## The Logic of Logistics: Theory, Algorithms, and Applications for Logistics ManagementThis book grew out a number of distribution and logistics graduate courses we have taught over the last ten years. In the first few years, the emphasis was on very basic models such as the traveling salesman problem, and on the seminal papers of Haimovich and Rinnooy Kan (1985), which analyzed a simple vehicle routing problem, and Roundy (1985), which introduced power-of-two policies and proved that they are effective for the one warehouse multi-retailer distribution system. At that time, few results existed for more complex, realistic distribution problems, stochastic inventory problems or the integration of these issues. In the last few years however, there has been renewed interest in the area of logistics among both industry and academia. A number of forces have contributed to this shift. First, industry has realized the magnitude of savings that can be achieved by better planning and management of complex logistics systems. In deed, a striking example is Wal-Mart's success story which is partly attributed to implementing a new logistics strategy, called cross-docking. Second, advances in information and communication technologies together with sophisticated decision support systems now make it possible to design, implement and control logistics strategies that reduce system-wide costs and improve service level. These decision support systems, with their increasingly user-friendly interfaces, are fundamentally changing the management of logistics systems. |

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### Contents

Introduction | 1 |

12 Examples | 3 |

13 Modeling Logistics Problems | 6 |

14 Logistics in Practice | 7 |

15 Evaluation of Solution Techniques | 8 |

16 Additional Topics | 9 |

17 Book Overview | 10 |

PERFORMANCE ANALYSIS TECHNIQUES | 13 |

84 The Effectiveness of the SetPartitioning Formulation | 133 |

842 Proof of Theorem | 135 |

85 Exercises | 138 |

INVENTORY MODELS | 143 |

Economic Lot Size Models with Constant Demands | 145 |

912 The Finite Horizon Model | 147 |

913 Power of Two Policies | 149 |

92 MultiItem Inventory Models | 151 |

WorstCase Analysis | 15 |

22 The BinPacking Problem | 16 |

221 FirstFit and BestFit | 18 |

222 FirstFit Decreasing and BestFit Decreasing | 21 |

23 The Traveling Salesman Problem | 22 |

231 A Minimum Spanning Tree Based Heuristic | 23 |

232 The Nearest Insertion Heuristic | 24 |

233 Christofides Heuristic | 28 |

234 Local Search Heuristics | 29 |

24 Exercises | 32 |

AverageCase Analysis | 37 |

32 The BinPacking Problem | 38 |

33 The Traveling Salesman Problem | 43 |

34 Exercises | 48 |

Mathematical Programming Based Bounds | 51 |

42 An Asymptotically Tight Linear Program | 52 |

43 Lagrangian Relaxation | 55 |

44 Lagrangian Relaxation and the Traveling Salesman Problem | 57 |

442 The ITree Lower Bound and Lagrangian Relaxation | 59 |

45 The WorstCase Effectiveness of the 1tree Lower Bound | 60 |

46 Exercises | 64 |

VEHICLE ROUTING MODELS | 67 |

The Capacitated VRP with Equal Demands | 69 |

52 WorstCase Analysis of Heuristics | 70 |

53 The Asymptotic Optimal Solution Value | 75 |

54 Asymptotically Optimal Heuristics | 76 |

55 Exercises | 80 |

The Capacitated VRP with Unequal Demands | 81 |

63 WorstCase Analysis of Heuristics | 85 |

64 The Asymptotic Optimal Solution Value | 88 |

641 A Lower Bound | 89 |

642 An Upper Bound | 92 |

65 Probabilistic Analysis of Classical Heuristics | 94 |

651 A Lower Bound | 96 |

652 The UOPa Heuristic | 97 |

66 The Uniform Model | 99 |

67 The LocationBased Heuristic | 102 |

68 Rate of Convergence to the Asymptotic Value | 105 |

The VRP with Time Window Constraints | 107 |

73 The Asymptotic Optimal Solution Value | 109 |

74 An Asymptotically Optimal Heuristic | 114 |

741 The LocationBased Heuristic | 115 |

742 A Solution Method for CVLPTW | 116 |

743 Implementation | 118 |

744 Numerical Study | 119 |

75 Exercises | 122 |

Solving the VRP Using a Column Generation Approach | 125 |

82 Solving a Relaxation of the SetPartitioning Formulation | 126 |

83 Solving the SetPartitioning Problem | 130 |

831 Identifying Violated Clique Constraints | 132 |

922 Notation and Assumptions | 153 |

93 A Single Warehouse MultiRetailer Model | 158 |

94 Exercises | 163 |

Economic Lot Size Models with Varying Demands | 165 |

102 Models with Capacity Constraints | 171 |

103 MultiItem Inventory Models | 175 |

104 Exercises | 177 |

Stochastic Inventory Models | 179 |

112 Single Period Models | 180 |

113 Finite Horizon Models | 181 |

114 Quasiconvex Loss Functions | 188 |

115 Infinite Horizon Models | 192 |

116 MultiEchelon Systems | 195 |

117 Exercises | 197 |

HIERARCHICAL MODELS | 201 |

Facility Location Models | 203 |

122 An Algorithm for the p Median Problem | 204 |

123 An Algorithm for the SingleSource Capacitated Facility Location Problem | 208 |

124 A Distribution System Design Problem | 211 |

125 The Structure of the Asymptotic Optimal Solution | 215 |

126 Exercises | 216 |

Integrated Logistics Models | 219 |

132 Single Warehouse Models | 221 |

133 WorstCase Analysis of Direct Shipping Strategies | 222 |

1331 A Lower Bound | 223 |

1332 The Effectiveness of Direct Shipping | 224 |

134 Asymptotic Analysis of ZIO Policies | 225 |

1341 A Lower Bound on the Cost of Any Policy | 227 |

1342 An Efficient Fixed Partition Policy | 228 |

135 Asymptotic Analysis of CrossDocking Strategies | 232 |

136 An Algorithm for MultiEchelon Distribution Systems | 234 |

137 Exercises | 235 |

LOGISTICS ALGORITHMS IN PRACTICE | 237 |

A Case Study School Bus Routing | 239 |

142 The Setting | 240 |

143 Literature Review | 242 |

144 The Problem in New York City | 243 |

145 Distance and Time Estimation | 245 |

146 The Routing Algorithm | 247 |

147 Additional Constraints and Features | 251 |

148 The Interactive Mode | 253 |

149 Data Implementation and Results | 254 |

A Decision Support System for Network Configuration | 255 |

152 Data Collection | 257 |

153 The Baseline Feature | 262 |

154 Flexibility and Robustness | 263 |

155 Exercises | 264 |

265 | |

277 | |

### Common terms and phrases

algorithm analysis assigned assume assumption asymptotically optimal Bin-Packing Problem bus stop Capacitated Facility Location capacity constraint Chapter cluster compact support Consider construct convex CVRP cycle defined delivery denoted depot distribution edge Exercise facility feasible solution formulation graph Hence heuristic holding cost instance inventory level item sizes Lagrangian relaxation Lemma length linear program linear relaxation Location Problem logistics long-run average cost lower bound minimize minimum spanning tree nodes number of bins number of customers optimal solution value optimal traveling salesman packing period proof prove Region Partitioning relaxation of Problem reorder interval routing and scheduling scheduling problem Section segment sequence set-partitioning set-up cost Simchi-Levi solve Step strategy subregion subset Theorem total distance traveled Traveling Salesman Problem traveling salesman tour triangle inequality UCVRP unit upper bound variables vector vehicle routing problem vertex vertices VRPTW worst-case performance zero

### Popular passages

Page 267 - Vehicle Routing. In The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, EL Lawler, JK Lenstra, AHG Rinnooy Kan, and D. B. Shmoys, (eds), 43l-448.