001), postponement and order splitting

(τ = 0.101, p = 0.001), selective stocking and transshipments (τ = 0.098, p = 0.002), as well

as demand reshape and transshipments (τ = 0.095, p = 0.002) is relatively strongly corre-

lated. These concepts seem to be related and therefore to be known together: Postponement

and capacity pooling are popular and applied together e. g. in the auto industry. Both in

product substitution and demand reshape goods are substituted. One can offer a limited

number of products by product pooling or offer a variety of products (but not store all of

them) and apply demand reshape or transshipments. In order splitting certain steps in the

order and supplier delivery process may be postponed. If SKUs are only stocked at certain

locations (selective stocking), transshipments may be necessary between these locations.

Usually, we call a correlation in the social and economic sciences strong, if the measure

of correlation is > 0.5. In social and economic sciences any two characteristics are in gen-

eral only weakly connected, i. e. the measure of correlation is < 0.3 for a lot of bivariate

distributions of socio-scientific data, because social and economic interrelations are not

transparent at first glance, but multidimensional, flexible, and versatile.882 Furthermore, the

other nominally scaled measures of correlation show much higher values than Tau, but are

difficult to interpret except for Lambda. However, Lambda has the disadvantage of taking

the value 0, even if both variables are not independent.883 In our research the Tau values

are one half to one third of the other measures' ones.

A statistical correlation does not necessarily mean that there is a real cause and effect

relationship between two variables: First of all, with a 95 % confidence interval there is

still a 5 % chance that a measured correlation is coincidental. Secondly, without a theory

one cannot determine the cause and the effect. Thirdly, there might be a spurious causa-

tion, i. e. two characteristics change in the same way, although they are not connected.

They both are connected to and influenced by a third characteristic. In order to elucidate

these effects also statistically one has to analyze more than two variables collectively by

882 Müller-Benedict (2007: 197f.). 883 Müller-Benedict (2007: 203ff.).

Appendix A

153

multivariate data analysis.884 Multivariate analysis methods for only nominal data seem

less powerful and clear than the ones for metric data885 and are not widely available in

software packages886. If all variables are nominal, contingency table, configuration fre-

quency, log-linear, latent structure (if additional latent variables are used), and cluster

analysis can be employed. Most multivariate analysis methods require higher scales of

measurement.887 They should not be used without understanding them, their assumptions,

controversies, and theoretical foundations as modern software facilitate and some re-

searchers do.888

Knowledge of a risk pooling concept certainly is not only connected to the knowledge

of other risk pooling concepts and a company's industrial sector and size (number of em-

ployees), but also to other factors. Likewise, the application of a risk pooling concept

might be correlated to additional factors besides the awareness of this and other concepts,

the application of other concepts, and a company's sector of economic activity and size.

These other factors remain subject to further research.

884 Reynolds (1984: 72ff.), Müller-Benedict (2007: 267ff.). 885 Reynolds (1984: 78), Holtmann (2007). 886 Breakwell (2007: 441). 887 Holtmann (2007). 888 Breakwell (2007: 441f.).

Appendix A

154

Table A.2: Significant Correlations at the 5 % Level of the Knowledge of Risk Pooling Con-

cepts

a. Goodman and Kruskal’s Tau

b. Approximative significance based on chi-square approximation.

2.2.3 Association between Knowledge and Utilization of Risk Pooling

Concepts

There is a strong highly significant correlation between the knowledge of a risk pooling con-

cept and its application as the diagonal in the correlation matrix in Table A.3 at the end of this

section shows. This suggests that increasing practitioners' knowledge and understanding of risk

pooling by praxis-oriented research may increase its application. The strongest correlation ex-

ists between the knowledge and the application of virtual pooling (τ = 0.431, p = 0.000). That

means the error of predicting the variable utilization of virtual pooling can be reduced by

43.1 %, if the distribution of the variable knowledge of virtual pooling is known. Forty-six of

the 65 respondents who know virtual pooling also apply it. Of the 37 respondents who do not

know virtual pooling 36 also do not apply it. Consequently, one professional did not recognize

the concept perhaps by its name, but when reading the explanation he came to realize that his

Risk

Pooling

SRL PE Selective

Stocking

Commo‐

nality

Turnover

Curve

Product

Pooling

Product

Substi‐

tution

Demand

Reshape

Transship‐

ments

Postpone‐

ment

Virtual

Pooling

Capacity

Pooling

Central

Ordering

Order

Splitting

Risk

Pooling1

0.066a

(0.010b)

0.087

(0.003)

0.104

(0.001)

0.061

(0.013)

0.091

(0.002)

0.147

(0.000)

0.050

(0.025)

SRL 10.046

(0.031)

0.070

(0.008)

0.042

(0.040)

0.042

(0.040)

0.046

(0.032)

0.046

(0.032)

PE 10.067

(0.009)

Selective

Stocking1

0.059

(0.015)

0.038

(0.049)

0.098

(0.002)

0.042

(0.039)

Commo‐

nality

0.066

(0.010)

0.059

(0.015)1

0.056

(0.017)

0.046

(0.031)

0.044

(0.034)

0.088

(0.003)

Turnover

Curve

0.087

(0.003)

0.046

(0.031)1

0.042

(0.039)

0.052

(0.022)

0.054

(0.019)

0.054

(0.019)

0.045

(0.033)

0.071

(0.007)

Product

Pooling

0.104

(0.001)

0.056

(0.017)1

0.052

(0.022)

0.104

(0.001)

0.163

(0.000)

0.058

(0.016)

0.054

(0.020)

Product

Substitu‐

tion

0.052

(0.022)1

0.112

(0.001)

0.087

(0.003)

Demand

Reshape

0.061

(0.013)

0.038

(0.049)

0.042

(0.039)

0.104

(0.001)

0.112

(0.001)1

0.095

(0.002)

0.071

(0.007)

0.044

(0.035)

Trans‐

ship‐

ments

0.091

(0.002)

0.067

(0.009)

0.098

(0.002)

0.163

(0.000)

0.095

(0.002)1

0.135

(0.000)

0.139

(0.000)

Post‐

pone‐

ment

0.147

(0.000)

0.070

(0.008)

0.042

(0.039)

0.046

(0.031)

0.052

(0.022)

0.058

(0.016)

0.135

(0.000)1

0.116

(0.001)

0.042

(0.040)

0.101

(0.001)

Virtual

Pooling

0.050

(0.025)

0.042

(0.040)

0.054

(0.019)

0.087

(0.003)1

Capacity

Pooling

0.042

(0.040)

0.044

(0.034)

0.054

(0.019)

0.139

(0.000)

0.116

(0.001)1

Central

Ordering

0.045

(0.033)

0.071

(0.007)

0.042

(0.040)1

0.072

(0.007)

Order

Splitting

0.046

(0.032)

0.088

(0.003)

0.071

(0.007)

0.054

(0.020)

0.044

(0.035)

0.101

(0.001)

0.072

(0.007)1

Appendix A

155

company applies this concept. There are a few cases like that pertaining to the other risk pool-

ing concepts as well.

The next highest correlations exist between the knowledge and application of the SRL

(τ = 0.319, p = 0.000) and of commonality (τ = 0.317, p = 0.000).

The recognition of transshipments is significantly correlated with both the application

of selective stocking (τ = 0.088, p = 0.003) and risk pooling (τ = 0.071, p = 0.008), the

knowledge of postponement with the use of risk pooling (τ = 0.079, p = 0.005). This

highlights again that the respondents seem to mainly associate the popular concepts of

postponement and transshipments with risk pooling. The knowledge of transshipments

might favor the implementation of selective stocking, since products have to be exchanged

between locations as they are only stored at few locations for economical reasons.

Table A.3: Significant Correlations at the 5 % Level (except in the case Product Substitu-

tion/Demand Reshape) between Knowledge and Utilization of Risk Pooling Concepts



Utilization

Utilization

Knowledge

Risk

Pooling

SRL PE Selective

Stocking

Commo‐

nality

Turnover

Curve

Product

Pooling

Product

Substitu‐

tion

Demand

Reshape

Trans‐

ship‐

ments

Post‐

pone‐

ment

Virtual

Pooling

Capacity

Pooling

Central

Ordering

Order

Splitting

Centra‐

lization

past

Centra‐

lization

future

Decentra‐

lization

past

Decentra‐

lization

future

Risk Pooling0.202

a

(0.000b)

SRL0.319

(0.000)

0.047

(0.029)

PE0.291

(0.000)

Selective

Stocking

0.292

(0.000)

Commonality0.317

(0.000)

Turnover

Curve

0.288

(0.000)

0.058

(0.016)

0.053

(0.021)

0.039

(0.048)

Product

Pooling

0.098

(0.002)

Product

Substitution

0.119

(0.001)

0.037

(0.054)

Demand

Reshape

0.041

(0.043)

0.151

(0.000)

0.041

(0.042)

Transship‐

ments

0.071

(0.008)

0.088

(0.003)

0.304

(0.000)

Postponement0.079

(0.005)

0.178

(0.000)

0.039

(0.047)

Virtual Pooling0.045

(0.032)

0.431

(0.000)

Capacity

Pooling

0.301

(0.000)

Central

Ordering

0.128

(0.000)

Order Splitting0.141

(0.000)

Appendix A

156

2.2.4 Association of the Utilization of Different Risk Pooling Concepts

Most significantly and strongly associated is past decentralization with future decentralization

(τ = 0.253, p = 0.000), the utilization of product substitution and demand reshape (τ = 0.212,

p = 0.000), past centralization and decentralization (τ = 0.185, p = 0.000), the application of the

inventory turnover curve and transshipments (τ = 0.132, p = 0.000), commonality and product

pooling (τ = 0.127, p = 0.000), risk pooling and transshipments (τ = 0.121, p = 0.000), the

turnover curve and order splitting (τ = 0.117, p = 0.001), selective stocking and virtual pooling

(τ = 0.113, p = 0.001), transshipments and virtual pooling (τ = 0.113, p = 0.001), risk pooling

and postponement (τ = 0.109, p = 0.001), product substitution and transshipments (τ = 0.096,

p = 0.002), as well as product substitution and virtual pooling (τ = 0.096, p = 0.002) and vice

versa as shown in Table A.4 at the end of this section.

Eighty-four (99 %) of the 85 companies which did not decentralize in the past do not

intend to decentralize in the future. Eleven of the 17 companies which did decentralize will

continue to decentralize in the future. Eighty-four (88 %) of the 95 companies which do

not intend to decentralize their warehouse or logistics system, did not decentralize in the

past either. Six (86 %) of the seven companies planning to decentralize in the future, al-

ready decentralized in the past. It seems that these companies follow their warehouse or

logistics system strategy of decentralization or no decentralization consistently over time.

Fifty-one (94 %) of the 54 respondents who do not apply product substitution do not

apply demand reshape either. Twenty of the 48 respondents using product substitution

use demand reshape as well. Fifty-two of the 80 companies which do not reshape demand

do not substitute products in case of a stockout either. Twenty of the 22 demand reshaping

companies also use product substitution. It seems that companies which do not persuade

customers to buy a substitute product in case of a stockout mostly do not do so either, if the

desired product is available. This might occur, if a company does not sell substitute prod-

ucts. Ninety-one percent of demand reshapers also apply product substitution, perhaps be-

cause both strategies are similar in that they both substitute products.

If a company centralized in the past (49 companies), there was absolutely no decentra-

lization in the past. If a company conducted no centralization in the past, there was most-

ly no decentralization either: Of the 53 companies which did not centralize in the past only

17 decentralized in the past, 36 ones (68 %) did not. Past centralization and decentraliza-

tion thus show a rather negative correlation as the Phi value of -0.430 (p = 0.000) sug-

Appendix A

157

gests889. Forty-nine (58 %) of the 85 companies which did not decentralize centralized in

the past and none of the 17 companies which decentralized centralized in the past. It ap-

pears that decentralization excludes centralization and vice versa. The strategy of decentra-

lization, centralization, or no change is followed fairly consistently over time.

Thirty-four (97 %) of the 35 companies which do not transship do not use the inventory

turnover curve. Forty-three of the 67 transshipping companies utilize the turnover curve.

Thirty-four of the 77 responding companies which do not use the inventory turnover curve

do not take advantage of transshipments either. Twenty-four (96 %) of the 25 companies

using the turnover curve transship. One could assume that companies using the inventory

turnover curve attach great importance to inventory turnover. If therefore they tend to

mainly store fast movers at every location, this might explain why they also use transship-

ments to exchange e. g. slow movers between locations.

Forty (77 %) of the 52 companies which have not implemented component commonal-

ity do not use product pooling. Twenty-nine of the 50 companies using common compo-

nents also use product pooling. Forty of the 61 companies which have not implemented

product pooling have not implemented component commonality either. Twenty-nine

(71 %) of the 41 product pooling companies use common components as well. This comes

as no surprise as product pooling may rely on common components to satisfy customers

that were previously offered their own product variant with a single common product890.

Furthermore, both methods take advantage of standardization. “[S]tandardization enables

risk pooling across products, leading to lower inventories, and allows firms to use the in-

formation contained in aggregate forecasts more effectively”891.

Thirty-one (89 %) of the 35 companies not relying on transshipments likewise de-

clared that they did not apply risk pooling. Thirty-one of the 67 companies using trans-

shipments also use risk pooling. Thirty-six of the 67 companies which indicated that they

are not using risk pooling do not use transshipments either. Thirty-one (89 %) of the 35

ones using risk pooling do use transshipments as well. This highlights again that the re-

sponding professionals strongly associate risk pooling with transshipments.

Fifty-seven (74 %) of the 77 companies which do not use the turnover curve do not

apply order splitting either. Sixteen of the 25 companies employing the turnover curve

split orders as well. Fifty-seven (86 %) of the 66 companies not splitting orders do not use

889 Although we deal with nominal variables, we can exceptionally refer to a negative correlation here (cf.

Schulze 2007: 127). 890 Cachon and Terwiesch (2009: 330, 335). 891 Simchi-Levi et al. (2008: 357), cf. Reiner (2005: 434), Sheffi (2006, 2007: 186-193).

Appendix A

158

the turnover curve. Sixteen of the 36 companies that utilize order splitting use the invento-

ry turnover curve as well. Splitting an order into multiple orders or goods receipts may not

only decrease supplier lead time variability but also reduce average inventory and therefore

increase inventory turnover. The inventory turnover is reflected in the inventory turnover

curve. Inventory policies, which may be determined and controlled with the inventory

turnover curve, might lead to order splitting.

Twenty-seven of the 55 not virtually pooling companies do not store SKUs selectively

at warehouses. Thirty-nine (83 %) of the 47 companies which apply virtual pooling also

apply selective stocking. Twenty-five (71 %) of the 35 logistics professionals indicating

that their company does not rely on selective stocking do not pool virtually either. Thirty-

nine of the 67 companies using selective stock-keeping also apply virtual pooling. Virtual

pooling may entail selective stocking and vice versa: On the one hand, access to other loca-

tions' inventories via virtual pooling may favor a specialization in stock holding. On the

other hand, stocking products only at few locations due to cost considerations may necessi-

tate that these locations can access each other's inventories. For instance, a company may

choose to stock only fast movers at all regional warehouses and have slow movers drop-

shipped to customers or cross-filled. Thus inventories and demands at different locations

are pooled virtually.

Seventy-seven percent (27) of the companies not using transshipments (35), do not pool

virtually either. Fifty-eight percent (39) of the companies transshipping (67) use virtual

pooling in addition. Twenty-seven of the 55 responding companies which do not use vir-

tual pooling do not use transshipments either. However, thirty-nine (83 %) of the 47 vir-

tually pooling companies rely on transshipments. Extending a company's warehouse or

warehouses beyond its or their physical inventory to the inventory of other own locations

or of other companies' locations via information technology and the internet (virtual pool-

ing) often entails stock transfers between locations (transshipments). Virtual pooling re-

sembles transshipments, if it comprises drop-shipping892 or cross-filling893.

Of the 67 respondents who indicated not having implemented risk pooling 51 ones

(76 %) have not implemented postponement either. Twenty (57 %) of the 35 ones who

use risk pooling also use postponement. Fifty-one (77 %) of the 66 survey participants in-

dicating no postponement utilization also denied the use of risk pooling. Twenty (56 %) of

the 36 companies having implemented postponement also confirm the usage of risk pool-

892 Netessine and Rudi (2006: 845). 893 Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389).

Appendix A

159

ing. Consequently, the responding logisticians strongly associate risk pooling with post-

ponement.

Twenty-six (74 %) of the 35 companies that do not use transshipments do not substi-

tute products either. Thirty-nine of the 67 transshipping companies also use product sub-

stitution. Twenty-six of the 54 companies not substituting products do not use transship-

ments either. Thirty-nine (81 %) of the 48 product substitutionists use transshipments in

addition. This shows that product substitution and transshipments can be applied side by

side just like in the case of Papierco. For this company product substitution is the cheaper

option, so that it should only use transshipments as an alternative, if it is not possible to

substitute products in case of a stockout.

The same applies to virtual pooling: Thirty of the 48 companies which rely on product

substitution pool virtually as well. Thirty-seven (69 %) of the 54 ones not substituting

products, do not apply virtual pooling either. Thirty-seven (67 %) of the 55 companies not

pooling virtually do not use product substitution either. Thirty of the 47 ones pooling vir-

tually also substitute products.



form postponement at best only weakly for our sample: Postponement is only weakly and

at the 5 % level just not statistically significantly associated anymore with transshipments

(τ = 0.035, p = 0.059) and selective stocking (τ = 0.035, p = 0.059). Twenty-eight (42 %)

of the 67 companies stocking selectively thereby centralizing inventory also apply post-

ponement. Twenty-seven (77 %) of the 35 ones not using selective stocking do not use

postponement either. The same applies to transshipments.

Postponement is statistically significantly independent of past (τ = 0.000, p = 0.903)

and future centralization (τ = 0.009, p = 0.350). The contrary is true for its association with

risk pooling (τ = 0.109, p = 0.001) and component commonality (τ = 0.068, p = 0.009).

Forty of the 66 not postponing companies do not use component commonality. Twenty-

four (67 %) of the 36 postponing companies also employ common components. Forty

(77 %) of the 52 companies not applying component commonality do not apply postpone-

ment either. Twenty-four of the 50 users of common components also rely on postpone-

ment. This shows that the implementation of postponement and commonality may go hand

Appendix A

160

in hand894 as we already highlighted describing the Risk Pooling Decision Support Tool.

The implementation of postponement may even require component commonality.895

Table A.4: Significant Correlations at the 5 % Level between the Utilization of Risk Pooling

Concepts



894 Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al.

(1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al. (2008: 345).

895 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347).

Risk

Pooling

SRL PE Selective

Stocking

Commo‐

nality

Turnover

Curve

Product

Pooling

Product

Substi‐

tution

Demand

Reshape

Trans‐

ship‐

ments

Post‐

pone‐

ment

Virtual

Pooling

Capacity

Pooling

Central

Ordering

Order

Splitting

Centra‐

lization

past

Centra‐

lization

future

Decentra‐

lization

past

Decentra‐

lization

future

Risk

Pooling 10.066

a

(0.010b)

0.068

(0.009)

0.052

(0.022)

0.121

(0.000)

0.109

(0.001)

0.059

(0.014)

SRL 0.066

(0.010)1

PE1

0.077

(0.005)

0.039

(0.047)

0.074

(0.006)

0.069

(0.008)

Selective

Stocking1

0.051

(0.023)

0.068

(0.009)

0.113

(0.001)

0.045

(0.033)

0.038

(0.049)

Commo‐

nality1

0.127

(0.000)

0.068

(0.009)

Turnover

Curve

0.068

(0.009)1

0.04

(0.045)

0.132

(0.000)

0.088

(0.003)

0.117

(0.001)

Product

Pooling

0.127

(0.000)1

0.05

(0.025)

Product

Substi‐

tution

0.052

(0.022)

0.077

(0.005)

0.051

(0.023)1

0.212

(0.000)

0.096

(0.002)

0.096

(0.002)

Demand

Reshape

0.039

(0.047)

0.04

(0.045)

0.212

(0.000)1

0.079

(0.005)

0.077

(0.005)

Transship‐

ments

0.121

(0.000)

0.074

(0.006)

0.068

(0.009)

0.132

(0.000)

0.096

(0.002)1

0.113

(0.001)

Postpone‐

ment

0.109

(0.001)

0.068

(0.009)1

Virtual

Pooling

0.059

(0.014)

0.113

(0.001)

0.088

(0.003)

0.096

(0.002)

0.079

(0.005)

0.113

(0.001)1

0.079

(0.008)

Capacity

Pooling1

0.052

(0.022)

Central

Ordering

0.052

(0.022)1

0.058

(0.016)

Order

Splitting

0.069

(0.008)

0.117

(0.001)

0.079

(0.008)1

Centra‐

lization

past

0.058

(0.016)1

0.185

(0.000)

Centra‐

lization

future

1

Decentra‐

lization

past

0.045

(0.033)

0.05

(0.025)

0.077

(0.005)

0.185

(0.000)1

0.253

(0.000)

Decentra‐

lization

future

0.038

(0.049)

0.253

(0.000)1

Appendix A

161

2.2.5 Risk Pooling Knowledge and Utilization in the Responding

Manufacturing and Trading Companies

Figure A.2: Risk Pooling Knowledge and Utilization in the Sample Manufacturing and

Trading Companies

Appendix A

162

When we subdivide the original sample for subanalyses in this section, we decrease our sample

size and therefore enlarge our confidence intervals896.

At the 5 % level Pearson's and Yates' chi-square and Fisher's exact test revealed signifi-

cant differences between manufacturing and trading companies in employing product sub-

stitution (Pearson's chi-square χ2 = 8.01, degrees of freedom df = 1, p = 0.004652), com-

monality (χ2 = 7.84, df = 1, p = 0.00511), and transshipments (χ2 = 6.19, df = 1,

p = 0.012847), in the knowledge of commonality (χ2 = 5.47, df = 1, p = 0.019346), and in

the utilization of postponement (χ2 = 4.52, df = 1, p = 0.033501897) in descending order of

asymptotic significance (two-sided).

The 75 manufacturing companies surveyed know central ordering, product substitution,

selective stocking, and order splitting the most, followed by transshipments, product pool-

ing, commonality, capacity pooling, virtual pooling, risk pooling, postponement, demand

reshape, the PE, inventory turnover curve, and SRL.

The 27 trading companies recognize central ordering, product substitution, selective

stocking, transshipments, order splitting, product pooling, the PE, virtual pooling, capacity

pooling, demand reshape, commonality, risk pooling, the inventory turnover curve, post-

ponement, and the SRL in decreasing order of awareness.

The manufacturing and trading companies do not differ statistically significantly at the

5 % level in their knowledge of the various risk pooling concepts, except for commonality.

Seventy-six percent of the manufacturing and 52 % of the trading companies are aware of

this concept.

Selective stocking (63 %), central ordering (61 %), transshipments (59 %), and com-

monality (57 %) are the concepts most frequently applied by the manufacturers. Capacity

pooling (47 %), centralization, virtual pooling, product pooling, postponement, product

substitution, order splitting, risk pooling, the PE, inventory turnover curve, demand re-

shape, the SRL, and decentralization follow in order of descending employment.

Trading companies apply transshipments (85 %), central ordering (78 %), selective

stocking (74 %), and product substitution (74 %) the most, followed by centralization

(63 %), virtual pooling, order splitting, risk pooling, the PE, product pooling, demand re-

shape, commonality, capacity pooling, the inventory turnover curve, postponement, decen-

tralization, and the SRL.

896 Vockell and Asher (1995: ch. 8). 897 However, in this case χY = 3.58 with df = 1 and p = 0.058479, but p = 0.037049 in Fisher's exact test.

Appendix A

163

All concepts are more widely used in the trading companies than in the manufacturing

companies, except for the SRL, commonality, the inventory turnover curve, product pool-

ing, postponement, and capacity pooling. As already mentioned above, this relationship is

statistically significant only for product substitution, commonality, transshipments, and

postponement at the 5 % level. This supports our hypothesis from the Risk Pooling Deci-

sion Support Tool that component commonality, postponement, and capacity pooling

are rather applied by manufacturers and might be more suitable in a manufacturing en-

vironment. However, the utilization of capacity pooling in manufacturing and trading

companies is just not statistically significantly different at the 5 % level anymore

(χ2 = 3.53, df = 1, p = 0.060268).

Forty-one percent of the manufacturing companies apply postponement. This matches

the more than 40 % of the manufacturers surveyed by Kisperska-Moroñ (2003: 131) in

Upper Silesia, Poland that gear total production towards customer orders.

Thirty-seven percent of the 27 electronics (classification numbers 30, 31, and 32) and

automotive (34) and 40 % of the five food (15) and clothing (18) manufacturers employ

postponement. Consequently, with our sample we cannot support at the 5 % level Van

Hoek (1998b), who finds that postponement is extensively applied in electronics and au-

tomotive and less extensively applied in food and clothing. The utilization of postpone-

ment by electronics and automotive and food and clothing manufacturers in our sample is

independent in the Fisher Exact Probability Test898 (p (two-tailed) = 1). It differs neither in

these two nor in the four groups significantly at the 5 % level. However, Van Hoek's

(1998b) observation may apply to the whole population, as the confidence interval for the

aforementioned conditions is very broad with 18.86 for electronics and automotive and

43.83 for food and clothing. For the same reasons as given earlier this confidence interval

can only serve as a crude estimate here. Only five answers from food and clothing manu-

facturers are probably not enough to compare postponement application between different

industrial sectors.

898 The Fisher Exact Probability Test is used, because some contingency table (crosstab) cells have expected

counts less than 5. Nevertheless, Pearson's and Yates' chi-square test led to the same conclusion.

Appendix A

164

2.2.6 Knowledge and Utilization of the Different Risk Pooling Concepts in

Small and Large Responding Companies

Figure A.3: Knowledge and Utilization of the Different Risk Pooling Concepts in Small and

Large Responding Companies

Appendix A

165

The answers of the 33 small (having less than 500 employees) and 69 large companies (having

500 or more employees according to the Deutsches Institut für Mittelstandsforschung (German

Institute for Midium-sized Businesses Research)) are independent (the null hypothesis that

there is no significant relationship between the answers cannot be rejected) in Pearson's and

Yates' chi-square and Fisher's exact test at the 5 % level, except for the usage of risk pooling

(χ2 = 5.63, df = 1, p = 0.017656), centralization in the past (χ2 = 4.75, df = 1, p = 0.029298),

and postponement (χ2 = 4.24, df = 1, p = 0.039482899). This means only for these last three

variables the distribution in the two groups of small and large companies differs statistically

significantly900, most significantly for risk pooling.

The small companies tend to have more knowledge of selective stocking, demand re-

shape, central ordering, product pooling, and order splitting, while a higher percentage of

large ones know the SRL and postponement. The large companies apply all concepts more

than small companies (especially risk pooling, postponement, transshipments, capacity

pooling, the PE, and product pooling) except for centralization in the past, demand re-

shape, commonality, product substitution, and central ordering in order of descending per-

centage difference of companies applying the respective concept. Hence, we can agree

with Huang and Li (2008b: 12) that large companies may apply postponement more than

small ones, since they may be better able to afford the redesign of products and/or

processes usually required by postponement901.

899 However, in this case χY = 3.37 with df = 1 and p = 0.066394, but p = 0.047623 in Fisher's exact test. 900 This means that one can be certain that this statistic is dependable, the difference is genuine and not by

coincidence. It does not mean that the difference is large, important, or useful (Walonick 2009). 901 Ernst and Kamrad (2000), Aviv and Federgruen (2001b).

166

3 Critical Appraisal

We need to point out that the assumption of the significance test of random sample data may

be violated. For population data any crosstable differences are real and thus significant. With

non-random sample data we cannot establish significance.902 However, significance tests are

sometimes used as rough approximations.903 For criticism of significance testing you may e. g.

refer to Carver (1978), Cohen (1994), and Thompson (1996). Statistical significance does not

tell if a research's results will reoccur904 or the strength and generalizability of relationships in a

sample and hence may divert attention from more crucial concerns905.

Although a thorough research process was followed, the limited representativeness of

this survey has to be acknowledged. This should be remedied in another survey by a higher

response rate. However, this might be difficult, as response rates for academic studies are

low906 and have been declining over the last years907. Perhaps there are so few surveys in

logistical research, since it is very difficult to obtain a random or at least representative

sample because of low response rates as we experienced. A lot of companies are swamped

with surveys and/or have a policy of not answering surveys. Some researchers pay compa-

nies to take part in surveys or give them other perquisites, which might also lead to a re-

sponse bias. Practitioners should not criticize business research as too theoretical on the

one hand and not take part in surveys on the other hand.

As it is laborious to design and administer surveys, the usually low response rates dis-

appoint the researcher and “imperil the strength of the research findings”908, and survey

research is prone to so many biases and errors909, one perhaps should consider other empir-

ical research. Netessine (2005: 6), for instance, suggests using university research data-

base, publicly available, consulting company, or industry journal data. Still for a Ph.D.

student with little funds it is difficult to access some of these data sources that are subject

to charges.

Besides, some specific data are not available at all or insufficient. For example, we

could not obtain any information about the number of warehouses from business and logis-

902 Garson (2009). 903 Dorofeev and Grant (2006: 253f.), Garson (2009). 904 Carver (1978). 905 Thompson (1994). 906 Bickard and Schmittlein (1999), Goldsby and Stank (2000). 907 Baruch (1999). 908 Griffis et al. (2003: 237). 909 Groves et al. (2004: 39ff., 377f., 380).

Appendix A

167

tics associations and federal statistical offices in Germany and the U.S. to derive how in-

ventories changed in dependence of the number of warehouses compared to SRL predic-

tions or how the number of warehouses changed over time. Some researchers expected the

number of warehouses to increase with increasing fuel costs.

Furthermore, the number of companies in the industrial sectors in different publications

of the German Federal Statistical Office differs, as it receives its information from different

data sources. If the industrial sectors are broken down further, only companies with 20 or

more employees are considered.910 If all companies with any number of employees are

considered, they are not subdivided into detailed industrial sectors.911 This impaired our

retrospective quota sampling.

Another survey could also shed light onto the companies' reasons for and against as well

as the manner, degree, benefits, and costs of applying the risk pooling concepts, as we in-

tended in the six-page version of this survey that yielded a uselessly low response rate. As

risk pooling can affect the whole supply chain, another survey could consider a supply

chain wide perspective rather than single companies.

A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It

appears that mainly transshipments and postponement are associated with risk pooling.

Although at least in our sample the risk pooling concepts are known fairly well (central

ordering, product substitution, and selective stocking the most), only selective stocking,

transshipments, and central ordering are widely applied. Transshipments912 are more im-

portant and applied, postponement913 and product pooling914 less than suggested by some

publications mostly for other regions.

Nearly half the sample centralized its warehouse or logistics system in the past. This is

less than overall in Europe915. In contrast to the expected trend to decentralize due to in-

creasing transportation costs, only seven percent will increase, six percent even decrease

the number of warehouse or production locations in the future. It seems that the companies

are very consistent in their strategy of centralization, decentralization, or no change over

time.

910 For example Statistisches Bundesamt Deutschland (2009i: 371). 911 For example Statistisches Bundesamt Deutschland (2009i: 378). 912 CLM (1995), Herer et al. (2006). 913 CLM (1995: 209), McKinnon and Forster (2000: 5), Chiou et al. (2002), Alfaro and Corbett (2003: 12),

Oracle (2004), Huang and Li (2008b). 914 Alfaro and Corbett (2003: 12). 915 CLM (1995).

Appendix A

168

The utilization and knowledge of a risk pooling concept are correlated. This suggests

that improving the knowledge about risk pooling may increase its application. Research

needs to convey to practitioners under what conditions and how the different risk pooling

concepts can be applied successfully. This research constitutes one step in this direction.

Prominently associated is past decentralization with future decentralization, the utiliza-

tion of product substitution and demand reshape, past centralization and decentralization

(the only negative correlation), the application of the inventory turnover curve and trans-

shipments, commonality and product pooling, risk pooling and transshipments, the inven-

tory turnover curve and order splitting, selective stocking and virtual pooling, transship-

ments and virtual pooling, risk pooling and postponement, product substitution and trans-

shipments, product substitution and virtual pooling, as well as postponement and commo-

nality and vice versa.



form postponement at best only weakly for our sample.

Trading companies seem to apply transshipments and product substitution more than

manufacturing companies. The opposite is true for commonality and postponement. In

contrast to Van Hoek (1998b) our sample shows no significant difference in the application

of postponement by electronics, automotive, food, and clothing manufacturers.

More large companies appear to use risk pooling and postponement than smaller ones,

perhaps because they can afford to invest in expensive risk pooling strategies as suggested

by Huang and Li (2008b: 12). More small companies have centralized their warehouse or

logistics system in the past than large ones in our sample.

Our survey shows that different risk pooling methods are and can be applied together as

we already suggested in the Risk Pooling Decision Support Tool and the Papierco example.

169

4 Questionnaire

Figure A.4: Questionnaire

use?YesNo

YesNo

Yes Yes

Yes Yes

Yes Yes

Yes Yes

(planned) warehouse throughput (shipments from the warehouse or sa les).

Yes Yes

or reducing the number of productsown product version with fewer products.)

Yes Yes

the original customer wish is out of stockYesNo

YesNo

YesNo

YesNo

Yes Yes

Yes

No

Yes

No

Yes Yes

YesNo

YesNo

Yes Yes

Yes Yes

Yes

No No

2 Number of employees in Germany

3 Your position (e. g. logistics manager)

1 Line of business

No No

No No

17 Central Ordering for several locations and later allocation of the orders (perhaps by a depot)

6 The Portfolio Effect shows the reduction in aggregate safety stock by consolidating several ware-houses' inventories in one warehouse in percent.

10 Product Pooling (Unification of several product designs to a single generic or universal design

b) Do you intend to centralize your warehouse/logistics system?

20 a) Did you decentralize your warehouse/logistics system (increase the number of warehouse

production locations)?

or production locations)?b) Do you intend to decentralize your warehouse/logistics system?

warehouses or stores) for example in case of a stockout. No No

19 a) Did you centralize your warehouse/logistics system (reduce the number of warehouse or Yes

Yes

Yes

No

No

No

No

4 Risk Pooling (Demand and/or lead time variability is reduced, if one aggregates demands and/or lead times e. g. across locations, because it becomes more likely that higher-than-average de-mands and/or lead times will be offset by lower-than-average ones. This reduction in variability allowsto reduce safety stock and therefore reduces average inventory without reducing the service level.)5 Square Root Law (Total (safety) stock in n warehouses = (safety) stock in 1 centralizedwarehouse * square root of the number of warehouses n.) No No

7 Selective Stock Keeping/Specialization (Reducing inventory carrying cost treating products

11 Product Substitution (One tries to make customers buy another alternative product, because

12

No No

by Dipl.-Kfm. Gerald Oeser

Do you know the following concepts? Does your company use them? Known? In

No No

to the distribution points or requisitioners according to recent demand inform ation.

No No

9 The Inventory Turnover Curve shows average inventory in dependence of the inventorythroughput for a specific company. It can be used to estimate the average inventory for any

thereby serving demands that were previously served by their No No

riability of demand.) No No8 Component Commonality (Products are designed sharing components. This reduces the va-

ty of demand and inventory costs.)

production locations)?

Please push to send answers

Survey on Risk Pooling in Business Log

13 Transshipments/Inventory Sharing Inventory transfers among locations (e. g. between

differently without reducing the service level substant ially. For example, products with a low turn-

14 Delayed Product Differentiation and Postponement

16 Capacity Pooling

18 Order plitting

15 Virtual Inventory/Warehouse/Pooling:

170

5 Answers

1 = Yes, 0 = No

Respondent

Industry

classification

Employees

Risk Pooling

SRL

PE

Selective

Stocking

Commonality

Turnover Curve

Product Pooling

Product

Substitution

Demand Reshape

Transshipments

Postponement

Virtual Pooling

Capacity Pooling

Central Ordering

Order Splitting

Risk Pooling

SRL

PE

Selective

Stocking

Commonality

Turnover Curve

Product Pooling

Product

Substitution

Demand Reshape

Transshipments

Postponement

Virtual Pooling

Capacity Pooling

Central Ordering

Order Splitting

Centralization

past

Centralization

future

Decentralization

past

Decentralization

future

1 52.42 16,000 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1

2 52.42 5 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0

3 29 2,000 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0

4 29 3,000 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0

5 29 100 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0

6 34 60 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0

7 25 190 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0

8 31 2,000 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0

9 31 50 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1

10 37 120 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0

11 33 133,000 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0

12 34 78,000 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

13 32 500 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0

14 29 150 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0

15 52.42 100 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0

16 30 1,600 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0

17 34 13,000 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0

18 37 9,000 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

19 52.11 121,000 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1

20 51.46 30 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0

21 45.2 120 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0

22 25 143 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0

23 35 1,500 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0

24 29 47,296 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0

25 31 1,000 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0

26 52.11 170,000 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0

27 52.42 20 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0

28 52.11 150 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0

29 52.11 65 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0

30 28 346 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0

31 16 2,500 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0

32 15 500 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0

33 34 2,000 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

34 29 600 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1

35 52.42 12,000 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0

36 51.53.1 22 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0

37 51.46 20 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0

38 29 114,000 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0

39 15 800 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0

40 21 100 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0

41 52.42 7,000 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 0

42 34 10,000 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0

43 34 25,103 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0

44 37 500 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0

45 36 120 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0

46 34 12,000 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0

47 15 2,000 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0

48 29 36,000 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0

49 32 12,600 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0

50 52.11 15,000 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0

51 31 200 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0

52 31 550 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0

53 34 5,000 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0

54 34 2,000 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 0

55 52.11 73,000 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0

56 35 8,000 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0

57 34 95,500 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0

58 52.42 10,000 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0

59 35 3,000 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0

60 52.46 14,000 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0

61 33 100 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0

62 24 50 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0

63 28 900 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0

64 40 66,000 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0

65 27 10 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0

66 31 150 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0

67 28 150 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0

68 34 27,000 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0

69 34 37,000 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0

70 52.42 29,000 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0

71 22 850 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0

72 26 1,000 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0

73 31 20 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0

74 28 1,200 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0

75 11 7,000 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0

76 29 50,000 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0

77 51.53.1 9,500 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0

78 52.48.6 110 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1

79 24 60,000 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0

80 52.11 50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0

81 29 850 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1

82 29 12,800 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0

83 18 1,980 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0

84 15 3,000 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0

85 24 10,767 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0

86 52.42 6,342 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0

87 36 242 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0

88 29 107 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0

89 51.88 40 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0

90 51.47.8 65 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0

91 21 5,700 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0

92 22 3,200 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0

93 52.42 956 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0

94 29 1,000 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0

95 34 60,000 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0

96 40 1,850 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0

97 32 60,000 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0

98 32 6,000 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0

99 32 4,500 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0

100 51.47.8 9 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0

101 34 182,739 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0

102 51.47.8 1,652 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1

KNOWLEDGE UTILIZATION

Appendix A

171

Table A.5: Survey Participants' Answers to the Questionnaire

Industry Classification Description

11 Extraction of crude petroleum and natural gas; service activities incidental to oil and gas

extraction, excluding surveying

15 Manufacture of food products and beverages

16 Manufacture of tobacco products

18 Manufacture of wearing apparel; dressing and dyeing of fur

21 Manufacture of pulp, paper and paper products

22 Publishing, printing and reproduction of recorded media

24 Manufacture of chemicals and chemical products

25 Manufacture of rubber and plastic products

26 Manufacture of other non‐metallic mineral products

27 Manufacture of basic metals

28 Manufacture of fabricated metal products, except machinery and equipment

29 Manufacture of machinery and equipment n.e.c.

30 Manufacture of office machinery and computers

31 Manufacture of electrical machinery and apparatus n.e.c.

32 Manufacture of radio, television and communication equipment and apparatus

33 Manufacture of medical, precision and optical instruments, watches and clocks

34 Manufacture of motor vehicles, trailers and semi‐trailers

35 Manufacture of other transport equipment

36 Manufacture of furniture; manufacturing n.e.c.

37 Recycling

40 Electricity, gas, steam and hot water supply

45.2 Building of complete constructions or parts thereof; civil engineering

51.46 Wholesale of pharmaceutical goods

51.47.8 Wholesale of paper and paperboard, stationery, books, newspapers, journals and periodicals

51.53.1 Non‐specialized wholesale of wood, construction materials and sanitary equipment

51.88 Wholesale of agricultural machinery and accessories and implements, including tractors

52.11 Retail sale in non‐specialized stores with food, beverages or tobacco predominating

52.42 Retail sale of clothing

52.46 Retail sale of hardware, paints and glass

52.48.6 Retail sale of games and toys

172

Appendix B: Proof of the Square Root Law for Regular,

Safety, and Total Stock

Based on a numerical example in Ballou (2004b: 379f.) and in a manner different from the

flawed916 one in Maister (1976), we formally prove that under certain assumptions the SRL

applies to regular, safety, and total stock.

Let average regular stock at location i be the economic order quantity (EOQ) Qi divided

by two:

, (B1)

where di is demand at warehouse i, S the fixed order cost, I the inventory carrying cost rate and

C the product value per unit. Regular system inventory for n decentralized warehouses equals

∑ ∑. (B2)

Regular stock in one centralized warehouse is

916 Das (1978: 334) correctly remarks “But Maister's proof is incorrect due to a combination of faulty algebra

and possible misprints” without pointing out the mistakes. Indeed, we found e. g. that it is supposed to be

. . . ∑ instead of . . . ∑ (Maister 1976: 129) and ∑

∑ instead of

∑

∑ (Maister 1976: 130). The expression

∑

∑∑ (Maister 1976: 130) is also in-

correct. Furthermore, it has to be 0.2 0.005 instead of 0.02 0.005 (Maister 1976: 129).

Changing a three-location to a one-location system reduces inventory by 42 (not 43) % and changing a ten-location to a four-location system reduces inventory by 37 (not 38) % according to the SRL (Maister

1976: 131). Maister (1976: 132) wrongly states ∑

∑ √ , although he ear-

lier notes that ∑ 1 (Maister 1976: 127). He also explains “If the original decentralised system had 16 locations, and inventory costs account for one-half of total costs in this system, then inventory savings

from centralisation equal

1√

. But transportation must represent 1 , or

in the decentralised system. Hence, we can afford to almost double transportation expenses and still retain a system cost less than in the original system” (Maister 1976: 133). However, we can only afford 1.75 times and not almost double the transportation cost or, in other words, we could only increase transporta-tion cost by 75 % at the most. But if all inventory savings were spent on increased transportation costs, we would not retain a system cost less than in the original system. The centralized and decentralized sys-tem costs would be equal and we would be indifferent between them. Nevertheless, Das (1978: 333) also misprinted 1 and incorrectly uses the equality instead of the ap-proximation sign, although the power (square root) function cannot equal a linear one. Furthermore, , , . . . , should be , , . . . , and ∑ should be ∑ (Das 1978: 334). Das (1978: 332) also

refers to a proof to his solution in the appendix, but the journal does not contain it. Professor emeritus Chandrasekhar Das, College of Business Administration, University of Northern Iowa, Department of Management, agreed with us and kindly rewrote the proof, as it was not available at the publisher any-more in 2009 (personal correspondence on February 27, 2009).

Appendix B

173

∑

∑.

(B3)

Regular stock in one centralized warehouse times a factor α equals regular system stock

in n decentralized warehouses:

·∑

·∑

∑

∑

∑

∑·∑

∑.

(B4)

If demand at each warehouse is equal (d), the regular system inventory for n decentra-

lized warehouses equals the one in one centralized warehouse times the square root of the

number of warehouses n:

·∑ √

∑·√

√·√ √ √

√ √

· √ .

(B5)

This means the SRL applies to regular stock, if an EOQ order policy is followed, the

fixed cost per order and the per unit stock holding cost (inventory carrying cost rate times

the product value per unit), demand at every location, and total system demand is the same

both before and after centralization.917 However, according to Maister (1976: 128f.) the

SRL can also be “a good approximation when demand rates at all the field locations are not

equal”. If regular inventory in each of n locations in the decentralized system (RSs) is consi-

dered the following relationship holds:

·√ ·√

√ √ √√ . (B6)

This corresponds to equation 9-28 in Ballou (2004b: 380): √ . Safety stock in warehouse i is

√ , (B7)

where z is the same safety factor for every warehouse, sdi the standard deviation of demand at

warehouse i, and LT the constant replenishment lead time for every warehouse.

System safety stock in n decentralized warehouses is

√ ∑ . (B8)

917 Cf. Maister (1976: 125, 127, 131).

Appendix B

174

If the demands are uncorrelated, safety stock in the centralized warehouse is

√ ∑ . (B9)

Safety stock in one centralized warehouse times a factor α equals systemwide safety

stock in n decentralized warehouses:

· √ ∑ · √ ∑

√ ∑

√ ∑

∑

∑·

∑

∑.

(B10)

If the standard deviation of demand at each warehouse is equal (sd), the systemwide

safety stock in n decentralized warehouses is equal to the safety stock in one centralized

warehouse times the square root of the number of warehouses n:

·∑

∑· ·

√

· √ √

√· √ .

(B11)

This means the SRL applies to safety stock, if demands at the decentralized locations

are uncorrelated918, the variability (standard deviation) of demand at each decentralized

location919, the safety factor (safety stock multiple)920 and average lead time are the same

at all locations both before and after consolidation, average total system demand remains

the same after consolidation921, no transshipments occur922, lead times and demands are

independent and identically distributed random variables and independent of each other923,

the variances of lead time are zero924, and the safety-factor (kσ) approach is used to set

safety stock for all facilities both before and after consolidation925.

If demands at the warehouses are correlated, the SRL does not even yield an approxima-

tion. The safety stock savings through centralization decrease with increasing correlation

between demands at the warehouses and become zero with perfectly positive correlation.926

Total inventory is the sum of regular and safety stock.927 Therefore total inventory in the

decentralized system TId with n warehouses equals total inventory in one centralized ware-

house TIc times the square root of the number of warehouses n:

918 Maister (1976: 132). 919 Maister (1976: 130). 920 Maister (1976: 132). 921 Evers and Beier (1993: 110), Evers (1995: 4). 922 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 923 Evers and Beier (1993: 110), Evers (1995: 4). 924 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 925 Maister (1976: 129). 926 Maister (1976: 130).

Appendix B

175

· √ · √ · √ · √ . (B12)

The SRL applies to total inventory, if the assumptions stated above of the SRL both as

applied to regular and safety stock hold. For a critical review of these assumptions please

refer to Maister (1976: 125, 132f.), Das (1978: 331f.), McKinnon (1989: 102ff.), and Evers

(1995: 2, 14f.).

It should be checked whether the conditions or assumptions necessary for the SRL to hold

(necessary conditions) are also sufficient conditions, i. e. whether, if the SRL holds, these condi-

tions also automatically apply. This analysis, however, is beyond the scope of this thesis.

Ballou (2004b: 380) incorrectly states “The square-root rule […] measures only the

regular stock reduction, not both regular and safety stock effects […]. Assuming that an

inventory control policy based on the EOQ formula is being followed and that all stocking

points carry the same amount of inventory, the square-root rule can be stated as follows:

√ […]

where

AILT = the optimal amount of inventory to stock, if consolidated into one location in dollars,

pounds, cases, or other units

AILi = the amount of inventory in each of n locations in the same units as AILT

n = the number of stocking locations before consolidation”.

Traditionally the SRL has been mainly applied to safety stock, but as proven above it is also

valid for regular stock or both regular and safety stock, if the respective necessary assumptions

stated above hold. If it is only applied to regular stock as in Ballou's case, all the assumptions of

the SRL as applied to regular stock enumerated above must apply, not only the two mentioned

by Ballou here. Ballou's formulation of the second assumption may confuse, as Maister (1976:

125) assumes “the demand rates at all the field locations are equal”.928

927 Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou

2004b: 330f.), which is neglected here. 928 Professor emeritus Ronald H. Ballou, Weatherhead School of Management, Case Western Reserve Uni-versity, agreed with us in a personal correspondence on May 15, 2007.

176

Appendix C: What Causes the Savings in Regular Stock

through Centralization Measured by the SRL?

The total EOQ in the decentralized system is

∑ . (C1)

The EOQ in the centralized system is

∑ . (C2)

Due to the subadditive property of the square root, the sum of the square root of the de-

mands at the locations i is greater than or equal to the square root of the sum of these de-

mands:

∑ ∑ . (C3)

Therefore, the total EOQ in the decentralized system (the sum of the EOQs of the loca-

tions i) is greater than or equal to the EOQ in the centralized system:

∑ ∑ . (C4)

However, the total EOQ in the decentralized and centralized system are only equal, if

demands or demand forecasts at at least n-1 locations are zero929, which is unusual:

∑ ∑ ∑ ∑

∑ 2∑ ∑ ∑ ∑ ∑ 0. (C5)

If n-1 di equal zero, (C4) becomes

(C6)

for this single non-zero di. If all di are zero, (C4) becomes

0 . (C7)

Therefore, if demands (at at least two locations) are larger than zero, the EOQ and

therefore the average regular inventory and thus the inventory holding costs are lower in

the centralized system. However, under the above condition the EOQ per decentralized

location i is less than the one for the centralized one, as n > 1:

929 This theoretically questions Wanke and Saliby's (2009: 680) general statement that “[t]he cycle stock

savings are based on the fact that the square-root of the aggregate demand is always smaller than the sum of the square roots of individual demands”.

Appendix C

177

∑ ∑ ∑ . (C8)

The total number of orders in the decentralized system is

∑ ∑ ∑ ∑ . (C9)

The number of orders in the centralized system is

∑ ∑

∑∑ . (C10)

Due to the subadditive property of the square root, the total number (the sum of the

numbers) of replenishment orders in the decentralized system is greater than or equal to the

number of orders in the centralized one:

∑ ∑ ∑ ∑ . (C11)

In analogy to (C5)-(C7), if demands (at at least two locations) are larger than zero930,

the total number of replenishment orders in the decentralized system is greater than the

number of orders in the centralized one resulting in lower total order fixed costs in the cen-

tralized system. However, in this case the number of orders (lead times) per decentralized

location i is smaller than the number of orders for the centralized one931, as n > 1:

∑ ∑

∑

∑

∑

∑ ∑ .

(C12)

The savings in regular stock stem from the assumption of an EOQ order policy, constant

fixed costs per order, holding costs (inventory carrying cost rate times product value per

unit), and total demand for all locations before and after centralization. In the centralized

system, usually the total order fixed cost is lower because of less orders and the inventory

holding cost is lower due to a smaller EOQ than in the decentralized system.932

930 Ronen (1990), Zinn et al. (1990), and Evers (1995) neglect this. 931 Cf. Ronen (1990: 132). Zinn et al. (1990: 139) state that “inventory centralization will increase the num-

ber of lead times per year if an EOQ ordering quantity is used”. “[A]n increase in the number of lead times with the same expected annual demand decreases the average base stock” (Zinn et al. 1990: 141). This is true for the centralized warehouse compared to each decentralized one.

932 Evers (1995: 5).

178

Appendix D: Tables

Table D.1: Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies

1=Yes, 0=No

Number 1 2 3 4 5 6 7 8 9 10 11

Country Denmark Germany Germany France Sweden U.S. U.S. Italy U.S. U.S. Germany

Industry Paper

wholesale

Paper

production

Paper

production

Reusable

packagingAutomotive Utilities Electronics

Paper

wholesale

Semicon‐

ductors

Wireless

telecom

Paper

wholesale

Employees 65 40,000 200 10,000 60,000 1,850 60,000 9 4,500 6,000 1,652

Position

Logistics

Manager

Logistics

Analyst

Director of

Logistics &

IT

Marketing

Manager

Functional

Integrator

Lead

Materials

Manager

Supply

Chain

Optimiza‐

tion

Manager

Adminis‐

trator

Vice‐

president

Supply

Chain

Supply

Chain

Manager

Director of

Logistics

Central

warehouses2 0 5 10 5 2 0 1 1 2 0

Regional

warehouses0 100 0 10 66 8 24 2 5 12 21

Demands iid

(are indepen‐

dent and

identically

distributed

random

variables)

0 1 0 0 0 0 0 0 1 1 1

Locations'

demands

uncorrelated

0 1 1 1 0 1 1 0 1 1 0

Locations'

demand

variance the

same

0 0 1 0 1 1 0 1 0 1 0

Zero supplier

lead time

variance

0 0 0 0 0 0 0 0 0 0 0

Locations face

same average

lead time

0 0 0 1 0 0 0 1 1 1 1

Lead times iid 1 1 0 0 1 1 1 1 1 1 1

Lead times

and demands

independent

of each other

0 0 0 0 0 0 0 0 0 0 0

Safety factor

approach

used

0 0 0 0 0 0 1 0 0 0 0

Locations use

same safety

factor

1 0 0 0 0 1 0 0 0 0 0

No transship‐

ments

between

locations

0 0 0 0 0 0 0 1 0 1 0

Safety Stock/

Regular Stock

Average total

system

demand

remains the

same after

consolidation

0 1 1 0 0 1 0 1 1 1 0

Locations'

demands the

same

0 0 1 0 0 0 0 1 0 0 0

EOQ Order

Policy0 0 1 0 1 1 0 0 1 0 0

Locations'

fixed order

cost the same

1 0 1 0 0 1 0 0 1 0 0

Locations' per

unit holding

cost the same

1 0 1 0 0 0 1 0 1 1 0

Safety Stock

Regular Stock

Assumptions of the SRL when applied to

Survey respondents

Appendix D

179

Table D.2: Comparison of Important Inventory Consolidation Effect, Portfolio Effect, and

Square Root Law Models

Appendix D

180

Continuation of Table D.2

Appendix D

181

Pi

onee

rs

C

ritic

s

Var

iabl

e le

ad ti

me

Tr

anss

hipm

ents

Opt

imal

con

solid

atio

n

Net

wor

k de

sign

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Appendix D

182


Appendix D

183


Appendix D

184

Table D.2 shows the different SRL and PE models and the assumptions they are based

upon. With the help of this table one can choose the model best fit for assessing inventory

changes from centralization or decentralization for given conditions. The corresponding

formulae for calculating the inventory savings achievable by inventory pooling can be

found on the respective publication's page noted in the first or second row of this table.

In order to facilitate readability the assumptions are grouped according to the rubrics

stock-, inventory-policy-, demand-, and lead-time-related. The columns or models are

arranged chronologically according to their year of publication, so that the development

and adding or dropping of assumptions over time can be retraced where possible.

The models are also grouped by colors according to their main contribution or focus,

although this is not too definite, as they are very different or overlapping and the terms

SRL and PE are sometimes used interchangeably.

Maister (1976) showed the SRL for the EOQ and the safety factor approach for both

cycle and safety stock, Eppen (1979) for the newsvendor model and expected costs, Zinn et

al. (1989) the PE as a generalization of the SRL, Mahmoud (1992) the Portfolio Quantity

and Portfolio Cost Effect, Evers (1995) the Consolidation Effect, Caron and Marchet

(1996) the impact of centralization on safety stock in a special two-echelon system, i. e. the

ratio of safety stock levels in a coupled system and an independent system, first (pioneers).

Das (1978) and Ronen (1990)933 (critics) critically review Maister's (1976) SRL and Zinn

et al.'s (1989) PE respectively. Evers and Beier (1993, 1998) and Tallon (1993) consider

variable lead times, Evers (1996, 1997) transshipments, Tyagi and Das (1998), Das and

Tyagi (1999), Wanke (2009), and Wanke and Saliby (2009) optimal consolidation

schemes, and Croxton and Zinn (2005) inventory pooling effects with the SRL in network

design.

Of course all researchers may be considered critical pioneers as they all contribute

something novel and critically review previous work, which is the essence of scientific

research. Mahmoud (1992: 198, 212) also considers the optimal consolidation scheme and

criticizes that the PE is not sufficient to define it. Evers and Beier (1993) and Evers (1995)

criticize Maister's (1976) SRL. Evers and Beier (1993) and Tyagi and Das (1998) consider

multiple consolidation points and the equal partitioning of demand assumption. Wanke and

Saliby (2009) also deal with regular transshipments. Important distinguishing assumptions

made or not made by the various models are highlighted in grey.

933 Ronen (1990) and Zinn et al. (1989, 1990) have a scientific dispute. For details please refer to the respec-

tive publications.

Appendix D

185

Table D.3: Conditions Favoring the Various Risk Pooling Methods

Appendix D

186


Appendix D

187


Appendix D

188


Appendix D

189


Appendix D

190


Appendix D

191


Appendix D

192


Appendix D

193


Appendix D

194


Appendix D

195

Table D.4 The Risk Pooling Methods' Advantages, Disadvantages, Performance, and Trade-

Offs

Appendix D

196


Appendix D

197


Appendix D

198


Appendix D

199


Appendix D

200


Appendix D

201


202

Appendix E: Subadditivity Proof for the Order Quantity

Function (5.1)

The total system-wide order quantity in the centralized system is no greater than the one in

the decentralized system, because the order quantity function (5.1) is subadditive:

∑, ∑ , . (5.4)

In order to prove this, we first resort to two warehouses with forecast demand minus

available inventory (net demand) and and seek to prove:

, , , . (E1)

The order quantity function (5.1) is a compound function consisting of an outer

maximum function and an inner ceiling function, which we henceforth denote by and ,

respectively. The ceiling expression is a constant.

Recall that a function is called subadditive, if it obeys the inequality

(E2)

for any , from the function's domain.

We first show that is subadditive,

i. e. that the following holds for any , :

. (E3)

This can be verified by a case differentiation:

For s d , s d , (E4)

for s d , s ds d , s ds d , s d

, (E5)

where notation a b stands for „a divides b“ or, equivalently, “b is a multiple of a” and

designates negation.

We now prove that , is subadditive as well, i. e. that the following

holds for any , :

, , , . (E6)

For g , gg , g cg c, g

, , , . (E7)

For g c, g c , , , . (E8)

Appendix E

203

Then for the compound function holds:

, (E9)

since

, (E10)

where the first inequality is due to subadditivity of and non-decreasing behavior of and

the second inequality is due to subadditivity of . It is now straightforward to generalize (E9) to any number of summands. Given

, we by induction on n have:

, (E11)

which hence gives

∑ ∑ (E12)

and proves (5.4) to hold.

204

Bibliography

Abramowitz, M. & Stegun, I. A., eds. (1972), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover.

Ackerman, K. B. & Brewer, A. M. (2001), Warehousing: A key link in the supply chain, in Brewer, A. M., ed., Handbook of Logistics and Supply Chain Management, Elsevier Science, pp. 225-236.

Adam, D. (1979), Kostendegressionen und –progressionen, in Kern, W., ed., HWB der Produktionswirtschaft, Poeschel, pp. 939-955.

Adam, E. E. & Ebert, R. J. (1976), 'A comparison of human and statistical forecasting', AIIE Transactions 8, 120-127.

AFSAC (2001), U.S. DEPARTMENT OF AIR FORCE, 212-448-0496, AGENCY GROUP 09, REGION GROUP 06, 'Virtual warehouse offers global parts shopping', FDCH Regulatory Intelligence Database, 03/14/2001, http://search.ebscohost.com/ login.aspx?direct=true&db=buh&AN=32W20019200005928&site=ehost-live, accessed 03/17/2008.

Alderson, W. (1957), Marketing Behaviour and Executive Action, Richard D. Irwin.

Alfaro, J. A. & Corbett, C. J. (2003), 'The value of SKU rationalization in practice (the pooling effect under suboptimal inventory policies and nonnormal demand)', Production & Operations Management 12(1), 12-29.

Alfredsson, P. & Verrijdt, J. (1999), 'Modeling emergency supply flexibility in a two-echelon inventory system', Management Science 45(10), 1416-1431.

Alicke, K. (2005), Planung und Betrieb von Logistiknetzwerken: Unternehmensübergrei-fendes Supply Chain Management, Springer.

Alisch, K.; Arentzen, U. & Winter, E., eds. (2004), Gabler Wirtschaftslexikon, Gabler.

Alvarez, A. (2007), 'Competing with the internet', JCK 178(10), 117.

Anand, K. S. & Girotra, K. (2007), 'The strategic perils of delayed differentiation', Management Science 53(5), 697-712.

Andres, H. P. & Zmud, R. W. (2001), 'A contingency approach to software project coordination', Journal of Management Information Systems 18(3), 41-70.

Anupindi, R. & Bassok, Y. (1999), 'Centralization of stocks: Retailers vs. manufacturer', Management Science 45(2), 178-191.

Anupindi, R. & Jiang, L. (2008), 'Capacity investment under postponement strategies, market competition, and demand uncertainty', Management Science 54(11), 1876-1890.

Anupindi, R.; Bassok, Y. & Zemel, E. (2001), 'A general framework for the study of decentralized distribution systems', Manufacturing & Service Operations Management 3(4), 349-369.

Anupindi, R.; Chopra, S.; Deshmukh, S. D.; Van Mieghem, J. A. & Zemel, E. (2006), Managing Business Process Flows: Principles of Operations Management, Pearson/ Prentice Hall.

Bibliography

205

Anupindi, R.; Dada, M. & Gupta, S. (1998), 'Estimation of consumer demand with stock-out based substitution: An application to vending machine products', Marketing Science 17(4), 406-423.

Archibald, T. W. (2007), 'Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems', Journal of the Operational Research Society 58(7), 948-956.

Archibald, T. W.; Black, D. & Glazebrook, K. D. (2009), 'An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition', European Journal of Operational Research 192(1), 69-78.

Archibald, T. W.; Sassen, S. A. E. & Thomas, L. C. (1997), 'An optimal policy for a two depot inventory problem with stock transfer', Management Science 43(2), 173-183.

Arnold, J. & Köchel, P. (1996), Evolutionary optimization of a multi-location inventory model with lateral transshipments, in Grubbström, R. W., ed., 'Proceedings of the 9th International Working Seminar on Production Economics', Vol. 2, University of Innsbruck, pp. 401-412.

Arnold, J.; Köchel, P. & Uhlig, H. (1997), With parallel evolution towards the optimal order policy of a multi-location inventory with lateral transshipments, in Papachristos, S. & Ganas, I., eds., 'Proceedings of the 3rd ISIR Summer School on Inventory Modelling in Production and Supply Chains', International Society for Intentory Research, pp. 1-14.

Ashayeri, J. & Selen, W. (2005), 'An application of a unified capacity planning system', International Journal of Operations & Production Management 25(9), 917-937.

Ashford, M. (1997), Cases 4 and 5 - Hasbro Europe and Nike: Developing European logistics strategy, in Taylor, D. H., ed., Global Cases in Logistics and Supply Chain Management: Teachers' Manual, International Thomson Business Press, pp. 16-23.

ATL (2009), 'NCloc Deutschland- und europaweite Standortoptimierung', Fraunhofer Institut Integrierte Schaltungen, Arbeitsgruppe für Technologien der Logistik-Dienstleistungswirtschaft ATL, Nuremberg, http://www.atl.fhg.de/fileadmin/data/pro dukte_und_dienstleistungen/eus/NCloc_Flyer.pdf, accessed 07/18/2009.

Aviation Week & Space Technology (2006), 'A380 support', Aviation Week & Space Technology 165(12), 16.

Aviv, Y. & Federgruen, A. (1997), 'Stochastic inventory models with limited production capacity and periodically varying parameters', Probability in the Engineering and Informational Sciences 11(1), 107-135.

Aviv, Y. & Federgruen, A. (2001a), 'Capacitated multi-item inventory systems with random and seasonally fluctuating demands: Implications for postponement strategies', Management Science 47(4), 512-531.

Aviv, Y. & Federgruen, A. (2001b), 'Design for postponement: A comprehensive characterization of its benefits under unknown demand distributions', Operations Research 49(4), 578-598.

Axsäter, S. (1990), 'Modelling emergency lateral transshipments in inventory systems', Management Science 36(11), 1329-1338.

Axsäter, S. (2003a), 'A new decision rule for lateral transshipments in inventory systems', Management Science 49(9), 1168-1179.

Bibliography

206

Axsäter, S. (2003b), 'Evaluation of unidirectional lateral transshipments and substitutions in inventory systems', European Journal of Operational Research 149(2), 438-447.

Badinelli, R. & Schwarz, L. (1988), 'Backorders optimization in a one-warehouse n-identical retailer distribution system', Naval Research Logistics Quarterly 35(5), 427-440.

Bagchi, P. K. & Skjoett-Larsen, T. (2005), 'Supply chain integration: A European survey', International Journal of Logistics Management 16(2), 275-294.

Bagchi, U. & Gutierrez, G. (1992), 'Effect of increasing component commonality on service level and holding cost', Naval Research Logistics 39(6), 815-832.

Bailey, J. & Rabinovich, E. (2005), 'Internet book retailing and supply chain management: An analytical study of inventory location speculation and postponement', Logistics and Transportation Review 41(3), 159-177.

Baker, K. R. (1985), 'Safety stock and component commonality', Journal of Operations Management 6(1), 13-22.

Baker, K. R.; Magazine, M. J. & Nuttle, H. L. W. (1986), 'The effect of commonality on safety stock in a simple inventory model', Management Science 32(8), 982-988.

Ballou, R. H. & Burnetas, A. (2000), 'Planning virtual inventories', Technical Memorandum 742, Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH.

Ballou, R. H. & Burnetas, A. (2003), 'Planning multiple location inventories', Journal of Business Logistics 24(2), 65-89.

Ballou, R. H. (1979), 'An extended distribution analysis to support marketing and production planning', Journal of Business Logistics 1(1), 63-75.

Ballou, R. H. (1981), 'Estimating and auditing aggregate inventory levels at multiple stocking points', Journal of Operations Management 1(3), 143-153.

Ballou, R. H. (2000), 'Evaluating inventory management performance using a turnover curve', International Journal of Physical Distribution & Logistics Management 30(1), 72-88.

Ballou, R. H. (2003a), 'PowerPoint presentation chapter 8: Forecasting supply chain requirements', 27/08/2003, http://www.pearsonhighered.com/educator/product/Instruc tors-Download-Site-with-Instructors-Manual-5E/9780131428010.page, accessed 23/07/ 2009.

Ballou, R. H. (2003b), 'PowerPoint presentation chapter 9: Inventory policy decisions', 27/08/2003, http://www.pearsonhighered.com/educator/product/Instructors-Download-Site-with-Instructors-Manual-5E/9780131428010.page, accessed 02/12/2009.

Ballou, R. H. (2004a), 'Expressing inventory control policy in the turnover curve', Technical Memorandum 794, Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH.

Ballou, R. H. (2004b), Business Logistics / Supply Chain Management, Pearson/Prentice Hall.

Ballou, R. H. (2004c), 'Logware: Selected Computer Programs for Logistics/Supply Chain Planning: Version 5.0', Weatherhead School of Management, Case Western Reserve University, Cleveland, OH.

Bibliography

207

Ballou, R. H. (2005), 'Expressing inventory control policy in the turnover curve', Journal of Business Logistics 26(2), 143-164.

Bandy, D. B. (2005), 'In-class simulation of pooling safety stock', Decision Sciences Journal of Innovative Education 3(2), 375-380.

Bartholdi, J. J. & Kemahlioğlu-Ziya, E. (2005), Using Shapley value to allocate savings in a supply chain, in Geunes, J. & Pardalos, P. M., eds., Supply Chain Optimization, Springer, pp. 169-208.

Baruch, Y. (1999), 'Response rate in academic studies: A comparative analysis', Human Relations 42(4), 421-438.

Bassok, Y.; Anupindi, R. & Akella, R. (1999), 'Single-period multiproduct inventory models with substitution', Operations Research 47(4), 632-642.

Battezzati, L. & Magnani, R. (2000), 'Supply chains for FMCG and industrial products in Italy: Practices and the advantage of postponement', International Journal of Physical Distribution & Logistics Management 30(5), 413-424.

Bauer, H. (1974), Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie, de Gruyter.

Bender, T.; Hennes, H.; Kalcsics, J.; Melo, T. M. & Nickel, S. (2004), 8 Location software and interface with GIS and supply chain management, in Drezner, Z. & Hamacher, H. W., eds., Facility Location: Applications and Theory, Springer, pp. 233-274.

Bendoly, E. (2004), 'Integrated inventory pooling for firms servicing both on-line and store demand', Computers & Operations Research 31(9), 1465-1480.

Bendoly, E.; Blocher, D.; Bretthauer, K. M. & Venkataramanan, M. (2007), 'Service and cost benefits through clicks-and-mortar integration: Implications for the centralization/decentralization debate', European Journal of Operational Research 180(1), 426-442.

Benjaafar, S. & Kim, J.-S. (2001), 'When does higher demand variability lead to lower safety stocks?', technical report, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN.

Benjaafar, S.; Cooper, W. L. & Kim, J.-S. (2005), 'On the benefits of pooling in production-inventory systems', Management Science 51(4), 548-565.

Benjaafar, S.; ElHafsi, M. & De Véricourt, F. (2004a), 'Demand allocation in multiple-product, multiple-facility, make-to-stock systems', Management Science 50(10), 1431-1448.

Benjaafar, S.; Kim, J.-S. & Vishwanadham, N. (2004b), 'On the effect of product variety in production-inventory systems', Annals of Operations Research 126(1-4), 71-101.

Benton, W. C. & Krajewski, L. (1990), 'Vendor performance and alternative manufacturing environments', Decision Sciences 21(2), 403-415.

Ben-Zvi, N. & Gerchak, Y. (2007), 'Inventory centralization when shortage costs differ: Priorities and costs allocation', technical report, Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv, Israel.

Bernstein, F.; Kök, A. G. & Xie, L. (2009), 'The role of component commonality in product assortment decisions', technical report, Fuqua School of Business, Duke University, Durham, NC, 08/06/2009, http://faculty.fuqua.duke.edu/~agkok/papers/Com monality.pdf, accessed 01/03/2010.

Bibliography

208

Berry, W. L.; Tallon, W. J. & Boe, W. J. (1992), 'Product structure analysis for the master scheduling of assemble-to-order products', International Journal of Operations & Production Management 12(11), 24-41.

Bertrand, L. P. & Bookbinder, J. H. (1998), 'Stock redistribution in two-echelon logistics systems', Journal of the Operational Research Society 49(9), 966-975.

Beuthe, M. & Kreutzberger, E. (2001), Consolidation and trans-shipment, in Brewer, A. M.; Button, K. J. & Hensher, D. A., eds., Handbook of Logistics and Supply Chain Management, Elsevier Science, pp. 239-252.

Bhaumik, P. K. & Kataria, S. (2006), 'Lateral transshipment for managing excesses and shortages in a multilocation inventory system: A case study of Timex Watches Ltd.', International Journal of Services Technology & Management 7(5/6), 602-614.

Bickart, B. & Schmittlein, D. (1999), 'The distribution of survey contact and participation in the United States: Constructing a survey-based estimate', Journal of Marketing Research 36(2), 186-294.

Bidgoli, H., ed. (2010), The Handbook of Technology Management: Supply Chain Management, Marketing and Advertising, and Global Management, Wiley.

Blaikie, N. W. H. (1991), 'A critique of the use of triangulation in social research', Quality & Quantity 25(2), 115-136.

Böhnlein, C.-B. & Lünemann, P. (2008), Supply Chain Management in der Praxis - Status 2007, Vol. 8, Oxygon.

Bohr, K. (1996), Economies of scale and economies of scope, in Kern, W. & Schröder, H.-H., eds., Handwörterbuch der Produktionswirtschaft, Schäffer-Poeschel, pp. 375-386.

Bollapragada, S.; Akella, R. & Srinivasan, R. (1998), 'Centralized ordering and allocation policies in a two-echelon system with non-identical warehouses', European Journal of Operational Research 106(1), 74-81.

Boone, C. A.; Craighead, C. W. & Hanna, J. B. (2007), 'Postponement: An evolving supply chain concept', International Journal of Physical Distribution & Logistics Management 37(8), 594-611.

Bowersox, D. J. & Closs, D. J. (1996), Logistical Management: The Integrated Supply Chain Process, McGraw-Hill.

Bowersox, D. J.; Closs, D. J. & Cooper, M. B. (2002), Supply Chain Logistics Management, McGraw-Hill/Irwin.

Bowersox, D. J.; Closs, D. J. & Helferich, O. K. (1986), Logistical Management: A Systems Integration of Physical Distribution, Manufacturing Support, and Materials Procurement, MacMillan.

Bowersox, D. J.; Daugherty, P. J.; Dröge, C. L.; Germain, R. N. & Rogers, D. S. (1992), Logistical Excellence: It's Not Business as Usual, Digital Press.

Bowersox, D. J.; Smykay, E. W. & La Londe, B. J. (1968), Physical Distribution Management: Logistics Problems in the Firm, MacMillan.

Bowersox, D. J.; Stank, T. P. & Daugherty, P. J. (1999), 'Lean launch: Managing product introduction risk through response-based logistics', Journal of Product Innovation Management 16(6), 557-568.

Bibliography

209

Boyabatli, O. & Toktay, L. B. (2004), 'Operational hedging: A review with discussion', technical report, INSEAD, Fontainebleau, France, January 2004, http://www.prism.ga tech.edu/~bt71/articles/pompaper.pdf, accessed 05/20/2009.

Boysen, N. & Scholl, A. (2009), 'A general solution framework for component-commonality problems', Business Research 2(1), 86-106.

Bramel, J. & Simchi-Levi, D. (1997), The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, Springer.

Brandimarte, P. & Zotteri, G. (2007), Introduction to Distribution Logistics, Wiley.

Breakwell, G. M.; Hammond, S.; Fife-Schaw, C. & Smith, J. A. (2007), Research Methods in Psychology, Sage.

Bretzke, W.-R. (2008), Logistische Netzwerke, Springer.

Bretzke, W.-R. (2010), Logistische Netzwerke, Springer.

Bridgefield Group, Inc. (2006), 'Bridgefield Group ERP/supply chain glossary', http://www .bridgefieldgroup.com/bridgefieldgroup/glos5.htm, accessed 23/07/2009.

Brown, A. O.; Lee, H. L. & Petrakian, R. (2000), 'Xilinx improves its semiconductor supply chain using product and process postponement', Interfaces 30(4), 65-80.

Bryman, A. (1992), Quantitative and qualitative research: Further reflection on their integration, in Brannen, J., ed., Mixing Methods: Qualitative and Quantitative Research, Avebury, pp. 57-78.

Bucklin, L. P. (1965), 'Postponement, speculation and the structure of distribution channels', Journal of Marketing Research 2(1), 26-31.

Bunn, D. & Wright, G. (1991), 'Interaction of judgemental and statstical forecasting methods: Issues & analysis', Management Science 37(5), 501-518.

Burchell, B. (2009), 'Pooling pays', Aviation Week & Space Technology 171(14), 38.

Burer, S. & Dror, M. (2006), 'Newsvendor games: Convex optimization of centralized inventory operations', 09/28/2006, http://dollar.biz.uiowa.edu/~sburer/papers/014-inven tory.pdf, accessed 03/28/2008.

Burton, J. & Banerjee, A. (2005), 'Cost-parametric analysis of lateral transshipment policies in two-echelon supply chains', International Journal of Production Economics 93-94(1), 169-178.

Busse von Colbe, W. & Laßmann, G. (1986), Betriebswirtschaftstheorie, Band 1, Grundlagen, Produktions- und Kostentheorie, Springer.

BVdDP (2009), Bundesverband des Deutschen Papiergroßhandels e.V., 'Jahresbericht 2008', http://www.verband-papiergrosshandel.de/bvddp-jahresbericht.html, accessed 07/16/2009.

BVdDP (2010a), Bundesverband des Deutschen Papiergroßhandels e.V., 'Zahlen und Fakten', http://www.verband-papiergrosshandel.de/pdf/BVdDP.pdf, accessed 05/11/ 2010.

BVdDP (2010b), Bundesverband des Deutschen Papiergroßhandels e.V., 'Jahresbericht 2009', http://www.verband-papiergrosshandel.de/bvddp-jahresbericht.html, accessed 07/29/2010.

Cachon, G. & Terwiesch, C. (2009), Matching Supply with Demand: An Introduction to Operations Management, McGraw-Hill.

Bibliography

210

Cachon, G. P. & Lariviere, M. A. (2005), 'Supply chain coordination with revenue-sharing contracts: Strengths and limitations', Management Science 51(1), 30-44.

Cachon, G. P. (2003), Supply chain coordination with contracts, in de Kok, A. G. & Graves, S. C., eds., Handbooks in Operations Research and Management Science (Vol. 11): Supply Chain Management: Design, Coordination and Operation, North-Holland, ch. 6.

Cachon, G. P. (2004), 'Empiricism in supply chain management research', The Wharton School, University of Pennsylvania, Supply Chain Roundtable, July 2004, http://mba. tuck.dartmouth.edu/digital/Programs/CorporateEvents/SupplyChainThoughtLeaders/session1bSlides.pdf, accessed 10/20/2008.

Cachon, G. P.; Randall, T. & Schmidt, G. M. (2007), 'In search of the bullwhip effect', Manufacturing & Service Operations Management 9(4), 457-479.

Caddy, I. & Helou, M. (2000), Virtual inventories: Impact on inventory and logistics management, in Dahiya, S. B., ed., The Current State of Business Disciplines, Vol. 4, Management-I, Rohtak, pp. 1707-1723.

Campbell, J. F. (1993), 'One-to-many distribution with transshipments: An analytic model', Transportation Science 27(4), 330-340.

Campbell, J. Y.; Lettau, M.; Malkiel, B. G. & Xu, Y. (2001), 'Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk', Journal of Finance 56(1), 1-43.

Capgemini U.S. LLC. (2003), 'New supply chain study finds postponement strategies critical for reducing demand uncertainty and improving customer satisfaction: APICS, Cap Gemini Ernst & Young, and Oracle study cites perceived technology limitations and lack of postponement knowledge as top inhibitors', 10/07/2003, http://www.us.cap gemini.com/news/current_news.asp?ID=335&PRyear=2003, accessed 04/20/2009.

Caron, F. & Marchet, G. (1996), 'The impact of inventory centralization/decentralization on safety stock for two-echelon systems', Journal of Business Logistics 17(1), 233-257.

Carter, P. L. & Monczka, R. M. (1978), 'MRO inventory pooling', Journal of Purchasing & Materials Management 14(3), 27-33.

Carver, R. (1978), 'The case against statistical significance testing', Harvard Educational Review 48, 378-399.

Cattani, K. D. (2000), 'Demand pooling effects of a universal product when demand is from distinct markets', technical report, The University of North Carolina at Chapel Hill.

Cattrysse, D.; van Oudheusden, D. & Wong, H. (2009), 'Inventory pooling of repairable spare parts', Katholieke Universiteit Leuven, Centre for Industrial Management, http:// cib.kuleuven.be/research/reskt12.htm, accessed 03/03/2009.

Caux, C.; David, F. & Pierreval, H. (2006), 'Implementation of delayed differentiation in batch process industries: A standardization problem', International Journal of Production Research 44(16), 3243-3255.

Caves, D. W.; Christiansen, L. R. & Tretheway, M. W. (1984), 'Economies of density versus economies of scale: Why trunk and local service airline costs differ', Rand Journal of Economics 15(4), 471-488.

Bibliography

211

Cecere, L. & Keltz, H. (2008), 'Is your CP organization ready for rising demand variability?', 05/12/2008, http://www.terratechnology.com/assets/Uploads/Is-Your-CP-Organization-Ready-for-Rising-Demand-Variability.pdf, accessed 08/18/2010.

Chain Drug Review (2009a), 'SKU rationalization a new hurdle', Chain Drug Review 31(14), 22.

Chain Drug Review (2009b), 'Innovative items find way amid SKU rationalization', Chain Drug Review 31(17), 24.

Chandler, A. D. (1990), Scale and Scope - The Dynamics of Industrial Capitalism, Harvard University Press.

Chandra, C. & Kamrani, A. K. (2004), Mass Customization: A Supply Chain Approach, Kluwer.

Chang, P. & Lin, C. (1991), 'On the effect of centralization on expected costs in a multi-location newsboy problem', Journal of the Operational Research Society 42(11), 1025-1030.

Chang, P.-L.; Lin, C.-T. & Shen, P.-D. (1996), 'A note on centralized effect on expected costs in a multi-location newsboy problem', International Journal of Information and Management Sciences 7(1), 25-31.

Chauhan, S. S.; Martel, A. & D'Amour, S. (2008), 'Roll assortment optimization in a paper mill: An integer programming approach', Computers & Operations Research 35(2), 614-627.

Chen, C. & Ren, Y. (2007), 'Predictive methods for using capacity data to estimate market shares and the extent of risk pooling by airline alliance partners under parallel codesharing', Transportation Journal 46(4), 21-35.

Chen, F. C.-Y. & Chen, C. (2003), 'The effects of strategic alliances and risk pooling on the load factors of international airline operations', Transportation Research: Part E 39(1), 19-34.

Chen, L. & Lee, H. L. (2009), 'Information sharing and order variability control under a generalized demand model', Management Science 55(5), 781-797.

Chen, M. & Lin, C. (1989), 'Effects of centralization on expected costs in a multi-location newsboy problem', Journal of the Operational Research Society 40(6), 597-602.

Chen, X. & Zhang, J. (2007), 'Duality approaches to economic lot-sizing games', technical report, Operations Management Working Papers Series, New York University, May 2007, http://ssrn.com/abstract=1293131, accessed 06/10/2009.

Chen, X. & Zhang, J. (2009), 'A stochastic programming duality approach to inventory centralization games', Operations Research 57(4), 840-851.

Chen, X. (2009), 'Inventory centralization games with price-dependent demand and quantity discount', Operations Research 57(6), 1394-1406.

Cheng, F.; Ettl, M.; Lin, G.; Schwarz, M. & Yao, D. (2002), 'Flexible supply contracts via options', IBM Research Report, Yorktown Heights, NY, December 2002, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.5.5803&rep=rep1&type=pdf, accessed 09/10/2010.

Cherikh, M. (2000), 'On the effect of centralization on expected profits in a multi-location newsboy problem', Journal of the Operational Research Society 51(6), 755-761.

Bibliography

212

Chew, E. K. P.; Lee, L. H. & Lau, Y. L. (2006), 'Component commonality in assembled-to-stock systems', IIE Transactions 38(3), 239-251.

Chiang, C. & Benton, W. C. (1994), 'Sole sourcing versus dual sourcing under stochastic demands and lead times', Naval Research Logistics 41(5), 609-624.

Chiang, C. & Chiang, W.-C. (1996), 'Reducing inventory costs by order splitting in the sole sourcing environment', Journal of the Operational Research Society 47(3), 446-456.

Chiang, C. (2001), 'Order splitting under periodic review inventory systems', International Journal of Production Economics 70(1), 67-76.

Chikán, A. (2009), 'An empirical analysis of managerial approaches to the role of inventories', International Journal of Production Economics 118(1), 131-135.

Ching, W.-K.; Yuen, W.-O. & Loh, A. W. (2003), 'An inventory model with returns and lateral transshipments', Journal of the Operational Research Society 54(6), 636-641.

Chiou, C.-C. (2008), Transshipment problems in supply chain systems: Review and extensions, in Kordic, V., ed., Supply Chain: Theory and Applications, I-Tech Education and Publishing, pp. 427-448.

Chiou, J.-S.; Wu, L.-Y. & Hsu, J. C. (2002), 'The adoption of form postponement strategy in a global logistics system: The case of Taiwanese information technology industry', Journal of Business Logistics 23(1), 107-124.

Chmielewicz, K. (1994), Forschungskonzeptionen der Wirtschaftswissenschaft, Schäffer-Poeschel.

Chod, J. & Rudi, N. (2005), 'Resource flexibility with responsive pricing', Operations Research 53(3), 532-548.

Cholette, S. (2009), 'Mitigating demand uncertainty across a winery's sales channels through postponement', International Journal of Production Research 47(13), 3587-3609.

Chopra, S. & Meindl, P. (2007), Supply Chain Management: Strategy, Planning, and Operations, Pearson.

Chopra, S. & Sodhi, M. S. (2004), 'Managing risk to avoid supply-chain breakdown', MIT Sloan Management Review 46(1), 53-62.

Christopher, M. & Peck, H. (2003), Marketing Logistics, Butterworth-Heinemann.

Christopher, M. & Towill, D. (2001), 'An integrated model for the design of agile supply chains', International Journal of Physical Distribution and Logistics Management 31(4), 235-246.

Christopher, M. (1992), Logistics and Supply Chain Management: Strategies for Reducing Cost and Improving Service, Pitman.

Christopher, M. (1998), Logistics and Supply Chain Management: Strategies for Reducing Cost and Improving Service, Financial Times Professional.

Christopher, M. (2000), 'The agile supply chain: Competing in volatile markets', Industrial Marketing Management 29(1), 37-44.

Cioletti, J. (2007), 'Get the house in order', Beverage World 126(6), 86-89.

Clapham, C. & Nicholson, J. (2009), The Concise Oxford Dictionary of Mathematics, Oxford University Press.

Bibliography

213

clearpepper supply chain consulting & education (2009), 'Inventory down 80%, sales up 80%. How Sony achieved it', 05/05/2005, http://www.clearpepper.com/supplychain/ sales_up.PDF, accessed 02/18/2009.

CLM (1995), World-Class Logistics: The Challenge of Managing Continuous Change, Council of Logistics Management.

Cohen, J. (1994), 'The Earth is round (p<.05)', American Psychologist 49(12), 997-1003.

Cohen, M. A.; Hershey, J. C. & Weiss, E. N. (1980), 'Analysis of capacity decisions for progressive patient care hospital facilities', Health Services Research 15(2), 145-160.

Collier, D. A. (1981), 'The measurement and operating benefits of component part commonality', Decision Sciences 12(1), 85-96.

Collier, D. A. (1982), 'Aggregate safety stock levels and component part commonality', Management Science 28(11), 1296-1303.

Çömez, N.; Stecke, K. E. & Çakanyildirim, M. (2006), 'Virtual pooling considering transshipment lead time', technical report, School of Management, University of Texas at Dallas, Richardson, TX, 02/28/2006, http://som.utdallas.edu/faculty/working_papers/ SOM200672.pdf, accessed 03/28/2008.

Cooper, J. C. (1993), 'Logistics strategies for global business', International Journal of Physical Distribution & Logistics Management 23(4), 12-23.

Cooper, M. C. (1983), 'Freight consolidation and warehouse location strategies in physical distribution systems', Journal of Business Logistics 4(2), 53-74.

Corbett, C. J. & Rajaram, K. (2004), 'Aggregation of uncertainty and multivariate dependence: The value of pooling of inventories under non-normal dependent demand', technical report, UCLA Anderson School of Management, Los Angeles, CA.

Corbett, C. J. & Rajaram, K. (2006), 'A generalization of the inventory pooling effect to nonnormal dependent demand', Manufacturing & Service Operations Management 8(4), 351-358.

Covino, R. M. (2008), 'Kum & Go's prized prototype', Convenience Store News 44(12), 90-91.

Cox, W. M. & Alm, R. (1998), 'The right stuff: America’s move to mass customization', Federal Reserve Bank of Dallas 1998 Annual Report, 3-26.

Coyle, J. J.; Bardi, E. J. & Langley, C. J. J. (2003), The Management of Business Logistics: A Supply Chain Perspective, South-Western Thomson Learning.

Croston, J. D. (1972), 'Forecasting and stock control for intermittent demands', Operational Research Quarterly 23(3), 289-303.

Croxton, K. L. & Zinn, W. (2005), 'Inventory considerations in network design', Journal of Business Logistics 26(1), 149-168.

CSCMP (2010), Council of Supply Chain Management Professionals, 'CSCMP supply chain management definitions', http://cscmp.org/aboutcscmp/definitions.asp, accessed 01/15/2010.

Daft, R. L. (2009), Organization Theory and Design, South-Western Cengage Learning.

Dai, Y.; Fang, S.-C.; Ling, X. & Nuttle, H. L. W. (2008), 'Risk pooling strategy in a multi-echelon supply chain with price-sensitive demand', Mathematical Methods of Operations Research 67(3), 391-421.

Bibliography

214

Dana, J. & Spier, K. (2001), 'Revenue sharing and vertical control in the video rental industry', The Journal of Industrial Economics 49(3), 223-245.

Dapiran, P. (1992), 'Benetton - global logistics in action', International Journal of Physical Distribution & Logistics Management 22(6), 1-5.

Das, C. & Tyagi, R. (1997), 'Role of inventory and transportation costs in determining the optimal degree of centralization', Transportation Research: Part E: Logistics and Transportation Review 33(3), 171-179.

Das, C. & Tyagi, R. (1999), 'Effect of correlated demands on safety stock centralization: Patterns of correlation versus degree of centralization', Journal of Business Logistics 20(1), 205-213.

Das, C. (1975), 'Supply and redistribution rules for two-location inventory systems: One-period analysis', Management Science 21(7), 765-776.

Das, C. (1978), 'A reappraisal of the square root law', International Journal of Physical Distribution 8(6), 331-336.

Daskin, M. S. (2003), 'Research reports', Industrial Engineer: IE 35(4), 49-50.

Daskin, M. S.; Snyder, L. V. & Berger, R. T. (2005), Chapter 2: Facility location in supply chain design, in Langevin, A. & Riopel, D., eds., Logistics Systems: Design and Optimization, Springer, pp. 39-64.

Davila, T. & Wouters, M. (2007), 'An empirical test of inventory, service and cost benefits from a postponement strategy', International Journal of Production Research 45(10), 2245-2267.

Dekker, R.; Fleischmann, M.; Inderfurth, K. & Van Wassenhove, L. N. (2004), 2 Quantitative models for reverse logistics decision making, in Dekker, R.; Fleischmann, M.; Inderfurth, K. & Van Wassenhove, L. N., eds., Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains, Springer, pp. 29-44.

Delfmann, W. (1999), Industrielle Distributionslogistik, in Weber, J. & Baumgarten, H., eds., Handbuch Logistik: Management von Material- und Warenflußprozessen, Schäffer-Poeschel, pp. 181-201.

Delfmann, W. (2000), Logistikkonzeption, Kernelemente in Klaus, P. & Krieger, W., eds., Gabler Lexikon Logistik: Management logistischer Netzwerke und Flüsse, Gabler, pp. 322-326.

Denzin, N. K. & Lincoln, Y. S. (2005), The art and practices of interpretation, evaluation, and presentation, in Denzin, N. K. & Lincoln, Y. S., eds., The SAGE Handbook of Qualitative Research, Sage, pp. 909-914.

Denzin, N. K. (1978), The Research Act, McGraw-Hill.

Desai, P.; Kekre, S.; Radhakrishnan, S. & Srinivasan, K. (2001), 'Product differentiation and commonality in design: Balancing revenue and cost drivers', Management Science 47(1), 37-51.

Deshpande, V.; Cohen, M. A. & Donohue, K. (2003), 'A threshold inventory rationing policy for service-differentiated demand classes', Management Science 49(6), 683-703.

Deuermeyer, B. & Schwarz, L. (1981), A model for the analysis of system service-level in warehouse-retailer distribution systems: The identical retailer case in Schwarz, L. B., ed., Multi-Level Production/Inventory Control Systems: Theory and Practice, North-Holland, pp. 163-193.

Bibliography

215

Diks, E. B. & de Kok, A. G. (1996), 'Controlling a divergent 2-echelon network with transshipments using the consistent appropriate share rationing policy', International Journal of Production Economics 45(1-3), 369-379.

Dilts, D. M. (2005), 'Risk mitigation in supply chain management: Cost of SC disruptions & strategies to reduce or hedge uncertainty', Professor of Operations Management, Owen Graduate School of Management, Vanderbilt University, Nashville, TN, February 2005, http://www2.owen.vanderbilt.edu/david.dilts/Mgt472_SCM/Mgt472-11-Risk_Mi tigation.ppt, accessed 07/22/2008.

Diruf, G. (2005), 'Risk-Pooling-Strategien in der Modedistribution', technical report, Bamberger betriebswirtschaftliche Beiträge 138, Otto-Friedrich Universität Bamberg, Lehrstuhl für Produktion und Logistik.

Diruf, G. (2007), Risk-Pooling-Kooperationen im Modehandel: Erfolgsfaktoren und Verbesserungspotenziale, in Vahrenkamp, R. & Siepermann, C., eds., Risikomanagment in der Supply Chain: Gefahren abwehren, Chancen nutzen, Erfolg generieren, Erich Schmidt Verlag, pp. 235-252.

Dobos, I. & Richter, K. (2000), 'The integer EOQ repair and waste disposal model–further analysis', Central European Journal of Operations Research 8(2), 173-194.

Doch, S. A. (2009), Logistische Leistungsdifferenzierung im Supply Chain Management, Universitätsverlag der TU Berlin.

Dodge, Y., ed. (2006), The Oxford Dictionary of Statistical Terms, Oxford University Press.

Dogramaci, A. (1979), 'Design of common components considering implications of inventory costs and forecasting', AIIE Transactions 11(2), 129-135.

Dominguez, H. & Lashkari, R. S. (2004), 'Model for integrating the supply chain of an appliance company: A value of information approach', International Journal of Production Research 42(11), 2113-2140.

Domschke, W. & Drexl, A. (1996), Logistik: Standorte, Oldenbourg.

Donaldson, L. (1996), For Positivist Organization Theory, Sage.

Donaldson, L. (1999), Chapter 2: The normal science of structural contingency theory, in Clegg, S. R. & Hardy, C., eds., Studying Organization: Theory & Method, Sage, pp. 51-70.

Donaldson, L. (2001), The Contingency Theory of Organizations, Sage.

Dong, L. & Rudi, N. (2002), 'Supply chain interaction under transshipments: Exogenous vs. endogenous wholesale prices', technical report, Olin School of Business, Washington University, St. Louis, MO.

Dong, L. & Rudi, N. (2004), 'Who benefits from transshipment? Exogenous vs. endogenous wholesale prices', Management Science 50(5), 645-657.

Donnellan, B.; Larsen, T.; Levine, L. & DeGross, J., eds. (2006), The Transfer and Diffusion of Information Technology for Organizational Resilience: IFIP TC8 WG 8.6 International Working Conference, June 7-10, 2006, Galway, Ireland, Springer.

Dorofeev, S. & Grant, P. (2006), Statistics for Real-Life Sample Surveys: Non-Simple-Random Samples and Weighted Data, Cambridge University Press.

Drazin, R. & van de Ven, A. H. (1985), 'Alternative form of strategic fit in contingency theory', Administrative Science Quarterly 30(4), 514-539.

Bibliography

216

Drechsel, J. & Kimms, A. (2007), Berechnung von Kernelementen in kooperativen Bestellmengen-Spielen, in Koschke, R.; Herzog, O.; Rödiger, K.–H. & Ronthaler, M., eds., 'Lecture Notes in Informatics - Informatik 2007 Proceedings "Informatik trifft Logistik"', pp. 79-82.

Dröge, C. L.; Germain, R. N. & Spears, N. (1995), Form postponement as a strategic initiative affecting organizational design, in 'Proceedings of the American Marketing Association Summer Educators' Conference', pp. 163-169.

Dror, M. & Hartman, B. C. (2007), 'Shipment consolidation: Who pays for it and how much?', Management Science 53(1), 78-87.

Dror, M.; Guardiola, L.; Meca, A. & Puerto, J. (2008), 'Dynamic realization games in newsvendor inventory centralization', International Journal of Game Theory 37(1), 139-153.

Dubelaar, C.; Chow, G. & Larson, P. D. (2001), 'Relationships between inventory, sales and service in a retail chain store operation', International Journal of Physical Distribution & Logistics Management 31(2), 96-198.

Duller, C. (2008), Einführung in die nichtparametrische Statistik mit SAS und R: Ein anwendungsorientiertes Lehr- und Arbeitsbuch, Physica Verlag.

Durand, B. & Paché, G. (2006), From traditional retailing to e-tailing: The death and rebirth of the hypermarket format?, in Seppä, M. et al., eds., 'Conference Proceedings of the 5th Frontiers of e-Business Research', Tampere University of Technology (TUT) and University of Tampere (UTA), pp. 95-108.

Durand, B. (2007), Warehousing strategy: The limits of the theory of inventory centralization, in '42nd Canadian Transportation Research Forum', Winnipeg, June 3-6, 2007.

Duvall, M. (2000), 'Cost-saving idea: Virtual warehouses', Inter@ctive Week 7(42), 18.

Dzimbiri, L. B. (2009), Organisation and Management Theories: An African Focus, Cuvillier Verlag.

Electrical Wholesaling (1997), 'Trade Service creates virtual warehouse', Electrical Wholesaling 78(11), 11.

Electrical Wholesaling (2003), 'Distributors take advantage of immediate stock e-virtual warehouse', Electrical Wholesaling 84(9), 19.

ElMaraghy, H. A. & Mahmoudi, N. (2009), 'Concurrent design of product modules structure and global supply chain configurations', International Journal of Computer Integrated Manufacturing 22(6), 483-493.

Enarsson, L. (2006), Future Logistics Challenges, Copenhagen Business School Press.

Eppen, G. & Schrage, L. (1981), Centralized ordering policies in a multi-warehouse system with lead times and random demand, in Schwarz, L. B., ed., Multi-Level Production/Inventory Systems: Theory and Practice, North-Holland, pp. 51-67.

Eppen, G. D. (1979), 'Effects of centralization on expected costs in a multi-location newsboy problem', Management Science 25(5), 498-501.

Erkip, N.; Hausman, W. H. & Nahmias, S. (1990), 'Optimal centralized ordering policies in multi-echelon inventory systems with correlated demands', Management Science 36(3), 381-392.

Bibliography

217

Ernst, R. & Kamrad, B. (2000), 'Evaluation of supply chain structures through modularization and postponement', European Journal of Operational Research 124(3), 495-510.

Ernst, R. & Kouvelis, P. (1999), 'The effects of selling packaged goods on inventory decisions', Management Science 45(8), 1142-1155.

Evers, P. T. & Beier, F. J. (1993), 'The portfolio effect and multiple consolidation points: A critical assessment of the square root law', Journal of Business Logistics 14(2), 109-125.

Evers, P. T. & Beier, F. J. (1998), 'Operational aspects of inventory consolidation decision making', Journal of Business Logistics 19(1), 173-189.

Evers, P. T. (1994), 'The occurrence of statistical economies of scale in intermodal transportation', Transportation Journal 33(4), 51-63.

Evers, P. T. (1995), 'Expanding the square root law: An analysis of both safety and cycle stocks', Logistics and Transportation Review 31(1), 1-20.

Evers, P. T. (1996), 'The impact of transshipments on safety stock requirements', Journal of Business Logistics 17(1), 109-133.

Evers, P. T. (1997), 'Hidden benefits of emergency transshipments', Journal of Business Logistics 18(2), 55-76.

Evers, P. T. (1999), 'Filling customer orders from multiple locations: A comparison of pooling methods', Journal of Business Logistics 20(1), 121-139.

Evers, P. T. (2001), 'Heuristics for assessing emergency transshipments', European Journal of Operational Research 129(2), 311-316.

Eynan, A. & Fouque, T. (2003), 'Capturing the risk-pooling effect through demand reshape', Management Science 49(6), 704-717.

Eynan, A. & Fouque, T. (2005), 'Benefiting from the risk-pooling effect: Internal (component commonality) vs. external (demand reshape) efforts', International Journal of Services and Operations Management 1(1), 90-99.

Eynan, A. & Rosenblatt, M. J. (1996), 'Component commonality effects on inventory costs', IIE Transactions 28(2), 93-104.

Eynan, A. (1996), 'The impact of demands' correlation on the effectiveness of component commonality', International Journal of Production Research 34(6), 1581-1602.

Eynan, A. (1999), 'The multi-location inventory centralization problem with first-come, first-serve allocation', European Journal of Operational Research 114(1), 38-49.

Faloon, K. (1999), 'ARWI launches virtual warehouse', Supply House Times 42(9), 30.

Fawcett, P.; McLeish, R. E. & Ogden, I. D. (1992), Logistics Management, Pitman.

Feitzinger, E. & Lee, H. L. (1997), 'Mass customization at Hewlett-Packard: The power of postponement', Harvard Business Review 75(1), 116-121.

Fielding, N. & Fielding, J. L. (1986), Linking Data: The Articulation of Qualitative and Quantitative Methods in Social Research, Sage.

Fisher, M. & Raman, A. (1996), 'Reducing the cost of demand uncertainty through accurate response to early sales', Operations Research 44(1), 87-99.

Flaks, M. (1967), Total cost approach to physical distribution, in Marks, N. E. & Taylor, R. M., eds., Marketing Logistics: Perspectives and Viewpoints, Wiley, pp. 264-269.

Bibliography

218

Fleisch, E.; Österle, H. & Powell, S. (2004), 'Rapid implementation of enterprise resource planning systems', Journal of Organizational Computing & Electronic Commerce 14(2), 107-126.

Fleischmann, M.; Bloemhof-Ruwaard, J. M.; Beullens, P. & Dekker, R. (2004), 4 Reverse logistics network design, in Dekker, R.; Fleischmann, M.; Inderfurth, K. & Van Wassenhove, L. N., eds., Reverse Logistics: Quantitative Models for Closed-Loop Supply Chains, Springer, pp. 65-94.

Fliedner, G. & Vokurka, R. J. (1997), 'Agility: Competitive weapon of the 1990s and beyond?', Production and Inventory Management Journal 38(3), 19-24.

Flynn, B. B.; Sakakibara, S.; Schroeder, R. G.; Bates, K. A. & Flynn, E. J. (1990), 'Empirical research methods in operations management', Journal of Operations Management 9(2), 250-284.

Fong, D. K. H. & Gempeshaw, V. M. (1996), 'Evaluating re-order levels and probabilities of stockout during a lead time for some stock control models', Journal of Operational Research Society 47(2), 321-328.

Fong, D. K. H. & Ord, K. J. (1993), 'Estimating moments of the effective lead time for a stock control mode with independent normal lead time', Journal of Operational Research Society 44(3), 247-252.

Fong, D. K. H. (1992), 'A note on exact moment computation for normal lead times in the two-supplier case', Journal of Operational Research Society 43(1), 63-69.

Fong, D. K. H.; Gempeshaw, V. M. & Ord, K. J. (2000), 'Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times', European Journal of Operational Research 120(1), 97-107.

Fowler, F. (1993), Survey Research Methods, Sage.

FPT (2007a), 'For Paper Technology: Die Sicht der Papierindustrie: FPT Druckstudie – Teil II', technical report, Forschungsvereinigung Papiertechnik e.V. (FPT) c/o Papiertechnische Stiftung (PTS), Munich, 10/16/2007.

FPT (2007b), 'For Paper Technology: FPT-Workshop Nr. 4: Zukunft der Grafischen Papiere - Wie können Papiererzeuger und deren Zulieferer mit dem Papiergroßhandel und den Druckern über eine optimierte Sortenpolitik zu einer verbesserten Wertschöpfung gelangen?', technical report, Forschungsvereinigung Papiertechnik e.V. (FPT) c/o Papiertechnische Stiftung (PTS), Munich, 10/24/2007.

Franse, K. (1999), 'D&H unveils e-commerce division', VARBusiness 15(7), 20.

Frese, E. (1992), Organisationstheorie: Historische Entwicklung - Ansätze - Perspektiven, Gabler.

Frese, E. (2000), Grundlagen der Organisation, Gabler.

Friedman, J. P., ed. (2007), Dictionary of Business Terms, Barron's Educational Series.

Fritsch, M.; Wein, T. & Ewers, H.-J. (2001), Marktversagen und Wirtschaftspolitik: Mikroökonomische Grundlagen staatlichen Handelns, Vahlen.

Frontline Solutions Europe (2002), 'Walk through the virtual warehouse', Frontline Solutions Europe 11(6), 38.

Fung, S. H.; Cheung, C. F.; Lee, W. B. & Kwok, S. K. (2005), 'A virtual warehouse system for production logistics', Production Planning & Control 16(6), 597-607.

Bibliography

219

Ganesh, M.; Raghunathan, S. & Rajendran, C. (2008), 'The value of information sharing in a multi-product supply chain with product substitution', IIE Transactions 40(12), 1124-1140.

Ganeshan, R.; Ring, L. J. & Strong, J. S. (2007), 'A mathematical approach to designing central vs. local ordering in retail', International Journal of Production Economics 108(1-2), 341-348.

Ganeshan, R.; Tyworth, J. E. & Guo, Y. (1999), 'Dual sourced supply chains: The discount supplier option', Transportation Research: Part E: Logistics and Transportation Review 35(1), 11-23.

García-Dastugue, S. J. & Lambert, D. M. (2007), 'Interorganizational time-based postponement in the supply chain', Journal of Business Logistics 28(1), 57-81.

Garg, A. & Tang, C. S. (1997), 'On postponement strategies for product families with multiple points of differentiation', IIE Transactions 29(8), 641-650.

Garson, D. (2009), 'Chi-square significance tests', North Carolina State University, Raleigh, NC, http://faculty.chass.ncsu.edu/garson/PA765/chisq.htm, accessed 10/24/ 2009.

Gaukler, G. M. (2007), 'Supply chain concepts: Double marginalization and risk pooling', Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 11/14/2007, http://ise.tamu.edu/people/faculty/gaukler/scm.pdf, accessed 08/05/2008.

Gaur, S. & Ravindran, A. R. (2006), 'A bi-criteria model for the inventory aggregation problem under risk pooling', Computers & Industrial Engineering 51(3), 482-501.

Geetha, K. K. & Achary, K. K. (2000), 'Are more suppliers better? Generalizing the Guo and Ganeshan procedure', Journal of the Operational Research Society 51(10), 1179-1181.

Gerchak, Y. & Gupta, D. (1991), 'On apportioning costs to customers in centralized continuous review inventory systems', Journal of Operations Management 10(4), 546-551.

Gerchak, Y. & He, Q.-M. (2003), 'On the relation between the benefits of risk pooling and the variability of demand', IIE Transactions 35(11), 1027-1032.

Gerchak, Y. & Henig, M. (1986), 'An inventory model with component commonality', Operations Research Letters 5(3), 157-160.

Gerchak, Y. & Henig, M. (1989), 'Component commonality in assemble-to-order systems: Models and properties', Naval Research Logistics 36(1), 61-68.

Gerchak, Y. & Mossman, D. (1992), 'On the effect of demand randomness on inventories and costs', Operations Research 40(4), 804-808.

Gerchak, Y.; Magazine, M. J. & Gamble, A. B. (1988), 'Component commonality with service level requirements', Management Science 34(6), 753-760.

Gerchak, Y.; Tripathy, A. & Wang, K. (1996), 'Co-production models with random functionality yields', IIE Transactions 28(5), 391-403.

Ghemawat, P. & Nueno, J. L. (2003), Zara: Fast Fashion, Harvard Business School Publishing.

Ghiani, G.; Laporte, G. & Musmanno, R. (2004), Introduction to Logistics Systems and Planning Control, Wiley.

Bibliography

220

Ghobbar, A. A. & Friend, C. H. (2003), 'Evaluation of forecasting methods for intermittent parts demand in the field of aviation: A predictive model', Computers and Operations Research 30(14), 2097-2114.

Ghodsypour, S. H. & O'Brien, C. (2001), 'The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraint', International Journal of Production Economics 73(1), 15-27.

Gibson, G. & Horner, T. (2005), 'JDEtips on manufacturing: JD Edwards forecasting', JDEtips Journal VI(6), 1-10.

Gilmore, J. H. & Pine II, B. J. (1997), 'The four faces of mass customization', Harvard Business Review 75(1), 91-101.

Gobsch, B. (2007), Deterministische Losgrößenmodelle der Entsorgungslogistik und Reverse Logistics, Wissenschaftlicher Verlag Berlin.

Goldsby, T. J. & Stank, T. P. (2000), 'World class logistics performance and environmentally responsible logistics practices', Journal of Business Logistics 21(2), 187-208.

Gong, Y. & Yucesan, E. (2006), 'The multi-location transshipment problem with positive replenishment lead times', Research Paper ERS-2006-048-LIS Revision, Erasmus Re-search Institute of Management (ERIM), RSM Erasmus University, Rotterdam, 09/07/2006, http://publishing.eur.nl/ir/repub/asset/7947/ERS-2006-048-LIS.pdf, access 08/02/2008.

Gourmet Retailer (2002), 'Web site news', Gourmet Retailer 23(2), 12.

Goyal, M. & Netessine, S. (2005), 'Capacity investment and the interplay between volume flexibility and product flexibility', technical report, The Wharton School, University of Pennsylvania, Philadelphia, PA, May 2005, http://opimweb.wharton.upenn.edu/docu ments/research/Goyal%20Netessine%20b.pdf, accessed 09/10/2010.

Goyal, M. & Netessine, S. (2006), 'Strategic technology choice and capacity investment under demand uncertainty', working paper, The Wharton School, University of Pennsylvania, Philadelphia, PA, April 2006, http://www.rhsmith.umd.edu/faculty/mgo yal/Goyal%20Netessine_Tech-Choice.pdf, accessed 09/20/2009.

Goyal, M.; Netessine, S. & Randall, T. (2006), 'Deployment of manufacturing flexibility: An empirical analysis of the North American automotive industry', technical report, Robert H. Smith School of Business, University of Maryland, College Park, MD, March 2006, http://opimweb.wharton.upenn.edu/documents/research/GoyalNetessineRandall. pdf, accessed 09/11/2009.

Gradshteyn, I. S. & Ryzhik, M. (2007), Table of Integrals, Series and Products, Academic Press.

Grahovac, J. & Chakravarty, A. (2001), 'Sharing and lateral transshipment of inventory in a supply chain with expensive low-demand items', Management Science 47(4), 580-594.

Graman, G. A. & Magazine, M. J. (1998), An analysis of packaging postponement, in 'MSOM Conference Proceedings', University of Washington, Seattle, WA.

Graman, G. A. & Magazine, M. J. (2006), 'Implementation issues influencing the decision to adopt postponement', International Journal of Operations & Production Management 26(10), 1068-1083.

Graman, G. A. & Sanders, N. R. (2009), 'Modelling the tradeoff between postponement capacity and forecast accuracy', Production Planning & Control 20(3), 206-215.

Bibliography

221

Graman, G. A. (2010), 'A partial-postponement decision cost model', European Journal of Operational Research 201(1), 34-44.

Granot, D. & Sošić, G. (2003), 'A three-stage model for a decentralized distribution system of retailers', Operations Research 51(5), 771-784.

Granot, D. & Yin, S. (2008), 'Price and order postponement in a decentralized newsvendor model with multiplicative and price-dependent demand', Operations Research 56(1), 121-139.

Graves, S. C. (2008), Chapter 3: Flexibility principles, in Chhajed, D. & Lowe, T. J., eds., Building Intuition: Insights from Basic Operations Management Models and Principles, Springer, pp. 33-50.

Gravetter, F. J. & Wallnau, L. B. (2008), Statistics for the Behavioral Sciences, Cengage Learning.

Griffis, S. E.; Goldsby, T. J. & Cooper, M. (2003), 'Web-based and mail surveys: A comparison of response, data, and cost', Journal of Business Logistics 24(2), 237-258.

Grotzinger, S. J.; Srinivasan, R.; Akella, R. & Bollapragada, S. (1993), 'Component procurement and allocation for products assembled to forecast: Risk and pooling effects', IBM Journal of Research and Development 37(4), 523-536.

Groves, R. M.; Fowler Jr., F. J.; Couper, M. P.; Lepkowski, J. M.; Singer, E. & Tourangeau, R. (2004), Survey Methodology, John Wiley & Sons.

Grün, O.; Jammernegg, W. & Kummer, S. (2009), Grundzüge der Beschaffung, Produktion und Logistik, Pearson Studium.

Gürbüz, M. Ç.; Moinzadeh, K. & Zhou, Y.-P. (2007), 'Coordinated replenishment strategies in inventory/distribution systems', Management Science 53(2), 293-307.

Guerrero, H. H. (1985), 'The effect of various production strategies on product structures with commonality', Journal of Operations Management 5(4), 395-410.

Güttler, K. (2009), Formale Organisationsstrukturen in wachstumsorientierten kleinen und mittleren Unternehmen, Gabler.

Guglielmo, C. (1999), 'IQVC builds virtual warehouse', Inter@ctive Week 6(25), 37.

Guo, Y. & Ganeshan, R. (1995), 'Are more suppliers better?', Journal of the Operational Research Society 46(5), 892-896.

Gupta, D. & Benjaafar, S. (2004), 'Make-to-order, make-to-stock, or delay product differentiation? A common framework for modeling and analysis', IIE Transactions 36(6), 529-546.

Gupta, O. K. & Kini, R. B. (1995), 'Is price-quantity discount dead in a just-in-time environment?', International Journal of Operations and Production Management 15(9), 261-270.

Gutenberg, E. (1983), Grundlagen der Betriebswirtschaftslehre, Band 1, Die Produktion, Springer.

Gutierrez, R. S.; Solis, A. O. & Mukhopadhyay, S. (2008), 'Lumpy demand forecasting using neural networks', International Journal of Production Economics 111(2), 409-420.

Haimes, Y. Y. (2009), Risk Modeling, Assessment, and Management, John Wiley & Sons.

Bibliography

222

Hall, R. W. (2004), 'Domicile selection and risk pooling for trucking networks', IIE Transactions 36(4), 299-305.

Hammel, T.; Phelps, T. & Kuettner, D. (2002), 'The re-engineering of Hewlett-Packard's CD-RW supply chain', Supply Chain Management: An International Journal 7(3), 113-118.

Hamstra, M. (2009), 'Retailers increase focus on SKU rationalization', SN: Supermarket News 57(41), 28-30.

Harper, R. (2008), 'Silver medal: Ready Pac', SN: Supermarket News 56(40), 54.

Harris, R. G. (1977), 'Economies of traffic density in the rail freight industry', Bell Journal of Economics 8(2), 556-564.

Harrison, A. & Skipworth, H. (2008), 'Implications of form postponement to manufacturing: A cross case comparison', International Journal of Production Research 46(1), 173-195.

Hartman, B. & Dror, M. (1996), 'Cost allocation in continuous-review inventory models', Naval Research Logistics 43(4), 549-561.

Hartman, B. C. & Dror, M. (2003), 'Optimizing centralized inventory operations in a cooperative game theory setting', IIE Transactions 35(3), 243-258.

Hartman, B. C. & Dror, M. (2005), 'Allocation of gains from inventory centralization in newsvendor environments', IIE Transactions 37(2), 93-107.

Hartman, B. C.; Dror, M. & Shaked, M. (2000), 'Cores of inventory centralization games', Games and Economic Behavior 31(1), 26-49.

Hayes, R. & Wheelwright, S. (1984), Restoring Our Competitive Edge: Competing through Manufacturing, John Wiley & Sons.

Hayya, J. C.; Christy, D. P. & Pan, A. (1987), 'Reducing inventory uncertainty: A reorder point system with two vendors', Production and Inventory Management 28(2), 43-48.

Hearn, G. (2007), 'Shred or dread', Airfinance Journal April 1, 2007 (299), 9.

Heese, H. S. & Swaminathan, J. M. (2006), 'Product line design with component commonality and cost-reduction effort', Manufacturing & Service Operations Management 8(2), 206-219.

Heil, U. (2006), Kooperative Risk-Pooling-Strategien im Modehandel, Lang Verlag.

Hempel, C. G. (1970), Methods of concept formation in science, in Neurath, O.; Carnap, R. & Morris, C., eds., Formations of the Unity of Science, University of Chicago Press.

Hendricks, K. B. & Singhal, V. R. (2002), 'How supply chain glitches torpedo shareholder value', Supply Chain Management Review 6(1), 18-24.

Hendricks, K. B. & Singhal, V. R. (2003), 'The effect of supply chain glitches on shareholder wealth', Journal of Operations Management 21(5), 501-522.

Hendricks, K. B. & Singhal, V. R. (2005a), 'Association between supply chain glitches and operating performance', Management Science 51(5), 695-711.

Hendricks, K. B. & Singhal, V. R. (2005b), 'Supply-chain disruptions: Torpedo shareholder value and profitability', Metal Producing & Processing 43(6), 36-35.

Hendricks, K. B. & Singhal, V. R. (2005c), 'An empirical analysis of the effect of supply chain disruptions on long-run stock price performance and equity risk of the firm', Production & Operations Management 14(1), 35-52.

Bibliography

223

Henig, M.; Gerchak, Y.; Ernst, R. & Pyke, D. (1997), 'An inventory model embedded in designing a supply contract', Management Science 43(2), 184-189.

Herer, Y. T. & Rashit, A. (1999), 'Lateral stock transshipments in a two-location inventory system with fixed and joint replenishment costs', Naval Research Logistics 46(5), 525-547.

Herer, Y. T. & Tzur, M. (2003), 'Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs', IIE Transactions 35(5), 419-432.

Herer, Y. T.; Tzur, M. & Yücesan, E. (2002), 'Transshipments: An emerging inventory recourse to achieve supply chain leagility', International Journal of Production Economics 80(3), 201-213.

Herer, Y. T.; Tzur, M. & Yücesan, E. (2006), 'The multilocation transshipment problem', IIE Transactions 38(3), 185-200.

Herron, D. P. (1987), 'Integrated inventory management', Joumal of Business Logistics 8(1), 96-116.

Heskett, J. L. & Signorelli, S. (1984), Benetton (A), Harvard teaching case 9-685-014, Harvard Business Publishing.

Heskett, J. L.; Glaskowsky, N. A. J. & Ivie, R. M. (1974), Business Logistics, Ronald Press.

Hiddemann, T. (2007), Operatives Management und der Erfolg junger, innovativer Unternehmen: Die moderierende Wirkung der externen und internen Unsicherheit, DUV.

Hill, R. M. (1996), 'Order splitting in continuous review (Q, r) inventory models', European Journal of Operational Research 95(1), 53-61.

Hillier, M. S. (2002a), 'Using commonality as backup safety stock', European Journal of Operational Research 136(2), 353-365.

Hillier, M. S. (2002b), 'The costs and benefits of commonality in assemble-to-order systems with a (Q,r)-policy for component replenishment', European Journal of Operational Research 141(3), 570-586.

Hilmola, O.-P. & Szekely, B. (2006), 'Logistics development in Finnish and Swedish companies with respect of Russia and four Asian countries: Traffic flow and warehousing analysis from current situation and likely development trends', Research Report 175, Lappeenranta University of Technology, Department of Industrial Engineering and Management, Kouvola Research Unit, https://oa.doria.fi/bitstream/han dle/10024/31039/TMP.objres.384.pdf?sequence=1, accessed 09/10/2010.

Ho, T.-H.; Lim, N. & Cui, T. H. (2009), 'Is inventory centralization profitable? An experimental investigation', technical report, Haas School of Business, University of California at Berkeley; Bauer College of Business, University of Houston; Carlson School of Management, University of Minnesota, 01/31/2009, http://faculty.haas.berke ley.edu/hoteck/PAPERS/Risk.pdf, accessed 06/10/2009.

Hoffman, W. (2005), 'When supply chains shatter', Traffic World 269(26), 13.

Hoffman, W. (2008), 'Taking less stock', Journal of Commerce (15307557) 9(17), 44.

Bibliography

224

Höhne, E. (2009), Kontingenztheorie in Schwaiger, M. & Meyer, A., eds., Theorien und Methoden der Betriebswirtschaft: Handbuch für Wissenschaftler und Studierende, Vahlen, pp. 83-96.

Holtmann, D. (2007), Grundlegende multivariate Modelle der sozialwissenschaftlichen Datenanalyse, Universitätsverlag Potsdam.

Hong, J. D. & Hayya, J. C. (1992), 'Just-in-time purchasing: Single or multiple sourcing?', International Journal of Production Economics 27(2), 175-181.

Hong, J.-D.; Hayya, J. C. & Kim, S.-L. (1992), 'JIT purchasing and setup reduction in an integrated inventory model', International Journal of Production Research 30(2), 255-266.

Hong-Minh, S. M.; Disney, S. M. & Naim, M. M. (2000), 'The dynamics of emergency transhipment supply chains', International Journal of Physical Distribution & Logistics Management 30(9), 788-816.

Hoppe, B. & Tardos, E. (2000), 'The quickest transshipment problem', Mathematics of Operations Research 25(1), 36-62.

Howard, K. A. (1994), 'Postponement of packaging and product differentiation for lower logistics costs', Journal of Electronics Manufacturing 4(2), 65-69.

Hsu, A. & Bassok, Y. (1999), 'Random yield and random demand in a production system with downward substitution', Operations Research 47(2), 277-290.

HTT (2005), 'Pier 1 talks of plans for turnaround', Home Textiles Today 26(19), 4.

Hu, J.; Watson, E. & Schneider, H. (1997), Centralized versus individual ordering in multilocation inventory systems, in '1997 Proceedings - Decision Sciences Institute Annual Meeting', pp. 1486-1488.

Hu, J.; Watson, E. & Schneider, H. (2005), 'Approximate solutions for multi-location inventory systems with transshipments', International Journal of Production Economics 97(1), 31-43.

Hu, X.; Duenyas, I. & Kapuscinski, R. (2007), 'Existence of coordinating transshipment prices in a two-location inventory model', Management Science 53(8), 1289-1302.

Hu, X.; Duenyas, I. & Kapuscinski, R. (2008), 'Optimal joint inventory and transshipment control under uncertain capacity', Operations Research 56(4), 881-897.

Huang, C. W. & Lo, C. P. (2003), 'Using postponed manufacturing to reconfigure the supply chain in the desktop personal company industry: The case Taiwan', International Journal of Management 20(2), 241-256.

Huang, G. Q.; Zhang, X. Y. & Lo, V. H. Y. (2005), 'Optimal supply chain configuration for platform products: Impacts of commonality, demand variability and quantity discount', International Journal of Mass Customisation 1(1), 107-133.

Huang, X.; Gattiker, T. F. & Schroeder, R. G. (2008), 'Structure–infrastructure alignment: The relationship between TQM orientation and the adoption of supplier-facing electronic commerce among manufacturers', Journal of Supply Chain Management: A Global Review of Purchasing & Supply 44(1), 40-54.

Huang, Y.-Y. & Li, S.-J. (2008a), 'Suitable application situations of different postpone-ment approaches: Standardization vs. modularization', Journal of Manufacturing Sys-tems 27(3), 111-122.

Bibliography

225

Huang, Y.-Y. & Li, S.-J. (2008b), 'Postponement application in Greater China and its related determinants', Transportation Journal 47(3), 5-21.

Hubbard, D. (2009), The Failure of Risk Management: Why It's Broken and How to Fix It, John Wiley & Sons.

Hubbard, D. (2010), How to Measure Anything: Finding the Value of "Intangibles" in Business, John Wiley & Sons.

Hult, G. T. M.; Ketchen, D. J. & Arrfelt, M. (2007), 'Strategic supply chain management: Improving performance through a culture of competitiveness and knowledge development', Strategic Management Journal 28(10), 1035-1052.

Humair, S. & Willems, S. P. (2006), 'Optimizing strategic safety stock placement in supply chains with clusters of commonality', Operations Research 54(4), 725-742.

Hutchings, J. (1999), 'Internet taps into the horizontal supply chain', Modern Power Systems 19(11), 49.

Hwarng, H. B.; Chong, C. S. P.; Xie, N. & Burgess, T. F. (2005), 'Modelling a complex supply chain: Understanding the effect of simplified assumptions', International Journal of Production Research 43(13), 2829-2872.

Ihde, G. B. (1976), Größenersparnisse in der Distribution, Gabler.

Ihde, G. B. (2001), Transport, Verkehr, Logistik: Gesamtwirtschaftliche Aspekte und ein-zelwirtschaftliche Handhabung, Vahlen.

IMF (2009), 'World Economic Outlook Database, April 2009: Nominal GDP list of countries. Data for the year 2008', International Monetary Fund, Washington, D.C.

Inderfurth, K. (1991), 'Safety stock optimization in multi-stage inventory systems', International Journal of Production Economics 24(1-2), 103-113.

Iyer, A. V. & Jain, A. (2004), 'Modeling the impact of merging capacity in production-inventory systems', Management Science 50(8), 1082-1094.

Jabbonsky, L. (1994), 'Stop SKU-ing around', Beverage World 113(1574), 6.

Jackson, G. C. (1985), 'A survey of freight consolidation practices', Journal of Business Logistics 6(1), 13-34.

Jackson, P. & Muckstadt, J. (1989), 'Risk pooling in a two-period, two-echelon inventory stocking and allocation problem', Naval Research Logistics 36, 1-26.

Jackson, P. L. & Muckstadt, J. A. (1984a), 'A two-period, two-echelon inventory stocking and allocation problem', Technical Report 616, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY.

Jackson, P. L. & Muckstadt, J. A. (1984b), 'Risk pooling in a two-period, two-echelon inventory stocking and allocation problem', Technical Report 634, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY.

Jackson, P. L. (1988), 'Stock allocation in a two-echelon distribution system or "what to do until your ship comes in"', Management Science 34(7), 880-895.

Jain, A. (2007), 'Value of capacity pooling in supply chains with heterogeneous customers', European Journal of Operational Research 177(1), 239-260.

Jain, N. & Paul, A. (2001), 'A generalized model of operations reversal for fashion goods', Management Science 47(4), 595-600.

Bibliography

226

Jans, R.; Degraeve, Z. & Schepens, L. (2008), 'Analysis of an industrial component commonality problem', European Journal of Operational Research 186(2), 801-811.

Janssen, F.; de Kok, T. & van der D Schouten, F. (2000), 'Approximate analysis of the delivery splitting model', Journal of the Operational Research Society 51(10), 1136-1147.

Jayaraman, V. (1998), 'Transportation, facility location and inventory issues in distribution network design', International Journal of Operations & Production Management 18(5), 471-494.

Jiang, K.; Lee, H. L. & Seifert, R. W. (2006), 'Satisfying customer preferences via mass customization and mass production', IIE Transactions 38(1), 25-38.

Jick, T. D. (1979), 'Mixing qualitative and quantitative methods: Triangulation in action', Administrative Science Quarterly 24(4), 602-611.

Johnson, E. A. & Anderson, E. (2000), 'Postponement strategies for channel derivatives', International Journal of Logistics Management 11(1), 19-35.

Johnson, K. L. (2005), 'Inventory modeling', Intel Technology Journal 9(3), 233-238.

Johnson, P. F.; Leenders, M. R. & Fearon, H. E. (2006), 'Supply's growing status and influence: A sixteen-year perspective', Journal of Supply Chain Management: A Global Review of Purchasing & Supply 42(2), 33-43.

Johnston, F. R. & Boylan, J. E. (1996), 'Forecasting for items with intermittent demand', Journal of the Operational Research Society 47(1), 113-121.

Jönsson, H. & Silver, E. A. (1987a), 'Analysis of a two-echelon inventory control system with complete redistribution', Management Science 33(2), 215-227.

Jönsson, H. & Silver, E. A. (1987b), 'Stock allocation among a central warehouse and identical regional warehouses in a particular push inventory control system', International Journal of Production Research 25(2), 191-205.

Jönsson, H.; Jörnsten, K. & Silver, E. A. (1993), 'Application of the scenario aggregation approach to a two-stage, stochastic, common component, inventory problem with a budget constraint', European Journal of Operational Research 68(2), 196-211.

Jordan, W. C. & Graves, S. C. (1995), 'Principles on the benefits of manufacturing process flexibility', Management Science 41(4), 577-594.

Jorion, P. (2009), Financial Risk Manager Handbook, Wiley.

Jung, B.-R.; Sun, B.-G.; Kim, J.-S. & Ahn, S.-E. (2003), 'Modeling lateral transshipments in multiechelon repairable-item inventory systems with finite repair channels', Computers & Operations Research 30(9), 1401-1418.

Kang, H. (1986), 'Unstable weights in the combination of forecasts', Management Science 32(6), 683-695.

Kapuscinski, R. & Tayur, S. (1999), 'Variance vs. standard deviation: Variability reduction through operations reversal', Management Science 45(5), 765-767.

Kelle, P. & Miller, P. A. (2001), 'Stockout risk and order splitting', International Journal of Production Economics 71(1), 407-415.

Kelle, P. & Silver, E. A. (1990a), 'Safety stock reduction by order splitting', Naval Research Logistics 37(5), 725-743.

Bibliography

227

Kelle, P. & Silver, E. A. (1990b), 'Decreasing expected shortages through order splitting', Engineering Costs & Production Economics 19(1-3), 351-357.

Kemahlioğlu-Ziya, E. (2004), 'Formal methods of value sharing in supply chains', PhD thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, July 2004, http://smartech.gatech.edu/bitstream/1853/4965/1/kemahlioglu ziya_eda_200407_phd.pdf, accessed 09/10/2010.

Khazanchi, D. (2005), 'Information technology (IT) appropriateness: The contingency theory of "fit" and IT implementation in small and medium enterprises', Journal of Computer Information Systems 45(3), 88-95.

Kibat, K.-D. (2007), 'Steigende Kosten, Überkapazitäten und Preisdruck: Das für die deutsche Papierindustrie wichtige Inlandsgeschäft entwickelt sich sehr positiv', Holz-Zentralblatt 51/52(Zellstoff- und Papierindustrie), 1467.

Kieser, A. & Kubicek, H. (1992), Organisation, De Gruyter.

Kim, J.-S. & Benjaafar, S. (2002), 'On the benefits of inventory-pooling in production-inventory systems', Manufacturing & Service Operations Management 4(1), 12-16.

Kim, K. & Chhajed, D. (2000), 'Commonality in product design: Cost saving, valuation change and cannibalization', European Journal of Operational Research 125(3), 602-621.

Kim, K. & Chhajed, D. (2001), 'An experimental investigation of valuation change due to commonality in vertical product line extension', Journal of Product Innovation Management 18(4), 219-230.

Kisiel, R. (2000), 'Minneapolis test may shape GM's national web strategy', Automotive News 75(5904), 1-2.

Kisperska-Moroñ, D. (2003), 'Responsibilities for inventory decisions in Polish manufacturing companies', International Journal of Production Economics 81-82(1), 129-139.

Kistner, K.-P. & Steven, M. (2002), Betriebswirtschaftslehre im Grundstudium 1: Produktion, Absatz, Finanzierung, Physica Verlag.

Klaas, T. (2002), Logistik-Organisation. Ein konfigurationstheoretischer Ansatz zur logistikorientierten Organisationsgestaltung, DUV.

Klijn, F. & Slikker, M. (2005), 'Distribution center consolidation games', Operations Research Letters 33(3), 285-288.

Klose, A. & Stähly, P. (2000), Standortwahl, Modelle und Methoden, in Klaus, P. & Krieger, W., eds., Gabler Lexikon Logistik: Management logistischer Netzwerke und Flüsse, Gabler, pp. 434-440.

Klose, A. (2001), Standortplanung in distributiven Systemen: Modelle, Methoden, Anwendungen, Physica.

Kloster, T. (2002), Gestaltung von Logistik auf Basis von Netzeffekten, Lang.

Knight, F. H. (2005), Risk, Uncertainty and Profit, Cosimo, originally published by the University of Chicago Press in 1921.

Köchel, P. (1975), 'A stochastic inventory model for some interconnected locations', Mathematische Operationsforschung und Statistik, Series Optimization 6(3), 413-426.

Bibliography

228

Köchel, P. (1977), 'About the optimal inventory control in a system of locations: An approximate solution', Mathematische Operationsforschung und Statistik, Series Opti-mization 8(1), 105-118.

Köchel, P. (1982), 'A dynamic multi-location inventory model with transshipments between locations', Mathematische Operationsforschung und Statistik, Series Optimiza-tion 13(2), 267-286.

Köchel, P. (1988), 'Optimal adaptive inventory control for a multi-location model with redistribution', Mathematische Operationsforschung und Statistik, Series Optimization 19(4), 525-537.

Köchel, P. (1998a), A survey on multi-location inventory models with lateral trans-shipments, in Ganas, I. & Papachristos, S., eds., 'Proceedings of the Third ISIR Summer School on Inventory Modelling', University of Ioannina, Department of Mathematics, pp. 183-207.

Köchel, P. (1998b), Retrospective optimization of a two-location inventory model with lateral transshipments, in 'Proceedings of the 2nd International Conference on Traffic Science', pp. 129-139.

Köchel, P. (2007), 'Order optimisation in multi-location models with hub-and-spoke structure', International Journal of Production Economics 108(1-2), 368-387.

Kohn, C. & Brodin, M. H. (2008), 'Centralised distribution systems and the environment: How increased transport work can decrease the environmental impact of logistics', International Journal of Logistics Research and Applications 11(3), 229-245.

Kohn, C. (2005), 'Centralisation of distribution systems and its environmental effects', PhD thesis, Linköpings Universitet, Department of Management and Economics, Logistics Management, May 2005, http://www.diva-portal.org/smash/get/diva2:20333/FULLTEX T01, accessed 09/10/2010.

Köhne, M. F. (2007), Risikoartenübergreifende Steuerung in Industrieunternehmen in Kaiser, T., ed., Wettbewerbsvorteil Risikomanagement: Erfolgreiche Steuerung der Strategie-, Reputations- und operationellen Risiken, Erich Schmidt Verlag, pp. 307-326.

Kopczak, L. & Lee, H. (1994), Hewlett-Packard: Desktop printer supply chain (A), (B), Stanford University case, Stanford Graduate School of Business.

Korovessi, E. & Linninger, A. A. (2006), Batch Processes, CRC Press.

Kotha, S. (1995), 'Mass customization: Implementing the emerging paradigm for competitive advantage', Strategic Management Journal 16(1), 21-42.

Kotzab, H. (2000), Zum Wesen von Supply Chain Management vor dem Hintergrund der betriebswirtschaftlichen Logistikkonzeption - erweiterte Überlegungen, in Wildemann, H., ed., Supply Chain Management, TCW Transfer-Centrum-Verlag, pp. 21-47.

Kranenburg, A. A. & Van Houtum, G. J. (2009), 'A new partial pooling structure for spare parts networks', European Journal of Operational Research 199(3), 908-921.

Kreng, V. B. & Lee, T. P. (2004), 'Modular product design with grouping genetic algorithm - a case study', Computers & Industrial Engineering 46(3), 443-460.

Krishnan, K. S. & Rao, V. R. K. (1965), 'Inventory control in N warehouses', Journal of Industrial Engineering 16(3), 212-215.

Krishnan, V. & Gupta, S. (2001), 'Appropriateness and impact of platform-based product development', Management Science 47(1), 52-68.

Bibliography

229

Kroll, K. (2006), 'Virtual inventories get real', Multichannel Merchant 2(6), 1-54.

Kuhlang, P. & Matyas, K. (2005), 2 Entwicklung von Logistikprozessen in Schäppi, B.; Andreasen, M. M.; Kirchgeorg, M. & Radermacher, F. J., eds., Handbuch Produktentwicklung, Carl Hanser Verlag, pp. 657-676.

Kukreja, A. & Schmidt, C. P. (2005), 'A model for lumpy demand parts in a multi-location inventory system with transshipments', Computers & Operations Research 32(8), 2059-2075.

Kukreja, A.; Schmidt, C. P. & Miller, D. M. (2001), 'Stocking decisions for low-usage items in a multilocation inventory system', Management Science 47(10), 1371-1383.

Kulkarni, S. S.; Magazine, M. J. & Raturi, A. S. (2005), 'On the trade-offs between risk pooling and logistics costs in a multi-plant network with commonality', IIE Transactions 37(3), 247-265.

Kulpa, J. (2001), 'Magazine distributors pursue partnerships', Drug Store News 23(6), 33.

Kumar, A. & Schwarz, L. B. (1995), 'Risk-pooling along a fixed delivery route using a dynamic inventory-allocation policy', Management Science 41(2), 344-362.

Kumar, S. & Craig, S. (2007), 'Dell, Inc.'s closed loop supply chain for computer assembly plants', Information Knowledge Systems Management 6(3), 197-214.

Kumar, S. & Wilson, J. (2009), 'A manufacturing decision framework for minimizing inventory costs of a configurable off-shored product using postponement', International Journal of Production Research 47(1), 143-162.

Kumar, S.; Nottestad, D. A. & Murphy, E. E. (2009), 'Effects of product postponement on the distribution network: A case study', Journal of the Operational Research Society 60(4), 471-480.

Kutanoglu, E. & Mahajan, M. (2009), 'An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels', European Journal of Operational Research 194(3), 728-742.

Kutanoglu, E. (2008), 'Insights into inventory sharing in service parts logistics systems with time-based service levels', Computers & Industrial Engineering 54(3), 341-358.

Labro, E. (2004), 'The cost effects of component commonality: A literature review through a management-accounting lens', Manufacturing & Service Operations Management 6(4), 358-367.

Lahey, A. (1997), 'Less is more', Marketing Magazine 102(35), 12.

Larson, P. D. & Halldórsson, Á. (2004), 'Logistics versus supply chain management: An international survey', International Journal of Logistics: Research and Applications 7(1), 17-31.

Lau, H. S. & Lau, A. H. (1994), 'Coordinating two suppliers with offsetting lead time and price performance', Journal of Operations Management 11(4), 327-337.

Lau, H. S. & Zhao, L. G. (1993), 'Optimal ordering policies with two suppliers when lead times and demands are all stochastic', European Journal of Operational Research 68(1), 120-133.

Lau, H. S. & Zhao, L. G. (1994), 'Dual sourcing cost-optimization with unrestricted lead-time distributions and order-split proportions', IIE Transactions 26(5), 66-75.

Bibliography

230

Lau, R. S. M. (1995), 'Mass customization: The next industrial revolution', Industrial Management 37(5), 18-19.

Laudon, K. C. & Laudon, J. P. (2010), Management Information Systems: Managing the Digital Firms, Prentice Hall.

Lawrence, K. D. & Zanakis, S. H. (1984), Production Planning and Scheduling: Mathematical Programming Applications, Industrial Engineering and Management Press, Institute of Industrial Engineers.

LeBlanc, L. J.; Hill, J. A.; Harder, J. & Greenwell, G. W. (2009), 'Modeling uncertain forecast accuracy in supply chains with postponement', Journal of Business Logistics 30(1), 19-31.

Lee, D.-J. & Jeong, I.-J. (2009), 'Regression approximation for a partially centralized inventory system considering transportation costs', Computers and Industrial Engineering 56(4), 1169-1176.

Lee, H. L. & Nahmias, S. (1993), Chapter 1: Single-product, single-location models, in Graves, S. C.; Rinnooy Kan, A. H. G. & Zipkin, P. H., eds., Logistics of Production and Inventory, Elsevier, pp. 3-56.

Lee, H. L. & Tang, C. S. (1997), 'Modelling the costs and benefits of delayed product differentiation', Management Science 43(1), 40-53.

Lee, H. L. & Tang, C. S. (1998), 'Variability reduction through operations reversal', Management Science 44(2), 162-172.

Lee, H. L. (1987), 'A multi-echelon inventory model for repairable items with emergency lateral transshipments', Management Science 33(10), 1302-1316.

Lee, H. L. (1996), 'Effective inventory and service management through product and process redesign', Operations Research 44(1), 151-159.

Lee, H. L. (1998), Postponement for mass customization: Satisfying customer demands for tailor-made products, in Gattorna, J., ed., Strategic Supply Chain Alignment, Gower, pp. 77-91.

Lee, H. L.; Billington, C. & Carter, B. (1993), 'Hewlett Packard gains control of inventory and service through design for localization', Interfaces 23(4), 1-11.

Lee, H. L.; Padmanabhan, V. & Whang, S. (1997a), 'The bullwhip effect in supply chains', Sloan Management Review 38(3), 93-102.

Lee, H. L.; Padmanabhan, V. & Whang, S. (1997b), 'Information distortion in a supply chain: The bullwhip effect', Management Science 43(4), 546-558.

Lee, H. L.; Padmanabhan, V. & Whang, S. (2004), 'Information distortion in a supply chain: The bullwhip effect', Management Science 50, 1875-1886.

Lee, Y. H.; Jung, J. W. & Jeon, Y. S. (2007), 'An effective lateral transshipment policy to improve service level in the supply chain', International Journal of Production Economics 106(1), 115-126.

Lehrer, E. (2002), 'Allocation processes in cooperative games', International Journal of Game Theory 31, 341-351.

Lemoine, O. W. & Skjoett-Larsen, T. (2004), 'Reconfiguration of supply chains and implications for transport: A Danish study', International Journal of Physical Distribution & Logistics Management 34(10), 793-810.

Bibliography

231

Li, J.; Cheng, T. C. E. & Wang, S. (2007), 'Analysis of postponement strategy for perishable items by EOQ-based models', International Journal of Production Economics 107(1), 31-38.

Li, J.; Wang, S. & Cheng, T. E. (2008), 'Analysis of postponement strategy by EPQ-based models with planned backorders', Omega 36(5), 777-788.

Li, L. (2007), Supply Chain Management: Concepts, Techniques and Practices Enhancing Value through Collaboration, World Scientific.

Li, Q.; Wu, X. & Cheung, K. L. (2009), 'Optimal policies for inventory systems with separate delivery-request and order-quantity decisions', Operations Research 57(3), 626-636.

Lim, W.-S.; Ou, J. & Teo, C.-P. (2002), 'Inventory cost effect of consolidating several one-warehouse multiretailer systems', Operations Research 51(4), 668-672.

Lin, C.-T.; Chen, C.-B. & Hsieh, H.-J. (2001a), 'Effects of centralization on expected profits in a multi-location newsboy problem', Journal of the Operational Research Society 52(7), 839-844.

Lin, G. Y.; Breitwieser, R.; Cheng, F.; Eagen, J. T. & Ettl, M. (2001b), Product hardware complexity and its impact on inventory and customer on-time delivery (industrial application case: IBM), in Shaw, M. J., ed., Information-Based Manufacturing: Technology, Strategy, and Applications, Kluwer, pp. 61-80.

Liu, J. & Lee, C.-G. (2007), 'Evaluation of inventory policies with unidirectional substitutions', European Journal of Operational Research 182(1), 145-163.

Logistics & Transport Focus (2001), 'Living better with public transport', Logistics & Transport Focus 3(1), 14.

Lovell, A.; Saw, R. & Vermeulen, P. (2005), 'Sony's vision: Sales up 80% inventory down 80%', Logistics & Transport Focus 7(5), 40-44.

Lowe, D. (2002), The Dictionary of Transport and Logistics, Kogan Page Publishers.

Lue, N.-H. (2006), 'The simulation analysis of lateral transshipment and risk pooling for petrochemical supply chains', Master's thesis, Department of Logistics Management, National Kaohsiung First University of Science and Technology, Yenchao, Kaohsiung, Taiwan, Republic of China, 10/26/2006, http://ethesys.nkfust.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1026106-165702, accessed 03/29/2008.

Lüpschen, B. (2004), 'Kostendegressionspotenziale in Logistiksystemen', technical report, Arbeitsbericht 105, University of Cologne, Department of Business Policy and Logistics, http://www.spl.uni-koeln.de/fileadmin/user/dokumente/forschung/arbeitsbe richte/SPL-Arbeitsbericht_105-Luepschen.pdf, accessed 04/27/2008.

Ma, S.; Wang, W. & Liu, L. (2002), 'Commonality and postponement in multistage assembly systems', European Journal of Operational Research 142(3), 523-538.

Magretta, J. (1998), 'The power of virtual integration: An interview with Dell Computer's Michael Dell', Harvard Business Review 76(2), 72-84.

Mahajan, S. & Van Ryzin, G. (2001a), 'Stocking retail assortments under dynamic consumer substitution', Operations Research 49(3), 334-351.

Mahajan, S. & Van Ryzin, G. (2001b), 'Inventory competition under dynamic consumer choice', Operations Research 49(5), 646-657.

Bibliography

232

Mahar, S. & Wright, P. D. (2009), 'The value of postponing online fulfillment decisions in multi-channel retail/e-tail organizations', Computers & Operations Research 36(11), 3061-3072.

Mahar, S.; Bretthauer, K. M. & Venkataramanan, M. A. (2009), 'The value of virtual pooling in dual sales channel supply chains', European Journal of Operational Research 192(2), 561-575.

Mahmoud, M. M. (1992), 'Optimal inventory consolidation schemes: A portfolio effects analysis', Journal of Business Logistics 13(1), 193-214.

Maister, D. H. (1976), 'Centralisation of inventories and the "square root law"', International Journal of Physical Distribution 6(3), 124-134.

Makridakis, S.; Andersen, A.; Carbone, R.; Filder, R.; Hibon, M.; Lewandowski, R.; Newton, J.; Parzen, E. & Winkler, R. (1982), 'The accuracy of extrapolation (time series) methods: Results of a forecasting competition', Journal of Forecasting 1(2), 111-153.

March, C. (2009), Business Organisation for Construction, Taylor & Francis.

Martinez, S. L.; Arostegui, M. A. & Brady, S. P. (2002), 'Logistics support: Improving the logistics pipeline: Achieving agile combat supply support', Air Force Journal of Logistics 26(4), 12-21, 45.

Maskell, B. (1991), Performance Measurement for World Class Manufacturing: A Model for American Companies, Productivity Press.

Mason, J.; Scott, P.; Ribera, M.; Farris, J. A. & Kirk, R. G. (2003), 'Integrating the warehousing and the transportation functions of the supply chains', Transportation Research Part E 39(2), 141-159.

Masters, J. M. (1980), 'The effect of freight consolidation on consumer service', Journal of Business Logistics 2(1), 55-74.

Mathaisel, D. F. X.; Manary, J. M. & Comm, C. L. (2009), Military Enterprise Sustainability: Enhancing the Military's Ability to Perform its Mission, CRC Press Taylor & Francis Group.

Matthews, P. & Syed, N. (2004), 'The power of postponement', Supply Chain Management Review 8(3), 28-34.

Mayne, E.; Winter, D. & Schweinsberg, C. (2008), 'Production puzzle', Ward's AutoWorld, 08/01/2008, http://wardsautoworld.com/ar/auto_production_puzzle/index.html, access 09/04/2008.

McClain, J. O.; Maxwell, W. L.; Muckstadt, J. A.; Thomas, L. J. & Weiss, E. N. (1984), 'Comment on "Aggregate safety stock levels and component part commonality"', Management Science 30(6), 772-773.

McDermott, C. M. & Stock, G. N. (1994), 'The use of common parts and designs in high-tech industries: A strategic approach', Production & Inventory Management Journal 35(3), 65-69.

McGavin, E. J.; Schwarz, L. B. & Ward, J. E. (1993), 'Two-interval inventory-allocation policies in a one-warehouse n-identical-retailer distribution system', Management Science 39(9), 1092-1107.

McGillivary, A. & Silver, E. (1978), 'Some concepts for inventory control under substitutable demand', INFOR 16(1), 47-63.

Bibliography

233

McKinnon, A. & Forster, M. (2000), 'Full report of the delphi 2005 survey European logistical and supply chain trends: 1999-2005', technical report, Heriot-Watt University, Edinburgh, UK, http://www.sml.hw.ac.uk/logistics/pdf/delphi.pdf, accessed 06/03/2008.

McKinnon, A. (1997), Case 16 - Scottish brewers: The restructuring of a depot system, in Taylor, D. H., ed., Global Cases in Logistics and Supply Chain Management: Teachers' Manual, International Thomson Business Press, pp. 78-83.

McKinnon, A. C. (1989), Physical Distribution Systems, Routledge.

McKinnon, A. C. (2003), 'The effects of transport investment on logistical efficiency', Heriot-Watt University, Logistics Research Centre, Edinburgh, UK, 03/20/2003, http://www.sml.hw.ac.uk/logistics/downloads/congestion-reliabilitystudy/Transport%20 Investment%20and%20Logistical%20Efficiency%20(McKinnon%20-%20TSU%20Ox ford).pdf, accessed 09/09/2008.

Memon, F. (1997), 'Virtual warehouse keeps Toyota running', Inter@ctive Week 3(17), 40.

Mercer, A. & Tao, X. (1996), 'Alternative inventory and distribution policies of a food manufacturer', Journal of the Operational Research Society 47(6), 755-765.

Meyer, A. D.; Tsui, A. S. & Hinings, C. R. (1993), 'Configurational approaches to organizational analysis', Academy of Management Journal 36(6), 1175-1195.

Meyer, M. H. & Lehnerd, A. P. (1997), The Power of Product Platforms: Building Value and Cost Leadership, The Free Press.

Meyr, H. (2003), 'Die Bedeutung von Entkopplungspunkten für die operative Planung von Supply Chains', Zeitschrift für Betriebswirtschaft 73(9), 941-962.

Miller, D. & Friesen, P. H. (1978), 'Archetypes of strategy formulation', Management Science 24(9), 921-933.

Miller, D. & Friesen, P. H. (1980), 'Archetypes of organizational transition', Administrative Science Quarterly 25(2), 268-299.

Miller, D. (1981), 'Toward a new contingency approach: The search for organizational gestalts', Journal of Management Studies 18(1), 1-26.

Milner, J. M. & Kouvelis, P. (2007), 'Inventory, speculation, and sourcing strategies in the presence of online exchanges', Manufacturing & Service Operations Management 9(3), 312-331.

Minkowski, H. (1896), Geometrie der Zahlen, Teubner, reprint by VDM Verlag Dr. Müller, 2006.

Minner, S. & Silver, E. A. (2005), 'Evaluation of two simple extreme transshipment strategies', International Journal of Production Economics 93-94(1), 1-11.

Minner, S. (2003), 'Multiple-supplier inventory models in supply chain management: A review', International Journal of Production Economics 81-82(1), 265-279.

Minner, S.; Silver, E. A. & Robb, D. J. (2003), 'An improved heuristic for deciding on emergency transshipments', European Journal of Operational Research 148(2), 384-400.

Miranda, P. A. & Garrido, R. A. (2004), 'Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand', Transportation Research: Part E 40(3), 183-207.

Bibliography

234

Mirchandani, P. & Mishra, A. K. (2002), 'Component commonality: Models with product-specific service constraints', Production & Operations Management 11(2), 199-215.

Mishra, A. K. & Tadikamalla, P. R. (2006), 'Order splitting in single sourcing with scheduled-release orders', Journal of the Operational Research Society 57(2), 177-189.

MMR (2009), 'Impact brands should win in SKU rationalization', MMR 26(15), 19.

Modern Materials Handling (2002), 'Number of warehouses continues to shrink', Modern Materials Handling 57(14), 1.

Mohebbi, E. & Choobineh, F. (2005), 'The impact of component commonality in an assemble-to-order environment under supply and demand uncertainty', Omega 33(6), 472-482.

Mohebbi, E. & Posner, M. J. M. (1998), 'Sole versus dual sourcing in a continuous-review inventory system with lost sales', Computers in Industrial Engineering 34(2), 321-336.

Moinzadeh, K. & Nahmias, S. (1988), 'A continuous review model for an inventory system with two supply modes', Management Science 34(6), 761-773.

Monezka, R. M. & Carter, P. L. (1976), The economics of vendor pooling, in 'Academy of Management Proceedings', pp. 207-211.

Monopolkommission (1986), Gesamtwirtschaftliche Chancen und Risiken wachsender Unternehmensgrößen: Hauptgutachten 1984/1985, Nr. 6, Nomos Verlagsgesellschaft.

Mood, A. M.; Graybill, F. A. & Boes, D. C. (1974), Introduction to the Theory of Statistics, McGraw-Hill.

Morehouse, J. E. & Bowersox, D. J. (1995), 'Supply chain management: Logistics for the future', technical report, Food Marketing Institute, Washington, D.C.

Movianto GmbH (2010), 'Postponement', http://www.movianto.com/services-solutions/ma nufacturing-postponement.htm, accessed 01/22/2010.

Moyer, R. C.; McGuigan, J. R. & J., K. W. (1992), Contemporary Financial Management, West Publishing Company.

Muckstadt, J. A. & Thomas, L. J. (1980), 'Are multi-echelon inventory methods worth implementing in systems with low demand rate items?', Management Science 26(5), 483-494.

Muckstadt, J. A. (2005), Analysis and Algorithms for Service Parts Supply Chains, Springer.

Müller, A.; Scarsini, M. & Shaked, M. (2002), 'The newsvendor game has a nonempty core', Games and Economic Behavior 38(1), 118-126.

Müller-Benedict, V. (2007), Grundkurs Statistik in den Sozialwissenschaften, VS Verlag für Sozialwissenschaften.

Müller-Nedebock, S. (2009), Erfolgsfaktoren der Strategieimplementierung im Strategi-schen Management: Forschungsstand und Entwicklungstendenzen, IGEL Verlag.

Naesens, K.; Gelders, L. & Pintelon, L. (2007), 'A swift response tool for measuring the strategic fit for resource pooling: A case study', Management Decision 45(3), 434-449.

Nahmias, S. (2005), Production and Operations Analysis, McGraw-Hill/Irwin.

Nair, A. (2005), 'Linking manufacturing postponement, centralized distribution and value chain flexibility with performance', International Journal of Production Research 43(3), 447-463.

Bibliography

235

Narus, J. A. & Anderson, J. C. (1996), 'Rethinking distribution: Adaptive channels', Harvard Business Review 74(4), 112-120.

Naseraldin, H. & Herer, Y. T. (2008), 'Integrating the number and location of retail outlets on a line with replenishment decisions', Management Science 54(9), 1666-1683.

Neale, J. J.; Tomlin, B. T. & Willems, S. P. (2003), The role of inventory in superior supply chain performance, in Harrison, T. P.; Lee, H. L. & Neale, J. J., eds., The Practice of Supply Chain Management: Where Theory and Application Converge, Kluwer, pp. 31-60.

Needham, P. M. & Evers, P. T. (1998), 'The influence of individual cost factors on the use of emergency transshipments', Transportation Research: Part E: Logistics and Transportation Review 34(2), 149-160.

Netessine, S. & Rudi, N. (2003), 'Centralized and competitive inventory models with demand substitution', Operations Research 51(2), 329-335.

Netessine, S. & Rudi, N. (2006), 'Supply chain choice on the internet', Management Science 52(6), 844-864.

Netessine, S. (2005), 'From theory to empirical evidence and back: Integrating data-driven research into your portfolio', Purdue CIBER Consortium meeting on International Operations Management, 09/17/2005.

Neumann, K. (1996), Produktions- und Operations-Management, Springer.

Neus, W. (2009), Einführung in die Betriebswirtschaftslehre aus institutionenökonomi-scher Sicht, Mohr Siebeck.

Newson, P. L. (1978), The Future Role of Depots in a Distribution Network, Post Office.

Nobre, F. S.; Tobias, A. M. & Walker, D. S. (2009), Organizational and Technological Implications of Cognitive Machines: Designing Future Information Management Systems, Idea Group Inc. (IGI).

Nonås, L. M. & Jörnsten, K. (2005), Heuristics in the multi-location inventory system with transshipments, in Kotzab, H.; Seuring, S.; Müller, M. & Reiner, G., eds., Research Methodologies in Supply Chain Management, Physica Verlag, pp. 509-524.

Nonås, S. L. (2009), 'Finding and identifying optimal inventory levels for systems with common components', European Journal of Operational Research 193(1), 98-119.

Nozick, L. K. & Turnquist, M. A. (2001), 'Inventory, transportation, service quality and the location of distribution centers', European Journal of Operational Research 129(2), 362-371.

Obal, P. (2006), Glossary of Supply Chain Terminology: A Dictionary on Technology, Logistics, Transportation, Warehousing, Manufacturing, Purchasing, and More!, Verlag Industrial Data & Information Inc.

Olsson, F. (2009), 'Optimal policies for inventory systems with lateral transshipments', International Journal of Production Economics 118(1), 175-184.

Oracle Corporation (2004), 'The adaptive supply chain: Postponement for profitability', http://www.oracle.com/us/solutions/scm/018543.pdf, accessed 09/08/2009.

Oracle Corporation (2009), 'JD Edwards OneWorld Manual', Redwood Shores, CA.

Orgel, D. (2009), 'How partnerships succeeding in time of friction', SN: Supermarket News 57(41), 12.

Bibliography

236

Orlicky, J. A. (1975), Material Requirements Planning, McGraw-Hill.

Osteryoung, J. S.; Nosari, E.; McCarty, D. E. & Reinhart, W. J. (1986), 'Use of the EOQ model for inventory analysis', Production and Inventory Management 27(3), 39-46.

Özdemir, D.; Yücesan, E. & Herer, Y. T. (2006a), Multi-location transshipment problem with capacitated production and lost sales, in 'Proceedings of the 2006 Winter Simulation Conference', pp.1470-1476.

Özdemir, D.; Yücesan, E. & Herer, Y. T. (2006b), 'Multi-location transshipment problem with capacitated transportation', European Journal of Operational Research 175(1), 602-621.

Özen, U. & Sošić, G. (2006), 'A multi-retailer decentralized distribution system with updated demand information', BETA Working Paper 193, Eindhoven University of Technology, 08/18/2006, http://cms.ieis.tue.nl/Beta/Files/WorkingPapers/Beta_WP193. pdf, accessed 09/10/2010.

Özen, U.; Fransoo, J.; Norde, H. & Slikker, M. (2008), 'Cooperation between multiple newsvendors with warehouses', Manufacturing & Service Operations Management 10(2), 311-324.

Özen, U.; Norde, H. & Slikker, M. (2005), 'On the convexity of newsvendor games', Discussion Paper 103, Tilburg University, Center for Economic Research, 08/30/2005, http://ssrn.com/abstract=642401, accessed 09/10/2010.

Özen, U.; Sošić, G. & Slikker, M. (2010), 'A collaborative decentralized distribution system with demand forecast updates', 04/07/2010, http://ssrn.com/abstract=929652, ac-cessed 09/08/2010.

Özer, Ö. & Xiong, H. (2008), 'Stock positioning and performance estimation for distribution systems with service constraints', IIE Transactions 40(12), 1141-1157.

Özer, Ö. (2003), 'Replenishment strategies for distribution systems under advance demand information', Management Science 49(3), 255-272.

Ozsen, L.; Coullard, C. R. & Daskin, M. S. (2008), 'Capacitated warehouse location model with risk pooling', Naval Research Logistics 55(4), 295-312.

Pagh, J. D. & Cooper, M. C. (1998), 'Supply chain postponement and speculation strategies: How to choose the right strategy', Journal of Business Logistics 19(2), 13-33.

Pamplin, C. (2002), 'Casting a cold eye', Convenience Store News 38(9), 32-33.

Pan, A. C. & Liao, C.-J. (1989), 'An inventory model under just-in-time purchasing agreements', Production & Inventory Management Journal 30(1), 49-52.

Pan, A. C.; Ramasesh, R. V.; Hayya, J. C. & Ord, J. K. (1991), 'Multiple sourcing: The determination of lead times', Operations Research Letters 10(1), 1-7.

Paraschis, I. N. (1989), Optimale Gestaltung von Mehrprodukt-Distributionssystemen: Modelle - Methoden - Anwendungen, Physica Verlag.

Parlar, M. & Goyal, S. (1984), 'Optimal ordering decisions for two substitutable products with stochastic demands', Opsearch 21(1), 1-15.

Pasin, F.; Jobin, M.-H. & Cordeau, J.-F. (2002), 'An application of simulation to analyse resource sharing among health-care organisations', International Journal of Operations & Production Management 22(4), 381-393.

Bibliography

237

Pasternack, B. A. & Drezner, Z. (1991), 'Optimal inventory policies for substitutable commodities with stochastic demand', Naval Research Logistics 38, 221-240.

Paterson, C.; Kiesmüller, G.; Teunter, R. & Glazebrook, K. (2009), 'Inventory models with lateral transshipments: A review', BETA Working Paper 287, Eindhoven University of Technology, 08/26/2009, http://cms.ieis.tue.nl/Beta/Files/WorkingPapers/Beta_wp287. pdf, accessed 08/08/2010.

Petering, M. E. H. & Murty, K. G. (2009), 'Effect of block length and yard crane deployment systems on overall performance at a seaport container transshipment terminal', Computers & Operations Research 36(5), 1711-1725.

Peterson, R. (1969), 'A note on the determination of optimal forecasting strategy', Management Science 16(4), B165-B169.

Pfeifer, B. (2010), Zur Nachhaltigkeitsorientierung von Private Equity-Investoren, Josef Eul Verlag GmbH.

Pfohl, H.-C. (1994), Logistikmanagement: Funktionen und Instrumente, Springer.

Pfohl, H.-C. (2004a), Logistiksysteme: Betriebswirtschaftliche Grundlagen, Springer.

Pfohl, H.-C. (2004b), Logistikmanagement: Konzeption und Funktionen, Springer.

Pfohl, H.-C.; Zöllner, W. A. & Weber, N. (1992), 'Economies of scale in customer warehouses: Theoretical and empirical analysis', Journal of Business Logistics 13(1), 95-124.

Pine II, B. J.; Victor, B. & Boynton, A. C. (1993), 'Making mass customization work', Harvard Business Review 71(5), 108-118.

Pinto, D. (2009a), 'Outsiders bring new thinking to industry', Chain Drug Review 31(15), 16.

Pinto, D. (2009b), 'A merchandising cataclysm', MMR 26(15), 8.

Piontek, J. (2007), Bausteine des Logistikmanagements: Supply-Chain-Management, E-Logistics, Logistikcontrolling, Verlag Neue Wirtschafts-Briefe GmbH & Co.

Pishchulov, G. & Richter, K. (2009), 'Inventory rationing and sharing in pre-sell distribution with mobile communication technologies', International Journal of Production Economics 121(2), 584-600.

Pishchulov, G. (2008), Inventory Rationing and Sharing in Pre-Sell Distribution with Mobile Communication Technologies, Shaker.

Plambeck, E. & Taylor, T. (2003), 'Sell the plant? The impact of contract manufacturing on innovation, capacity, and profitability', technical report, Graduate School of Business, Stanford University, Palo Alto, Management Science, 51(1), 2005, 133-150.

Planning & Reporting (2001), 'How Insight Enterprises benchmarks 'virtual' inventory turnover', Financial Analysis, Planning & Reporting 1(5), 1-5.

Porter, M. E. (1985), Competitive Advantage, Free Press.

Porter, M. E. (2008), On Competition, Harvard Business School Publishing.

Pringle, D. (2003), 'Nokia eschews factories in most low-cost regions', The Wall Street Journal, 01/03/2003.

Progress Software Corporation (2007), 'Improving the business model with Progress Open-Edge®', http://www.progress.com/progress_software/docs/kingfield_health.pdf, access 06/02/2008.

Bibliography

238

Pugh, D. S. (1981), The Aston programme perspective, in Van de Ven, A. H. & Joyce, W. F., eds., Perspectives on Organization Design and Behavior, Wiley, pp. 135-166.

Purchasing (2000), 'Wareforce.com joins group of Commerce One suppliers', Purchasing 128(8), 132.

Qi, X. (2007), 'Order splitting with multiple capacitated suppliers', European Journal of Operational Research 178(2), 421-432.

Rabinovich, E. & Evers, P. T. (2003a), 'Product fulfillment in supply chains supporting internet-retailing operations', Journal of Business Logistics 24(2), 205-236.

Rabinovich, E. & Evers, P. T. (2003b), 'Postponement effects on inventory performance and the impact of information systems', International Journal of Logistics Management 14(1), 33-48.

Raghunathan, S. (2003), 'Impact of demand correlation on the value of and incentives for information sharing in a supply chain', European Journal of Operational Research 146(3), 634-649.

Rajaram, K. & Tang, C. (2001), 'The impact of product substitution on retail merchandising', European Journal of Operational Research 135(3), 582-601.

Ramasesh, R. V. (1990), 'Recasting the traditional inventory model to implement just-in-time purchasing', Production and Inventory Management 31(1), 71-75.

Ramasesh, R. V. (1991), 'Procurement under uncertain supply lead times–a dual-sourcing technique could save costs', Engineering Costs and Production Economics 21(1), 59-68.

Ramasesh, R. V.; Ord, J. K. & Hayya, J. C. (1993), 'Note: Dual sourcing with nonidentical suppliers', Naval Research Logistics 40(2), 279-288.

Ramasesh, R. V.; Ord, J. K.; Hayya, J. C. & Pan, A. (1991), 'Sole versus dual sourcing in stochastic lead-time (s, Q) inventory models', Management Science 37(4), 428-443.

Ramdas, K. & Sawhney, M. S. (2001), 'A cross-functional approach to evaluating multiple line extensions for assembled products', Management Science 47(1), 22-36.

Randall, T.; Netessine, S. & Rudi, N. (2002), 'Should you take the virtual fulfillment path?', Supply Chain Management Review 6(6), 54-58.

Randall, T.; Netessine, S. & Rudi, N. (2006), 'An empirical examination of the decision to invest in fulfillment capabilities: A study of internet retailers', Management Science 52(4), 567-580.

Reihlen, M. (1997), Entwicklungsfähige Planungssysteme. Grundlagen, Konzepte und Anwendungen zur Bewältigung von Innovationsproblemen, Gabler.

Reiner, G. (2005), Supply chain management research methodology using quantitative models based on empirical data, in Kotzab, H.; Seuring, S.; Müller, M. & Reiner, G., eds., Research Methodologies in Supply Chain Management, Physica Verlag, pp. 431-444.

Reyes, P. M. & Meade, L. M. (2006), 'Improving reverse supply chain operational performance: A transshipment application study for not-for-profit organizations', Journal of Supply Chain Management: A Global Review of Purchasing & Supply 42(1), 38-48.

Reynolds, H. T. (1984), Analysis of Nominal Data, Vol. 7, Sage.

Bibliography

239

Richter, K. & Dobos, I. (1999), 'Analysis of the EOQ repair and waste disposal problem with integer setup numbers', International Journal of Production Economics 59(1), 463-467.

Richter, K. & Dobos, I. (2003a), Production-inventory control in an EOQ-type reverse logistics system, in Dyckhoff, H.; Lackes, R. & Reese, J., eds., Supply Chain Management and Reverse Logistics, Springer, pp. 139-160.

Richter, K. & Dobos, I. (2003b), A reverse logistics model with integer setup numbers, in Leopold-Wildburger, U.; Rendl, F. & Wäscher, G., eds., 'Operations Research Proceedings 2002', Springer, pp. 95-101.

Richter, K. & Gobsch, B. (2005), 'Kreislauf-Logistik mit Losgrößenrestriktionen', ZfB Special Issue 4/2005: Reverse Logistics II, 57-79.

Richter, K. & Sombrutzki, M. (2000), 'Remanufacturing planning for the reverse Wagner/Whitin models', European Journal of Operational Research 121(2), 304-315.

Richter, K. & Weber, J. (2001), 'The reverse Wagner/Whitin model with variable manufacturing and remanufacturing cost', International Journal of Production Economics 71(1-3), 447-456.

Richter, K. (1996a), 'The extended EOQ repair and waste disposal model', International Journal of Production Economics 45(1-3), 443-447.

Richter, K. (1996b), 'The EOQ repair and waste disposal model with variable setup numbers', European Journal of Operational Research 95(2), 313-324.

Richter, K. (1997), 'Pure and mixed strategies for the EOQ repair and waste disposal problem', OR-Spektrum 19(2), 123-129.

Robinson, L. W. (1990), 'Optimal and approximate policies in multiperiod, multilocation inventory models with transshipments', Operations Research 38(2), 278-295.

Robinson, L. W. (1993), 'A comment on Gerchak and Gupta's "On apportioning cost to customers in centralized continuous review inventory systems"', Journal of Operations Management 11(1), 99-102.

Romano, P. (2006), 'Supply chain risk pooling', Blackwell Encyclopedic Dictionary of Operations Management, p. 320, http://www.blackwellreference.com/public/tocnode?id =g9780631233176_chunk_g978140511096923_ss32-1, accessed 09/01/2010.

Ronen, D. (1990), 'Inventory centralization/decentralization–the "square root law" revisited again', Journal of Business Logistics 11(2), 129-138.

Roque, I. M. (1977), Production-inventory system economy using a component standardization factor, in 'Proceedings of the Midwest American Institute for Decision Sciences'.

Ross, D. F. (1996), Distribution Planning and Control, Chapman & Hall.

Röttgen, W. (1987), 'Der Feinpapiergroßhandel als Absatzmittler für graphische Papiere', Master's thesis, Universität zu Köln, Seminar für Handelsbetriebslehre, Prof. Dr. F. Klein-Blenkers.

Rudi, N.; Kapur, S. & Pyke, D. F. (2001), 'A two-location inventory model with transshipment and local decision making', Management Science 47(12), 1668-1680.

Rumyantsev, S. & Netessine, S. (2007), 'What can be learned from classical inventory models? A cross-industry exploratory investigation', Manufacturing & Service Operations Management 9(4), 409-429.

Bibliography

240

Ruusunen, J.; Ehtamo, H. & Hamalainen, R. (1991), 'Dynamic cooperative electricity exchange in a power pool', IEEE Transactions on Systems, Management, and Cybernetics 21(4), 758-766.

Ryan, T. (2009), 'Retailwire discussion: SKU rationalization reshapes retail shelves', Private Label Buyer 23(9), 10.

Ryu, S. W. & Lee, K. K. (2003), 'A stochastic inventory model of dual sourced supply chain with lead-time reduction', International Journal of Production Economics 81-82(1), 513-527.

Sajadieh, M. S. & Eshghi, K. (2009), 'Sole versus dual sourcing under order dependent lead times and prices', Computers & Operations Research 36(12), 3272-3280.

Samuelson, P. A. & Nordhaus, W. D. (1998), Volkswirtschaftslehre, Ueberreuter.

Savage, S.; Scholtes, S. & Zweidler, D. (2006), 'Probability management', OR/MS Today 33(1), 21-28.

Sawyers, A. (2003), 'Web E.L.V.I.S.: A whole lot of selling going on', Automotive News 77(6029), 6.

Scherer, A. G. & Beyer, R. (1998), 'Der Konfigurationsansatz im strategsichen Management – Rekonstruktion und Kritik', Die Betriebswirtschaft (DBW) 58(3), 332-347.

Scherer, F. M. & Ross, D. (1990), Industrial Market Structure and Economic Performance, Houghton Mifflin Company.

Schmitt, A. J.; Snyder, L. V. & Shen, Z.-J. M. (2008a), 'Centralization versus decentralization: Risk pooling, risk diversification, and supply uncertainty in a one-warehouse multiple-retailer system', 02/29/2008, http://ssrn.com/abstract=1115392, ac-cessed 06/02/2008.

Schmitt, A. J.; Snyder, L. V. & Shen, Z.-J. M. (2008b), Centralization versus decentralization: Risk pooling, risk diversification, and supply uncertainty in a one-warehouse multiple-retailer system, in 'Manufacturing & Service Operations Management Conference Proceedings', June 5-6, 2008, http://www.lehigh.edu/~ajs404/ MSOM_conf_08_OWMR.pdf, accessed 06/02/2008.

Schneekloth, U. & Leven, I. (2003), 'Woran bemisst sich eine gute Bevölkerungsumfrage? Analysen zu Ausmaß, Bedeutung und zu den Hintergründen von Nonresponse in stichprobenbasierten Zufallserhebungen am Beispiel des ALLBUS', ZUMA-Nachrichten 53, 16-57.

Schneider, D. (1987), Allgemeine Betriebswirtschaftslehre, Oldenbourg.

Schnuckel, M. (2010), Optimierung der Beschaffung durch vertikale Kooperation: Zur Relevanz des Bullwhip-Effekts aus der Perspektive des Einzelhandels, in Fröhlich-Glantschnig, E. & Lingohr, T., eds., Gibt es die optimale Einkaufsorganisation? Organisatorischer Wandel und pragmatische Methoden zur Effizienzsteigerung, Gabler, pp. 147-166.

Schoenmeyr, T. (2005), '"Centralized ordering policies in a multi-warehouse system with lead times and random demand" A paper by Gary Eppen and Linus Schrage: Presenta-tion by Tor Schoenmeyr', Lecture Notes, Massachusetts Institute of Technology, http:// ocw.mit.edu/courses/sloan-school-of-management/15-764-the-theory-of-operations-ma nagement-spring-2004/lecture-notes/lec2_schoenmeyr.pdf, accessed 09/10/2010.

Bibliography

241

Schreyögg, G. (1995), Umwelt, Technologie und Organisationsstruktur: Eine Analyse des kontingenztheoretischen Ansatzes, Haupt.

Schreyögg, G. (2008), Organisation, Gabler.

Schröder, R. (2008), Strategische Orientierungen für junge Technologieunternehmen, Gabler.

Schulte, C. (1999), Logistik: Wege zur Optimierung des Material- und Informationsflusses, Vahlen.

Schulze, P. M. (2007), Beschreibende Statistik, Oldenbourg Wissenschaftsverlag.

Schwarz, L. B. (1981), 'Physical distribution: The analysis of inventory and location', AIIE Transactions 13(2), 138-150.

Schwarz, L. B. (1989), 'A model for assessing the value of warehouse risk-pooling: Risk-pooling over outside-supplier leadtimes', Management Science 35(7), 828-842.

Schwarz, L. B.; Deuermeyer, B. L. & Badinelli, R. D. (1985), 'Fill-rate optimization in a one-warehouse n-identical retailer distribution system', Management Science 31(4), 488-498.

Scott, W. R. (1981), Organizations: Rational, Natural, and Open Systems, Prentice Hall.

Sculli, D. & Shum, Y. W. (1990), 'Analysis of a continuous review stock-control model with multiple suppliers', Journal of the Operational Research Society 41(9), 873-877.

Sculli, D. & Wu, S. Y. (1981), 'Stock control with two suppliers and normal lead times', Journal of the Operational Research Society 32(11), 1003-1009.

SDM (2001), 'Virtual warehouse created for Edge members', SDM: Security Distributing & Marketing 31(14), 26.

Sedarage, D.; Fujiwara, O. & Luong, H. T. (1999), 'Determining optimal order splitting and reorder level for N-supplier inventory systems', European Journal of Operational Research 116(2), 389-404.

Segal-Horn, S. & Faulkner, D. (2010), Understanding Global Strategy, South-Western Cengage Learning.

Shah, J. (2009), Supply Chain Management: Text and Cases, Pearson.

Shao, J.; Krishnan, H. & McCormick, S. T. (2009), 'Incentives for transshipment in a supply chain with decentralized retailers', technical report, Sauder School of Business, University of British Columbia, Vancouver, 09/25/2009, http://people.commerce.ubc.ca /phd/shao/Transshipment.pdf, accessed 01/07/2010.

Shao, X. & Ji, J. (2006), 'Reconfiguration of pharmaceutical logistics operations in China: An empirical study', Transportation Journal 45(4), 52-66.

Shao, X.-F. & Ji, J.-H. (2008), 'Evaluation of postponement strategies in mass customization with service guarantees', International Journal of Production Research 46(1), 153-171.

Shapiro, R. D. & Heskett, J. L. (1985), Logistics Strategy: Cases and Concepts, West Publishing.

Shapiro, R. D. (1984), 'Get leverage from logistics', Harvard Business Review 62(3), 119-126.

Bibliography

242

Shapley, L. S. (1953), A value for n-person games in Kuhn, H. W. & Tucker, A. W., eds., Contributions to the Theory of Games II (Annals of Mathematics Studies 28), Princeton University Press, pp. 307-317.

Sheffi, Y. (2004), Demand variability and supply chain flexibility: Driving from pure cost to lean flexibility supply chains, in Prockl, G.; Bauer, A.; Pflaum, A. & Müller-Steinfahrt, U., eds., Entwicklungspfade und Meilensteine moderner Logistik: Skizzen einer Roadmap, Gabler, pp. 85-117.

Sheffi, Y. (2006), Worst-Case-Szenario: Wie Sie Ihr Unternehmen auf Krisen vorbereiten und Ausfallrisiken minimieren, mi-Fachverlag, Redline GmbH.

Sheffi, Y. (2007), The Resilient Enterprise: Overcoming Vulnerability for Competitive Advantage, The MIT Press.

Shen, Z.-J. M.; Coullard, C. & Daskin, M. S. (2003), 'A joint location-inventory model', Transportation Science 37(1), 40-55.

Sherbrooke, C. C. (1992), 'Multiechelon inventory systems with lateral supply', Naval Research Logistics 39(1), 29-40.

Sheu, C. & Wacker, J. (1997), 'The effects of purchased parts commonality on manufacturing lead time', International Journal of Operations and Production Management 17(8), 725-745.

Shu, J.; Teo, C.-P. & Shen, Z.-J. M. (2005), 'Stochastic transportation-inventory network design problem', Operations Research 53(1), 48-60.

Silver, E. A.; Pyke, D. F. & Peterson, R. (1998), Inventory Management and Production Planning and Scheduling, John Wiley & Sons.

Simchi-Levi, D.; Kaminsky, P. & Simchi-Levi, E. (2008), Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies, McGraw-Hill/Irwin.

Simpson, T. W.; Seepersad, C. C. & Mistree, F. (2001), 'Balancing commonality and performance within the concurrent design of multiple products in a product family', Concurrent Engineering 9(3), 177-190.

Slack, N. (1999), The Blackwell Encyclopedic Dictionary of Operations Management, Wiley-Blackwell.

Slack, N.; Chambers, S. & Johnston, R. (2004), Operations Management, Prentice Hall.

Slikker, M.; Fransoo, J. & Wouters, M. (2001), 'Joint ordering in multiple newsvendor situations: A game theoretical approach', BETA Working Paper 64, Eindhoven University of Technology, 09/03/2001, http://alexandria.tue.nl/repository/books/553001 .pdf, accessed 09/23/2008.

Slikker, M.; Fransoo, J. & Wouters, M. (2005), 'Cooperation between multiple newsvendors with transshipments', European Journal of Operational Research 167(2), 370-380.

Smith, S. A. & Agrawal, N. (2000), 'Management of multi-item retail inventory systems with demand substitution', Operations Research 48(1), 50-64.

Snyder, K. (1995), 'New program set to provide ready inventory', Drug Topics 139(16), 19.

Snyder, L. V. & Shen, Z. J. M. (2006), 'Supply and demand uncertainty in multi-echelon supply chains', technical report, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA, http://citeseerx.ist.psu.edu/viewdoc/down load?doi=10.1.1.135.2642&rep=rep1&type=pdf, accessed 09/08/2010.

Bibliography

243

Snyder, L. V.; Daskin, M. S. & Teo, C.-P. (2007), 'The stochastic location model with risk pooling', European Journal of Operational Research 179(3), 1221-1238.

Soanes, C. & Hawker, S. (2008), Compact Oxford English Dictionary of Current English, Oxford University Press.

Sobel, M. J. (2008), Chapter 9: Risk pooling in Chhajed, D. & Lowe, T. J., eds., Building Intuition: Insights from Basic Operations Management Models and Principles, Springer, pp. 155-174.

Söllner, A. (2008), Einführung in das Internationale Management, Gabler.

Sommerrock, F. (2009), Erfolgreiche Post-Merger-Integration bei öffentlichen Institutionen: Fallstudienanalyse bei Sozialversicherungsträgern, Gabler.

Song, J.-S. & Zhao, Y. (2009), 'The value of component commonality in a dynamic inventory system with lead times', Manufacturing & Service Operations Management 11(3), 493-508.

Sošić, G. (2006), 'Transshipment of inventories among retailers: Myopic vs. farsighted stability', Management Science 52(10), 1493-1508.

Srinivasan, R.; Jayaraman, R.; Roundy, R. & Tayur, S. (1992), 'Procurement of common components in a stochastic environment', Research Report RC-18580, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 12/11/1992.

Staehle, W. (1994), Management: Eine verhaltenswissenschaftliche Perspektive, Vahlen.

Starbuck, W. H. (1981), A trip to view the elephants and rattlesnakes in the garden of Aston in Van de Ven, A. H. & Joyce, W. F., eds., Perspectives on Organization Design and Behavior, Wiley-Interscience, pp. 167-198.

Starbuck, W. H. (1982), 'Congealing oil: Inventing ideologies to justify acting ideologies out', Joumal of Management Studies 19(1), 3-27.

Statistisches Bundesamt Deutschland (2009a), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 1999', https://www-ec.de statis.de/csp/shop/sfg/bpm.html.cms.cBroker.cls?CSPCHD=00300001000048zs1kmC000000HLZWPabwm_rSQ$IqeQ26IQ--&cmspath=struktur,AeltereTitel.csp&ID=10226 16, accessed 07/16/2009.

Statistisches Bundesamt Deutschland (2009b), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2000', vide supra.

Statistisches Bundesamt Deutschland (2009c), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2001', vide supra.

Statistisches Bundesamt Deutschland (2009d), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2002', vide supra.

Statistisches Bundesamt Deutschland (2009e), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2003', vide supra.

Statistisches Bundesamt Deutschland (2009f), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2004', vide supra.

Statistisches Bundesamt Deutschland (2009g), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2005', vide supra.

Bibliography

244

Statistisches Bundesamt Deutschland (2009h), 'Beschäftigte, Umsatz, Aufwendungen, Lagerbestände usw. im Handel - Fachserie 6 Reihe 4 - 2006', https://www-ec.destatis.de /csp/shop/sfg/bpm.html.cms.cBroker.cls?cmspath=struktur,vollanzeige.csp&ID=1022616, accessed 07/16/2009.

Statistisches Bundesamt Deutschland (2009i), Statistisches Jahrbuch 2009 für die Bundesrepublik Deutschland, Statistisches Bundesamt Deutschland.

Statman, M. (1987), 'How many stocks make a diversified portfolio?', Journal of Financial & Quantitative Analysis 22(3), 353-363.

Staudinger, M. (2007), Supply Management im industriellen Großanlagenbau, LIT Verlag.

Stein, A. (2000), Gestaltungsoptionen der Umschlagsknoten, in Klaus, P. & Krieger, W., eds., Gabler Lexikon Logistik: Management logistischer Netzwerke und Flüsse, Gabler, pp. 485-488.

Stulman, A. (1987), 'Benefits of centralized stock for the multi-centre newsboy problem with first come, first served allocation', Journal of the Operational Research Society 38(9), 827-832.

Su, X. (2008), 'Bounded rationality in newsvendor models', Manufacturing & Service Operations Management 10(4), 566-589.

Sucky, E. (2009), 'The bullwhip effect in supply chains – An overestimated problem?', International Journal of Production Economics 118(1), 311-322.

Sugumaran, V. & Arogyaswamy, B. (2003), 'Measuring IT performance: "Contingency" variables and value modes', Journal of Computer Information Systems 44(2), 79-86.

Sussams, J. (1986), 'Buffer stocks and the square root law', Focus on Physical Distribution and Logistics Management 5(5), 8-10.

Swaminathan, J. M. & Lee, H. L. (2003), Chapter 5: Design for postponement in De Kok, A. G. & Graves, S. C., eds., Handbooks in Operations Research and Management Science: Supply Chain Management: Design, Coordination and Operation, Elsevier, pp. 199-226.

Swaminathan, J. M. & Tayur, S. R. (1998), 'Managing broader product lines through delayed differentiation using vanilla boxes', Management Science 44(12), S161-S172.

Swaminathan, J. M. (2001), 'Enabling customization using standardized operations', California Management Review 43(3), 125-135.

Syntetos, A. A. & Boylan, J. E. (2001), 'On the bias of intermittent demand estimates', International Journal of Production Economics 71(1-3), 457-466.

Syntetos, A. A. & Boylan, J. E. (2005), 'The accuracy of intermittent demand estimates', International Journal of Forecasting 21(2), 303-314.

Syntetos, A. A. & Boylan, J. E. (2006), 'On the stock control performance of intermittent demand estimators', International Journal of Production Economics 103(1), 36-47.

Syntetos, A. A.; Boylan, J. E. & Croston, J. D. (2005), 'On the categorisation of demand patterns', Journal of the Operational Research Society 56(5), 495-503.

Taaffe, K.; Geunes, J. & Romeijn, H. E. (2008), 'Target market selection and marketing effort under uncertainty: The selective newsvendor', European Journal of Operational Research 189(3), 987-1003.

Bibliography

245

Tagaras, G. & Cohen, M. A. (1992), 'Pooling in two-location inventory systems with non-negligible replenishment lead times', Management Science 38(8), 1067-1083.

Tagaras, G. & Vlachos, D. (2002), 'Effectiveness of stock transshipment under various demand distributions and nonnegligible transshipment times', Production & Operations Management 11(2), 183-198.

Tagaras, G. (1989), 'Effects of pooling on the optimization and service levels of two-location inventory systems', IIE Transactions 21(3), 250-257.

Tagaras, G. (1999), 'Pooling in multi-location periodic inventory distribution systems', Omega 27(1), 39-59.

Tallon, W. J. (1993), 'The impact of inventory centralization on aggregate safety stock: The variable supply lead time case', Journal of Business Logistics 14(1), 185-203.

Taylor, D. A. (2004), Supply Chains: A Manager's Guide, Addison-Wesley.

Taylor, G. D., ed. (2008), Logistics Engineering Handbook, CRC Press Taylor & Francis Group.

Tempelmeier, H. (2006), Inventory Management in Supply Networks, Books on Demand.

Teo, C. P.; Ou, J. & Goh, M. (2001), 'Impact on inventory costs with consolidation of distribution centers', IIE Transactions 33(2), 99-110.

Teunter, R. & Sani, B. (2009), 'Calculating order-up-to levels for products with intermittent demand', International Journal of Production Economics 118(1), 82-86.

Thayer, W. (2009), 'Kroger powers ahead', Refrigerated & Frozen Foods Retailer 7(3), 16-26.

Thomas, D. & Hackman, S. (2003), 'A committed delivery strategy with fixed frequency and quantity', European Journal of Operational Research 148(2), 363-373.

Thomas, D. J. & Tyworth, J. E. (2006), 'Pooling lead-time risk by order splitting: A critical review', Transportation Research: Part E 42(4), 245-257.

Thomas, D. J. & Tyworth, J. E. (2007), 'Is pooling lead-time risk by splitting orders simultaneously worthwhile?', Journal of Business Logistics 28(1), 169-193.

Thomas, L. C.; Possani, E. & Archibald, T. W. (2003), 'How useful is commonality? Inventory and production decisions to maximize survival probability in start-ups', IMA Journal of Management Mathematics 14(4), 305-320.

Thompson, B. (1994), 'The concept of statistical significance testing', Practical Assessment, Research & Evaluation 4(5), retrieved 10/24/2009 from http://PAREonline. net/getvn.asp?v=4\&n=5.

Thompson, B. (1996), 'AERA editorial policies regarding statistical significance testing: Three suggested reforms', Educational Researcher 25(2), 26-30.

Thonemann, U. (2005), Operations Management: Konzepte, Methoden und Anwendungen, Pearson Studium.

Thonemann, U. W. & Brandeau, M. L. (2000), 'Optimal commonality in component design', Operations Research 48(1), 1-19.

Tiacci, L. & Saetta, S. (2009), 'An approach to evaluate the impact of interaction between demand forecasting method and stock control policy on the inventory system performances', International Journal of Production Economics 118(1), 63-71.

Bibliography

246

Tomlin, B. & Wang, Y. (2005), 'On the value of mix flexibility and dual sourcing in unreliable newsvendor networks', Manufacturing & Service Operations Management 7(1), 37-57.

Treece, J. B. (1996), 'Saturn picks Japan helper', Automotive News 71(5675), 43.

Tsubone, H.; Matsuura, H. & Satoh, S. (1994), 'Component part commonality and process flexibility effects on manufacturing performance', International Journal of Production Research 32(10), 2479-2493.

Turner, N. (2001), 'Choosing the most appropriate warehouse management system', Logistics & Transport Focus 3(7), 30-33.

Tyagi, R. & Das, C. (1998), 'Extension of the square-root law for safety stock to demands with unequal variances', Journal of Business Logistics 19(2), 197-203.

Tyagi, R. & Das, C. (1999), 'Grouping customers for better allocation of resources to serve correlated demands', Computers and Operations Research 26(10-11), 1041-1058.

Tyworth, J. E. & Ruiz-Torres, A. (2000), 'Transportation's role in the sole versus dual-sourcing decisions', International Journal of Physical Distribution and Logistics Management 30(2), 128-136.

U.S. Census Bureau (2009), 'Latest monthly wholesale trade report', http://www2.census. gov/wholesale/xls/mwts/historic1.xls, accessed 07/16/2009.

Ulrich, K. & Ellison, D. J. (1999), 'Holistic customer requirements and the design-select decision', Management Science 45(5), 641-658.

Upton, D. M. (1994), 'The management of manufacturing flexibility', California Management Review 36(2), 72-89.

Upton, D. M. (1995), 'What really makes factories flexible?', Harvard Business Review 73(4), 74-84.

Vahrenkamp, R. (2000), Logistikmanagement, Oldenbourg.

Vakharia, A.; Parmenter, D. A. & Sanchez, S. (1996), 'The operating impact of parts commonality', Journal of Operations Management 14(1), 3-18.

Van Hoek, R. I. & Van Dierdonck, R. (2000), 'Postponed manufacturing supplementary to transportation services?', Transportation Research: Part E 36(3), 205-217.

Van Hoek, R. I. (1997), 'Postponed manufacturing: A case study in the food supply chain', Supply Chain Management: An International Journal 2(2), 63-75.

Van Hoek, R. I. (1998a), 'Reconfiguring the supply chain to implement postponed manufacturing', International Journal of Logistics Management 9(1), 95-110.

Van Hoek, R. I. (1998b), 'Logistics and virtual integration: Postponement, outsourcing and the flow of information', International Journal of Physical Distribution & Logistics Management 28(7), 508-523.

Van Hoek, R. I. (2000a), 'The thesis of leagility revisited', International Journal of Agile Management Systems 2(3), 196-201.

Van Hoek, R. I. (2000b), 'The role of third-party logistics providers in mass customization', International Journal of Logistics Management 11(1), 37-46.

Van Hoek, R. I. (2001), 'The rediscovery of postponement: A literature review and directions for research', Journal of Operations Management 19(2), 161-184.

Bibliography

247

Van Hoek, R. I.; Commandeur, H. R. & Vos, B. (1998), 'Reconfiguring logistics systems through postponement strategies', Journal of Business Logistics 19(1), 33-54.

Van Hoek, R. I.; Peelen, E. & Commandeur, H. R. (1999a), 'Achieving mass customization through postponement: A study of international changes', Journal of Market Focused Management 3(3-4), 353-368.

Van Hoek, R. I.; Vos, B. & Commandeur, H. R. (1999b), 'Restructuring European supply chains by implementing postponement strategies', Long Range Planning 32(5), 505-518.

Van Mieghem, J. A. & Dada, M. (1999), 'Price versus production postponement: Capacity and competition', Management Science 45(12), 1631-1649.

Van Mieghem, J. A. (2004), 'Note–Commonality strategies: Value drivers and equivalence with flexible capacity and inventory substitution', Management Science 50(3), 419-424.

Van Mieghem, J. A. (2007), 'Risk mitigation in newsvendor networks: Resource diversification, flexibility, sharing, and hedging', Management Science 53(8), 1269-1288.

Van Mieghem, J. A. (2008), Operations Strategy: Principles and Practice, Dynamic Ideas.

Verkoeijen, P. C. F. M. & deHaas, R. C. T. (1998), 'Virtual warehousing, an inventory (virtual warehousing, een inventarisatie)', technical report, NASA no. 19990036800, NATO Maintenance and Supply Agency (NASA).

Vidyarthi, N.; Çelebi, E.; Elhedhli, S. & Jewkes, E. (2007), 'Integrated production-inventory-distribution system design with risk pooling: Model formulation and heuristic solution', Transportation Science 41(3), 392-408.

Vockell, E. L. & Asher, J. W. (1995), Educational Research, Allyn & Bacon.

Voorhees, R. D. & Sharp, M. K. (1978), 'The principles of logistics revisited', Transportation Journal 18(1), 69-84.

Wacker, J. G. & Treleven, M. (1986), 'Component part standardization: An analysis of commonality sources and indices', Journal of Operations Management 6(2), 219-244.

Wacker, J. G. (2004), 'A theory of formal conceptual definitions: Developing theory-building measurement instruments', Journal of Operations Management 22(6), 629-650.

Wagner, G. R. (1997), Betriebswirtschaftliche Umweltökonomie, Lucius & Lucius.

Wagner, S. M. & Bode, C. (2008), 'An empirical examination of supply chain performance along several dimensions of risk', Journal of Business Logistics 29(1), 307-325.

Walleigh, R. (1989), 'Product design for low-cost manufacturing', Journal of Business Strategy 10(4), 37-41.

Waller, M. A.; Dabholkar, P. A. & Gentry, J. J. (2000), 'Postponement, product customization, and market-oriented supply chain management', Journal of Business Logistics 21(2), 133-160.

Walonick, D. (2009), Survival Statistics, StatPac, Inc.

Wang, H. W.; Chen, R. Q. & Li, Y. (2006), 'Case study on the application of postponement strategy and managerial insights', Asia Pacific Management Review 11(3), 141-153.

Wang, Y.; Jiang, L. & Shen, Z. J. (2004), 'Channel performance under consignment contract with revenue sharing', Management Science 50(1), 34-47.

Bibliography

248

Wanke, P. (1999), 'Formalizando uma Política de Estoques para a Cadeia de Suprimentos', Revista Tecnologística 5(48), 22-29.

Wanke, P. F. & Saliby, E. (2009), 'Consolidation effects: Whether and how inventories should be pooled', Transportation Research: Part E 45(5), 678-692.

Wanke, P. F. & Zinn, W. (2004), 'Strategic logistics decision making', International Journal of Physical Distribution & Logistics Management 34(6), 466-478.

Wanke, P. F. (2009), 'Consolidation effects and inventory portfolios', Transportation Research: Part E 45(1), 107-124.

Wannenwetsch, H. (2009), Integrierte Materialwirtschaft und Logistik: Beschaffung, Logistik, Materialwirtschaft und Produktion, Springer.

Watson, M. & Morton, J. (2000), 'Designing perfect distribution channels: Software helps determine optimal plan', Parcel Shipping & Distribution Magazine, April, http://e-opt.informs.org/resources/uploads/ACF2CBF.pdf, accessed 03/28/2008.

Wazed, M. A.; Ahmed, S. & Yusoff, N. (2008), 'Commonality models in manufacturing resources planning: State-of-the-art and future directions', European Journal of Scientific Research 23(3), 421-435.

Wazed, M. A.; Ahmed, S. & Yusoff, N. (2009), 'Commonality and its measurement in manufacturing resources planning', Journal of Applied Sciences 9(1), 69-78.

Weber, M. (1980), Wirtschaft und Gesellschaft: Grundriß der verstehenden Soziologie, Mohr.

Wee, K. E. & Dada, M. (2005), 'Optimal policies for transshipping inventory in a retail network', Management Science 51(10), 1519-1533.

Wegner, U. (1996), Einführung in das Logistikmanagement: Prozesse, Strukturen, Anwendungen, Gabler.

Weisstein, E. W. (2010), 'Variance', http://mathworld.wolfram.com/Variance.html, access 02/26/2010.

Weng, Z. K. & McClurg, T. (2003), 'Coordinated ordering decisions for short life cycle products with uncertainty in delivery time and demand', European Journal of Operational Research 151(1), 12.

Weng, Z. K. (1998), 'Managing production with flexible capacity deployment for serial multi-stage manufacturing systems', European Journal of Operational Research 109(3), 587-598.

Weng, Z. K. (1999), 'Risk-pooling over demand uncertainty in the presence of product modularity', International Journal of Production Economics 62(1), 75-85.

Wessiepe, K. (2009), 'Das Postleitzahlen-Diagramm 3.7', http://www.klaus-wessiepe.de/ plz.htm, accessed 07/18/2009.

White, S. C. (2005), 'Freight consolidation', Special Report, Council of Supply Chain Management Professionals, April 2005, cscmp.org/downloads/public/resources/freight con.pdf, accessed 09/14/2009.

Whybark, D. C. (1989), Case 4-3: International plow, in 'International Operations Management: A Selection of IMEDE Cases', Irwin, pp. 267-274.

Bibliography

249

Wildemann, H. (2008), Produktkannibalisierung erkennen und vermeiden in Specht, D., ed., Produkt- und Prozessinnovationen in Wertschöpfungsketten: Tagungsband der Herbsttagung 2007 der Wissenschaftlichen Kommission Produktionswirtschaft im VHB, Gabler, pp. 71-83.

Willemain, T. R.; Smart, C. N.; Shockor, J. H. & DeSautels, P. A. (1994), 'Forecasting intermittent demand in manufacturing: A comparative evaluation of Croston's method', International Journal of Forecasting 10(4), 529-538.

Williams, J. (1975), 'Food distribution costs: Results of an inter-firm study of wholesale transportation and warehousing costs', technical report, National Materials Handling Center Cranfield, Cranfield, UK.

Wisner, J. D.; Tan, K.-C. & Leong, G. K. (2009), Principles of Supply Chain Management: A Balanced Approach, South-Western Cengage Learning.

Wong, C. Y. & Hvolby, H.-H. (2007), 'Coordinated responsiveness for volatile toy supply chains', Production Planning & Control 18(5), 407-419.

Wong, H. (2005), 'Pooling of repairable spare parts: A study on inventory policies', 4OR: A Quarterly Journal of Operations Research 3(3), 253-256.

Wong, H.; Cattrysse, D. & van Oudheusden, D. (2005a), 'Stocking decisions for repairable spare parts pooling in a multi-hub system', International Journal of Production Economics 93-94(1), 309-317.

Wong, H.; van Houtum, G. J.; Cattrysse, D. & van Oudheusden, D. (2005b), 'Simple, efficient heuristics for multi-item multi-location spare parts systems with lateral transshipments and waiting time constraints', Journal of the Operational Research Society 56(12), 1419-1430.

Wong, H.; van Oudheusden, D. & Cattrysse, D. (2007a), 'Cost allocation in spare parts inventory pooling', Transportation Research: Part E 43(4), 370-386.

Wong, H.; van Oudheusden, D. & Cattrysse, D. (2007b), 'Two-echelon multi-item spare parts systems with emergency supply flexibility and waiting time constraints', IIE Transactions 39(11), 1045-1057.

Wong, H.; Wikner, J. & Naim, M. (2009), 'Analysis of form postponement based on optimal positioning of the differentiation point and stocking decisions', International Journal of Production Research 47(5), 1201-1224.

Woolsey, G. (1988), 'A requiem for the EOQ: An editorial', Production and Inventory Management Journal 29(3), 68-72.

Wright, P. B. (1994), 'The humana case and other tax issues', Risk Management (00355593) 41(5), 77-78.

Xu, K. & Evers, P. T. (2003), 'Managing single echelon inventories through demand aggregation and the feasibility of a correlation matrix', Computers & Operations Research 30(2), 297-309.

Xu, K.; Evers, P. T. & Fu, M. C. (2003), 'Estimating customer service in a two-location continuous review inventory model with emergency transshipments', European Journal of Operational Research 145(3), 569-585.

Yanagi, S. & Sasaki, M. (1992), 'An approximation method for the problem of a repairable-item inventory system with lateral resupply', IMA Journal of Mathematics Applied in Business and Industry 3(4), 305-314.

Bibliography

250

Yang, B.; Burns, N. & Backhouse, C. (2004), 'Management of uncertainty through postponement', International Journal of Production Research 42(6), 1049-1064.

Yang, B.; Burns, N. D. & Backhouse, C. J. (2005a), 'The application of postponement in industry', IEEE Transactions on Engineering Management 52(2), 238-248.

Yang, B.; Burns, N. D. & Backhouse, C. J. (2005b), 'An empirical investigation into the barriers to postponement', International Journal of Production Research 43(5), 991-1005.

Yang, B.; Yang, Y. & Wijngaard, J. (2007), 'Postponement: An inter-organizational perspective', International Journal of Production Research 45(4), 971-988.

Yang, H. & Schrage, L. (2003), 'An inventory anomaly: Risk pooling may increase inventory', technical report, Graduate School of Business, University of Chicago, IL.

Yang, H. & Schrage, L. (2009), 'Conditions that cause risk pooling to increase inventory', European Journal of Operational Research 192(3), 837-851.

Yang, J. & Qin, Z. (2007), 'Capacitated production control with virtual lateral transshipments', Operations Research 55(6), 1104-1119.

Yeung, J. H. Y.; Selen, W.; Deming, Z. & Min, Z. (2007), 'Postponement strategy from a supply chain perspective: Cases from China', International Journal of Physical Distribution & Logistics Management 37(4), 331-356.

Yu, J. & Cooper, H. (1983), 'A quantitative review of research design effects on response rates to questionnaires', Journal of Marketing Research 20(1), 36-44.

Yu, Y.; Benjaafar, S. & Gerchak, Y. (2008), 'Capacity pooling and cost sharing among independent firms in the presence of congestion', 02/27/2008, http://www.me.umn.edu/ research/faculty/pdf/ybg-2-27-08.pdf, accessed 03/28/2008.

Zhang, D. & Cooper, W. L. (2005), 'Revenue management for parallel flights with customer-choice behavior', Operations Research 53(3), 415-431.

Zhang, J. (2005), 'Transshipment and its impact on supply chain members' performance', Management Science 51(10), 1534-1539.

Zhang, J. (2009), 'Cost allocation for joint replenishment models', Operations Research 57(1), 146-156.

Zhang, Q.; Vonderembse, M. A. & Lim, J.-S. (2002), 'Value chain flexibility: A dichotomy of competence and capability', International Journal of Production Research 40(3), 561-583.

Zhao, H.; Deshpande, V. & Ryan, J. K. (2006), 'Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests', Naval Research Logistics 53(6), 547-567.

Zhao, H.; Deshpande, V. & Ryan, J. K. (2005), 'Inventory sharing and rationing in decentralized dealer networks', Management Science 51(4), 531-547.

Zhao, H.; Ryan, J. K. & Deshpande, V. (2008), 'Optimal dynamic production and inventory transshipment policies for a two-location make-to-stock system', Operations Research 56(2), 400-410.

Zhao, X. & Atkins, D. (2009), 'Transshipment between competing retailers', IIE Transactions 41(8), 665-676.

Bibliography

251

Zhou, L. & Grubbström, R. W. (2004), 'Analysis of the effect of commonality in multi-level inventory systems applying MRP theory', International Journal of Production Economics 90(2), 251-263.

Zhou, L. G. & Lau, H. S. (1992), 'Reducing inventory costs and choosing suppliers with order splitting', Journal of the Operational Research Society 43(10), 1003-1008.

Zinn, W. & Bowersox, D. J. (1988), 'Planning physical distribution with the principle of postponement', Journal of Business Logistics 9(2), 117-136.

Zinn, W. (1990), 'Developing heuristics to estimate the impact of postponement on safety stock', International Journal of Logistics Management 1(2), 11-16.

Zinn, W.; Levy, M. & Bowersox, D. J. (1989), 'Measuring the effect of inventory centralization/decentralization on aggregate safety stock: The "square root law" revisited', Journal of Business Logistics 10(1), 1-14.

Zinn, W.; Levy, M. & Bowersox, D. J. (1990), 'On assumed assumptions and the inventory centralization/decentralization issue', Journal of Business Logistics 11(2), 139-142.

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