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The Logic of Logistics: Theory, Algorithms, and Applications for Logistics and Supply Chain Management
Second Edition

Preface v
1 Introduction 1
1.1 What Is Logistics Management?
1.2 Managing Cost and Uncertainty
1.3 Examples
1.4 Modeling Logistics Problems
1.5 Logistics in Practice
1.6 Evaluation of Solution Techniques
1.7 Additional Topics
1.8 Book Overview
I Performance Analysis Techniques
2 Convexity and Supermodularity
2.1 Introduction
2.2 Convex Analysis
2.2.1 Convex Sets and Convex Functions
2.2.2 Continuity and Differentiability Properties
2.2.3 Characterization of Convex Functions
2.2.4 Convexity and Optimization
2.3 Supermodularity
2.4 Exercises
3 Worst-Case Analysis
3.1 Introduction
3.2 The Bin-Packing Problem
3.2.1 First-Fit and Best-Fit
3.2.2 First-Fit Decreasing and Best-Fit Decreasing
3.3 The Traveling Salesman Problem
3.3.1 AMinimum Spanning Tree Based Heuristic
3.3.2 The Nearest Insertion Heuristic
3.3.3 Christofides’ Heuristic
3.3.4 Local Search Heuristics
3.4 Exercises
4 Average-Case Analysis
4.1 Introduction
4.2 The Bin-Packing Problem
4.3 The Traveling Salesman Problem
4.4 Exercises
5 Mathematical Programming Based Bounds
5.1 Introduction
5.2 An Asymptotically Tight Linear Program
5.3 Lagrangian Relaxation
5.4 Lagrangian Relaxation and the Traveling Salesman Problem
5.4.1 The 1-Tree Lower Bound
5.4.2 The 1-Tree Lower Bound and Lagrangian Relaxation
5.5 TheWorst-Case Effectiveness of the 1-tree Lower Bound
5.6 Exercises
II Inventory Models
6 Economic Lot Size Models with Constant Demands
6.1 Introduction
6.1.1 The Economic Lot SizeModel
6.1.2 The Finite HorizonModel
6.1.3 Power of Two Policies
6.2 Multi-Item InventoryModels
6.2.1 Introduction
6.2.2 Notation and Assumptions
6.2.3 Worst-Case Analyses
6.3 A SingleWarehouseMulti-RetailerModel
6.3.1 Introduction
6.3.2 Notation and Assumptions
6.4 Exercises
7 Economic Lot Size Models with Varying Demands
7.1 TheWagner-WhitinModel
7.2 Models with Capacity Constraints
7.3 Multi-Item InventoryModels
7.4 Exercises
8 Stochastic Inventory Models
8.1 Introduction
8.2 Single PeriodModels
8.2.1 TheModel
8.3 Finite HorizonModels
8.3.1 Model Description
8.3.2 K-Convex Functions
8.3.3 Main Results
8.4 Quasiconvex Loss Functions
8.5 Infinite HorizonModels
8.6 Multi-Echelon Systems
8.7 Exercises
9 Integration of Inventory and Pricing
9.1 Introduction
9.2 Single PeriodModels
9.3 Finite HorizonModels
9.3.1 Model Description
9.3.2 Symmetric K-Convex Functions
9.3.3 Additive Demand Functions
9.3.4 General Demand Functions
9.3.5 Special Case: Zero Fixed Ordering Cost
9.3.6 Extensions and Challenges
9.4 Risk Averse InventoryModels
9.4.1 Expected utility risk averse models
9.4.2 Exponential utility risk averse models
9.5 Exercises
III Design and Coordination Models
10 Procurement Contracts
10.1 Introduction
10.2 Wholesale Contracts
10.3 Buy Back Contracts
10.4 Revenue Sharing Contracts
10.5 Portfolio Contracts
10.6 Exercises
11 Supply Chain Planning Models
11.1 Introduction
11.2 The Shipper Problem
11.2.1 The ShipperModel
11.2.2 A Set-Partitioning Approach
11.2.3 Structural Properties
11.2.4 Solution Procedure
11.2.5 Computational Results
11.3 Safety Stock Optimization
11.4 Exercises
12 Facility Location Models
12.1 Introduction
12.2 An Algorithm for the p-Median Problem
12.3 An Algorithm for the Single-Source Capacitated Facility Location Problem
12.4 A Distribution System Design Problem
12.5 The Structure of the Asymptotic Optimal Solution
12.6 Exercises
IV Vehicle Routing Models
13 The Capacitated VRP with Equal Demands
13.1 Introduction
13.2 Worst-Case Analysis of Heuristics
13.3 The Asymptotic Optimal Solution Value
13.4 Asymptotically Optimal Heuristics
13.5 Exercises
14 The Capacitated VRP with Unequal Demands
14.1 Introduction
14.2 Heuristics for the CVRP
14.3 Worst-Case Analysis of Heuristics
14.4 The Asymptotic Optimal Solution Value
14.4.1 A Lower Bound
14.4.2 An Upper Bound
14.5 Probabilistic Analysis of Classical Heuristics
14.5.1 A Lower Bound
14.5.2 The UOP(α) Heuristic
14.6 The UniformModel
14.7 The Location-Based Heuristic
14.8 Rate of Convergence to the Asymptotic Value
14.9 Exercises
15 The VRP with Time Window Constraints
15.1 Introduction
15.2 TheModel
15.3 The Asymptotic Optimal Solution Value
15.4 An Asymptotically Optimal Heuristic
15.4.1 The Location-Based Heuristic
15.4.2 A SolutionMethod for CVLPTW
15.4.3 Implementation
15.4.4 Numerical Study
15.5 Exercises
16 Solving the VRP Using a Column Generation Approach
16.1 Introduction
16.2 Solving a Relaxation of the Set-Partitioning Formulation
16.3 Solving the Set-Partitioning Problem
16.3.1 Identifying Violated Clique Constraints
16.3.2 Identifying Violated Odd Hole Constraints
16.4 The Effectiveness of the Set-Partitioning Formulation
16.4.1 Motivation
16.4.2 Proof of Theorem8.4.1
16.5 Exercises
V Logistics Algorithms in Practice
17 Network Planning
17.1 Introduction
17.2 Network Design
17.3 Strategic Safety Stock
17.4 Resource Allocation
17.5 Summary
17.6 Exercises
18 A Case Study: School Bus Routing
18.1 Introduction
18.2 The Setting
18.3 Literature Review
18.4 The Problem in New York City
18.5 Distance and Time Estimation
18.6 The Routing Algorithm
18.7 Additional Constraints and Features
18.8 The InteractiveMode
18.9 Data, Implementation and Results
19 References
Index

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