The logic of logistics : theory, algorithms, and applications for logistics and supply chain management

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Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state-of-the-art in the science of logistics management. this field that many practitioners and researchers will find makes an invaluable companion to their work.

Preface	p. v
1 Introduction	p. 1
1.1 What Is Logistics Management?	p. 1
1.2 Managing Cost and Uncertainty	p. 3
1.3 Examples	p. 4
1.4 Modeling Logistics Problems	p. 7
1.5 Logistics in Practice	p. 7
1.6 Evaluation of Solution Techniques	p. 9
1.7 Additional Topics	p. 10
1.8 Book Overview	p. 11
I Performance Analysis Techniques	p. 12
2 Convexity and Supermodularity	p. 13
2.1 Introduction	p. 13
2.2 Convex Analysis	p. 13
2.2.1 Convex Sets and Convex Functions	p. 13
2.2.2 Continuity and Differentiability Properties	p. 16
2.2.3 Characterization of Convex Functions	p. 20
2.2.4 Convexity and Optimization	p. 23
2.3 Supermodularity	p. 24
2.4 Exercises	p. 31
3 Worst-Case Analysis	p. 33
3.1 Introduction	p. 33
3.2 The Bin-Packing Problem	p. 34
3.2.1 First-Fit and Best-Fit	p. 36
3.2.2 First-Fit Decreasing and Best-Fit Decreasing	p. 39
3.3 The Traveling Salesman Problem	p. 40
3.3.1 A Minimum Spanning Tree Based Heuristic	p. 41
3.3.2 The Nearest Insertion Heuristic	p. 42
3.3.3 Christofides' Heuristic	p. 46
3.3.4 Local Search Heuristics	p. 49
3.4 Exercises	p. 50
4 Average-Case Analysis	p. 55
4.1 Introduction	p. 55
4.2 The Bin-Packing Problem	p. 56
4.3 The Traveling Salesman Problem	p. 61
4.4 Exercises	p. 66
5 Mathematical Programming Based Bounds	p. 69
5.1 Introduction	p. 69
5.2 An Asymptotically Tight Linear Program	p. 70
5.3 Lagrangian Relaxation	p. 73
5.4 Lagrangian Relaxation and the Traveling Salesman Problem	p. 75
5.4.1 The 1-Tree Lower Bound	p. 76
5.4.2 The 1-Tree Lower Bound and Lagrangian Relaxation	p. 77
5.5 The Worst-Case Effectiveness of the 1-tree Lower Bound	p. 78
5.6 Exercises	p. 82
II Inventory Models	p. 84
6 Economic Lot Size Models with Constant Demands	p. 85
6.1 Introduction	p. 85
6.1.1 The Economic Lot Size Model	p. 85
6.1.2 The Finite Horizon Model	p. 87
6.1.3 Power of Two Policies	p. 89
6.2 Multi-Item Inventory Models	p. 91
6.2.1 Introduction	p. 91
6.2.2 Notation and Assumptions	p. 93
6.2.3 Worst-Case Analyses	p. 93
6.3 A Single Warehouse Multi-Retailer Model	p. 98
6.3.1 Introduction	p. 98
6.3.2 Notation and Assumptions	p. 98
6.4 Exercises	p. 103
7 Economic Lot Size Models with Varying Demands	p. 105
7.1 The Wagner-Whitin Model	p. 105
7.2 Models with Capacity Constraints	p. 111
7.3 Multi-Item Inventory Models	p. 114
7.4 Exercises	p. 116
8 Stochastic Inventory Models	p. 119
8.1 Introduction	p. 119
8.2 Single Period Models	p. 120
8.2.1 The Model	p. 120
8.3 Finite Horizon Models	p. 121
8.3.1 Model Description	p. 121
8.3.2 K-Convex Functions	p. 123
8.3.3 Main Results	p. 126
8.4 Quasiconvex Loss Functions	p. 127
8.5 Infinite Horizon Models	p. 130
8.6 Multi-Echelon Systems	p. 137
8.7 Exercises	p. 139
9 Integration of Inventory and Pricing	p. 141
9.1 Introduction	p. 141
9.2 Single Period Models	p. 142
9.3 Finite Horizon Models	p. 145
9.3.1 Model Description	p. 145
9.3.2 Symmetric K-Convex Functions	p. 148
9.3.3 Additive Demand Functions	p. 153
9.3.4 General Demand Functions	p. 155
9.3.5 Special Case: Zero Fixed Ordering Cost	p. 156
9.3.6 Extensions and Challenges	p. 157
9.4 Risk Averse Inventory Models	p. 158
9.4.1 Expected utility risk averse models	p. 159
9.4.2 Exponential utility risk averse models	p. 161
9.5 Exercises	p. 163
III Design and Coordination Models	p. 166
10 Procurement Contracts	p. 167
10.1 Introduction	p. 167
10.2 Wholesale Contracts	p. 169
10.3 Buy Back Contracts	p. 171
10.4 Revenue Sharing Contracts	p. 172
10.5 Portfolio Contracts	p. 173
10.6 Exercises	p. 177
11 Supply Chain Planning Models	p. 179
11.1 Introduction	p. 179
11.2 The Shipper Problem	p. 180
11.2.1 The Shipper Model	p. 181
11.2.2 A Set-Partitioning Approach	p. 182
11.2.3 Structural Properties	p. 186
11.2.4 Solution Procedure	p. 187
11.2.5 Computational Results	p. 190
11.3 Safety Stock Optimization	p. 194
11.4 Exercise	p. 196
12 Facility Location Models	p. 199
12.1 Introduction	p. 199
12.2 An Algorithm for the p-Median Problem	p. 200
12.3 An Algorithm for the Single-Source Capacitated Facility Location Problem	p. 204
12.4 A Distribution System Design Problem	p. 207
12.5 The Structure of the Asymptotic Optimal Solution	p. 212
12.6 Exercises	p. 213
IV Vehicle Routing Models	p. 215
13 The Capacitated VRP with Equal Demands	p. 217
13.1 Introduction	p. 217
13.2 Worst-Case Analysis of Heuristics	p. 218
13.3 The Asymptotic Optimal Solution Value	p. 223
13.4 Asymptotically Optimal Heuristics	p. 225
13.5 Exercises	p. 228
14 The Capacitated VRP with Unequal Demands	p. 229
14.1 Introduction	p. 229
14.2 Heuristics for the CVRP	p. 229
14.3 Worst-Case Analysis of Heuristics	p. 233
14.4 The Asymptotic Optimal Solution Value	p. 236
14.4.1 A Lower Bound	p. 237
14.4.2 An Upper Bound	p. 240
14.5 Probabilistic Analysis of Classical Heuristics	p. 242
14.5.1 A Lower Bound	p. 244
14.5.2 The UOP([alpha]) Heuristic	p. 246
14.6 The Uniform Model	p. 248
14.7 The Location-Based Heuristic	p. 250
14.8 Rate of Convergence to the Asymptotic Value	p. 253
14.9 Exercises	p. 254
15 The VRP with Time Window Constraints	p. 257
15.1 Introduction	p. 257
15.2 The Model	p. 257
15.3 The Asymptotic Optimal Solution Value	p. 259
15.4 An Asymptotically Optimal Heuristic	p. 265
15.4.1 The Location-Based Heuristic	p. 265
15.4.2 A Solution Method for CVLPTW	p. 267
15.4.3 Implementation	p. 269
15.4.4 Numerical Study	p. 269
15.5 Exercises	p. 272
16 Solving the VRP Using a Column Generation Approach	p. 275
16.1 Introduction	p. 275
16.2 Solving a Relaxation of the Set-Partitioning Formulation	p. 276
16.3 Solving the Set-Partitioning Problem	p. 280
16.3.1 Identifying Violated Clique Constraints	p. 282
16.3.2 Identifying Violated Odd Hole Constraints	p. 282
16.4 The Effectiveness of the Set-Partitioning Formulation	p. 283
16.4.1 Motivation	p. 284
16.4.2 Proof of Theorem 8.4.1	p. 285
16.5 Exercises	p. 288
V Logistics Algorithms in Practice	p. 292
17 Network Planning	p. 293
17.1 Introduction	p. 293
17.2 Network Design	p. 294
17.3 Strategic Safety Stock	p. 305
17.4 Resource Allocation	p. 313
17.5 Summary	p. 317
17.6 Exercises	p. 318
18 A Case Study: School Bus Routing	p. 319
18.1 Introduction	p. 319
18.2 The Setting	p. 320
18.3 Literature Review	p. 322
18.4 The Problem in New York City	p. 323
18.5 Distance and Time Estimation	p. 325
18.6 The Routing Algorithm	p. 327
18.7 Additional Constraints and Features	p. 331
18.8 The Interactive Mode	p. 333
18.9 Data, Implementation and Results	p. 334
19 References	p. 337
Index	p. 350

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