Cooperative Lot Sizing Games in Supply Chains (eBook)

Julia Drechsel worked as research assistant at the universities of Freiberg and Duisburg-Essen, Germany from 2005-2009. Since 2009 she is Senior Process Specialist for Supply Chain Optimization with Bayer Technology Services.

Preface 6
Contents 8
List of Figures 12
List of Tables 14
Chapter 1 Introduction 16
Chapter 2 Selected Topics in Cooperative Game Theory 19
2.1 History of Game Theory 19
2.2 Basics in Cooperative Game Theory 22
2.2.1 A Cooperative Game 23
2.2.2 Properties of Cooperative Games 25
2.2.3 Variants and Fundamental Applications of the Classical Cooperative Game 27
2.2.4 Interval-Valued Games 29
2.3 Allocating Cooperative Costs 31
2.3.1 Motivation and Classification of Allocation Methods 31
2.3.2 Properties of Cost Allocations 32
2.3.3 Non-Game-Theoretical Cost Allocation Methods 34
2.3.4 The Core 36
2.3.5 Additive Core Variants 40
2.3.6 Multiplicative Core Variants 43
2.3.7 The Subcoalition-Perfect Core 46
2.3.8 The Interval Core 50
2.3.9 The Shapley Value 51
2.3.10 Conclusions 52
Chapter 3 Algorithmic Game Theory 54
3.1 Literature 55
3.2 Computing Core Cost Allocations 56
3.3 Theoretical Background 58
3.4 Including Fairness Criteria 59
3.5 Computing Core Variants 62
3.6 Computing Interval Core Elements 64
3.7 Conclusions 65
Chapter 4 Cooperation in Supply Chains 67
4.1 Horizontal versus Vertical Cooperation 68
4.2 Supply Chain Games in the Literature 71
Chapter 5 An Economic Lot Sizing Game 74
5.1 Cooperative Ordering Situations 74
5.1.1 The Underlying Problem 74
5.1.2 Properties of the ELS Game 76
5.2 Computing Core Cost Allocations for the ELS Game 76
5.2.1 The Row Generation Procedure 77
5.2.2 A Numerical Example 80
5.3 Computational Study for the ELS Game 84
5.4 Extensions for the ELS Game 90
Chapter 6 A Lot Sizing Game with Uncertain Demand 92
6.1 The Underlying Problem 92
6.2 Special Phenomena of Interval Cores 93
6.3 A New Definition of the Interval Core and Its Computation 94
6.4 Computational Study for the Interval ELS Game 96
Chapter 7 A Capacitated Lot Sizing Game with Transshipments, Scarce Capacities, and Player-Dependent Cost Coefficients 97
7.1 Cooperative Production Situations 97
7.1.1 The Underlying Problem 97
7.1.2 The CLSP Game 99
7.1.3 Properties of the CLSP Game 103
7.2 Solving the Cooperative CLSP 104
7.2.1 A Lagrangean Relaxation Based Heuristic 104
7.2.2 A Fix-and-Optimize Heuristic 108
7.3 Computing Core Cost Allocations for the CLSP Game 111
7.3.1 The Row Generation Procedure 111
7.3.2 Computing the Subcoalition-Perfect Core 114
7.3.3 Computing the Minmax Core 116
7.4 Computational Study for the CLSP Game 116
7.4.1 Computational Study: Lagrangean RelaxationBased Heuristic 117
7.4.2 Computational Study: Fix-and-Optimize Heuristic 119
7.4.3 Computational Study: Subcoalition-Perfect Core 124
7.4.4 Computational Study: Minmax Core 125
7.5 Extensions for the CLSP Game 127
Chapter 8 A Multilevel Lot Sizing Game with Restricted Cooperation 129
8.1 Cooperative Supply Situations 129
8.1.1 The Underlying Problem 129
8.1.2 Games with Restricted Cooperation 134
8.1.3 Properties of the MLCLSP Game 139
8.2 Computing Core Cost Allocations for the MLCLSP Game 139
8.2.1 The Row Generation Procedure 140
8.2.2 A Numerical Example 143
8.2.3 Computing Core Variants 145
8.3 Computational Study for the MLCLSP Game 146
Chapter 9 Conclusions and Future Research 151
Appendix A Computational Study CLSP Game 154
A.1 Computational Study: Lagrangean Relaxation Based Heuristic 154
A.2 Computational Study: Fix-and-Optimize Heuristic 158
Appendix B Computational Study MLCLSP Game 159
Bibliography 163