David Simchi-Levi Xin Chen Julien Bramel The Logic of Logistics Theory, Algorithms, and Applications for Logistics Management Third Edition ^ Springer
Contents 1 Introduction 1 1.1 What Is Logistics Management? 1 1.2 Managing Cost and Uncertainty 3 1.3 Examples 4 1.4 Modeling Logistics Problems 7 1.5 Logistics and Supply Chain in Practice 8 1.6 Evaluation of Solution Techniques 9 1.7 Additional Topics 10 1.8 Book Overview 11 Part I Performance Analysis Techniques 13 2 Convexity and Super-modularity 15 2.1 Convex Analysis 15 2.1.1 Convex Sets and Convex Functions 15 2.1.2 Continuity and Differentiability Properties 18 2.1.3 Characterization of Convex Functions 23 2.1.4 Convexity and Optimization 25 2.2 Supermodularity 27 2.3 Discrete Convex Analysis 35 2.3.1 Z^-Convexity 36 2.3.2 M^-Convexity 39 2.4 Exercises 42 xi
xii Contents 3 Game Theory 45 3.1 Noneooperative Game Theory 46 3.1.1 Definition and Existence of Nash Equilibrium 47 3.1.2 Uniqueness of Nash Equilibrium 50 3.2 Cooperative Game Theory 52 3.2.1 Core 55 3.2.2 Nucleolus 59 3.2.3 Shapley Value 61 3.3 Exercises 63 4 Worst-Case Analysis 65 4.1 Introduction 65 4.2 The Bin-Packing Problem 6G 4.2.1 First-Fit and Best-Fit 68 4.2.2 First-Fit Decreasing and Best-Fit Decreasing 71 4.3 The Traveling Salesman Problem 72 4.3.1 A Minimum Spanning Tree-Based Heuristic 73 4.3.2 The Nearest-Insertion Heuristic 75 4.3.3 Christofides' Heuristic 78 4.3.4 Local Search Heuristics 80 4.4 Exercises 81 5 Average-Case Analysis 85 5.1 Introduction 85 5.2 The Bin-Packing Problem 86 5.3 The Traveling Salesman Problem 91 5.4 Exercises 96 6 Mathematical Programming-Based Bounds 99 6.1 Introduction 99 6.2 An Asymptotically Tight Linear Program 100 6.3 Lagrangian Relaxation 103 6.4 Lagrangian Relaxation and the Traveling Salesman Problem... 105 6.4.1 The 1-Tree Lower Bound 106 6.4.2 The 1-Tree Lower Bound and Lagrangian Relaxation... 107 6.5 The Worst-Case Effectiveness of the 1-Tree Lower Bound 108 6.6 Exercises 112 Part II Inventory Models 115 7 Economic Lot Size Models with Constant Demands 117 7.1 Introduction 117 7.1.1 The Economic Lot Size Model 117
Contents xiii 7.1.2 The Finite-Horizon Model 119 7.1.3 Powcr-of-Two Policies 121 7.2 Multi-Item Inventory Models 122 7.2.1 Introduction 122 7.2.2 Notation and Assumptions 124 7.2.3 Worst-Case Analyses 125 7.3 A Single-Warehouse Multiretailcr Model 129 7.3.1 Introduction 129 7.3.2 Model and Analysis 130 7.4 Exercises 134 8 Economic Lot Size Models with Varying Demands 137 8.1 The Wagner-Whitin Model 137 8.2 Models with Capacity Constraints 143 8.3 Multi-Item Inventory Models 140 8.4 Single-Item Models with Pricing 148 8.5 Exercises 150 9 Stochastic Inventory Models 151 9.1 Introduction 151 9.2 Single-Period Models 152 9.2.1 The Model 152 9.3 Finite-Horizon Models 153 9.3.1 Model Description 153 9.3.2 K-Convex Functions 155 9.3.3 Main Results 158 9.4 Quasiconvex Loss Functions 159 9.5 Infinite-Horizon Models 103 9.6 Models with Positive Lead Times 169 9.7 Multi-Echelon Systems 172 9.8 Exercises 174... 194 10 Integration of Inventory and Pricing 177 10.1 Introduction 177 10.2 Demand Models 178 10.3 Single-Period Stochastic Models 179 10.4 Finite-Horizon Models 183 10.4.1 Model Description 183 10.4.2 Symmetric A'-Convex Functions 185 10.4.3 Additive Demand Functions 190 10.4.4 General Demand Functions 193 10.4.5 Special Case: Zero Fixed Ordering Cost 194 10.5 Alternative Approach to the Optimality of (s, 5, p) Policies 10.6 Extensions and Challenges 200
xiv Contents 10.7 Risk-Averse Inventory Models 201 10.7.1 Expected Utility Risk-Averse Models 203 10.7.2 Exponential Utility Risk-Averse Models 205 10.8 Exercises 207 Part III Competition, Coordination and Design Models 211 11 Supply Chain Competition and Collaboration Models 213 11.1 Inventory and Pricing Competition 213 11.2 Inventory Centralization Games 216 11.2.1 Model 217 11.2.2 Inventory Games with a Linear Ordering Cost 219 11.2.3 Inventory Games with Quantity Discounts 222 11.3 Exercises 228 12 Procurement Contracts 229 12.1 Introduction 229 12.2 Wholesale Price Contracts 231 12.3 Buy-Back Contracts 233 12.4 Revenue-Sharing Contracts 234 12.5 Portfolio Contracts 235 12.6 Exercises 239 13 Process Flexibility 241 13.1 Introduction 241 13.2 Supermodularity and Incremental Benefits of Long Chains 244 13.2.1 Supermodularity in Arc Capacities 245 13.2.2 Incremental Benefits in Long Chains 249 13.3 Characterizing the Performance of Long Chains 250 13.3.1 Decomposition of a Long Chain 251 13.3.2 Characterization and Optimality 253 13.3.3 Computing the Performance of a Long Chain 254 13.4 Performance of Long Chains 257 13.5 Extensions 261 13.6 Exercises 262 14 Supply Chain Planning Models 263 14.1 Introduction 263 14.2 The Shipper Problem 264 14.2.1 The Shipper Model 265 14.2.2 A Set-Partitioning Approach 266 14.2.3 Structural Properties 270
Contents xv 14.2.4 Solution Procedure 271 14.2.5 Computational Results 274 14.3 Safety Stock Optimization 279 14.4 Exercises 280 15 Facility Location Models 283 15.1 Introduction 283 15.2 An Algorithm for the p-median Problem 284 15.3 An Algorithm for the Single-Source Capacitated Facility Location Problem 287 15.4 A Distribution System Design Problem 291 15.5 The Structure of the Asymptotic Optimal Solution 296 15.6 Exercises 297 Part IV Vehicle Routing Models 299 16 The Capacitated VRP with Equal Demands 301 16.1 Introduction 301 16.2 Worst-Case Analysis of Heuristics 303 16.3 The Asymptotic Optimal Solution Value 307 16.4 Asymptotically Optimal Heuristics 308 16.5 Exercises 312 17 The Capacitated VRP with Unequal Demands 313 17.1 Introduction 313 17.2 Heuristics for the CVRP 313 17.3 Worst-Case Analysis of Heuristics 317 17.4 The Asymptotic Optimal Solution Value 320 17.4.1 A Lower Bound 321 17.4.2 An Upper Bound 324 17.5 Probabilistic Analysis of Classical Heuristics 326 17.5.1 A Lower Bound 328 17.5.2 The UOP(a) Heuristic 330 17.6 The Uniform Model 332 17.7 The Location-Based Heuristic 335 17.8 Rate of Convergence to the Asymptotic Value 337 17.9 Exercises 338 18 The VRP with Time-Window Constraints 341 18.1 Introduction 341 18.2 The Model 341 18.3 The Asymptotic Optimal Solution Value 343 18.4 An Asymptotically Optimal Heuristic 349 18.4.1 The Location-Based Heuristic 349
xvi Contents 18.4.2 A Solution Method for CVLPTW 351 18.4.3 Implementation 353 18.4.4 Numerical Study 353 18.5 Exercises 356 19 Solving the VRP Using a Column-Generation Approach 359 19.1 Introduction 359 19.2 Solving a Relaxation of the Set-Partitioning Formulation 360 19.3 Solving the Set-Partitioning Problem 364 19.3.1 Identifying Violated Clique Constraints 366 19.3.2 Identifying Violated Odd Hole Constraints 366 19.4 The Effectiveness of the Set-Partitioning Formulation 367 19.4.1 Motivation 368 19.4.2 Proof of Theorem 19.4.1 369 19.5 Exercises 372 Part V Logistics Algorithms in Practice 377 20 Network Planning 379 20.1 Introduction 379 20.2 Network Design 380 20.3 Strategic Safety Stock 391 20.4 Resource Allocation 397 20.5 Summary 400 20.6 Exercises 402 21 A Case Study: School Bus Routing 403 21.1 Introduction 403 21.2 The Setting 404 21.3 Literature Review 406 21.4 The Problem in New York City 407 21.5 Distance and Time Estimation 409 21.6 The Routing Algorithm 411 21.7 Additional Constraints and Features 415 21.8 The Interactive Mode 417 21.9 Data, Implementation, and Results 418 References 421 Index 441