Modelling Empty Container Repositioning Logistics

The book takes the inventory control perspective to tackle empty container repositioning logistics problems in regional transportation systems by explicitly considering the features such as demand imbalance over space, dynamic operations over time, uncertainty in demand and transport, and container leasing phenomenon. The book has the following unique features. First, it provides a discussion of broad empty equipment logistics including empty freight vehicle redistribution, empty passenger vehicle redistribution, empty bike repositioning, empty container chassis repositioning, and empty container repositioning (ECR) problems. The similarity and unique characteristics of ECR compared to other empty equipment repositioning problems are explained. Second, we adopt the stochastic dynamic programming approach to tackle the ECR problems, which offers an algorithmic strategy to characterize the optimal policy and captures the sequential decision-making phenomenon in anticipation of uncertainties over time and space. Third, we are able to establish closed-form solutions and structural properties of the optimal ECR policies in relatively simple transportation systems. Such properties can then be utilized to construct threshold-type ECR policies for more complicated transportation systems. In fact, the threshold-type ECR policies resemble the well-known (s, S) and (s, Q) policies in inventory control theory. These policies have the advantages of being decentralized, easy to understand, easy to operate, quick response to random events, and minimal on-line computation and communication. Fourth, several sophisticated optimization techniques such as approximate dynamic programming, simulation-based meta-heuristics, stochastic approximation, perturbation analysis, and ordinal optimization methods are introduced to solve the complex stochastic optimization problems. The book will be of interest to researchers and professionals in logistics, transport, supply chain, and operations research. Acknowledgements Contents 1 Empty Equipment Logistics and Empty Container Repositioning (ECR) 1.1 Empty Equipment Logistics 1.1.1 Empty Vehicle Redistribution: Freight Vehicle 1.1.2 Empty Vehicle Redistribution: Passenger Vehicle 1.1.3 Empty Bike Repositioning 1.1.4 Empty Container Chassis Repositioning 1.1.5 Empty Container Repositioning 1.2 ECR: Reasons and Characteristics 1.3 Modeling ECR Logistics 1.4 Structure of the Book References 2 Optimal ECR Policy in a Single-Depot System 2.1 Introduction 2.2 A Discrete Stochastic Dynamic Programming Model 2.2.1 The Structural Properties of the Value Function and the Optimal Control at Period N 2.2.2 The Structural Properties of the Value Function and the Optimal Control at Period n 2.3 A Fluid-Flow Model Based on Continuous-Time Dynamic Programming 2.3.1 Structural Properties of the Optimal Policy 2.3.2 Solving the Hamilton–Jacobi-Bellman Equations 2.3.3 Extension to More General Cases 2.3.4 Numerical Examples 2.4 Summary and Notes References 3 Optimal ECR Policy in Two-Depot System: Periodic Review 3.1 Introduction 3.2 A Discrete Stochastic Dynamic Programming Model 3.3 Optimal ECR Policy and Its Structural Properties 3.3.1 The Properties of the Value Function at Period N 3.3.2 The Structural Properties of the Value Function and the Optimal Control at Period n 3.3.3 Asymptotic Structural Properties of the Optimal Control Policy 3.4 Near-Optimal Threshold-Type Policy 3.5 Numerical Examples 3.6 Summary and Notes References 4 Optimal ECR Policy in Two-Depot Shuttle Systems: Continuous Review 4.1 Introduction 4.2 Problem Formulation 4.3 Convert into Discrete-Time Markov Decision Process 4.4 Solve the Discounted Cost Case 4.4.1 Optimal ECR Policy and Its Structural Properties 4.4.2 Closed-Form Objective Function and Optimal Threshold Values 4.4.3 Numerical Experiments 4.5 Solve the Long-Run Average Cost Case 4.5.1 Stationary Distribution Under Threshold Control Policy 4.5.2 Optimality of the Threshold Control Policy 4.5.3 Numerical Examples 4.6 Extension to Cases with External Supply and Demand 4.7 Summary and Notes References 5 Optimal and Near-Optimal ECR Policies in Hub-and-Spoke Systems: Continuous Review 5.1 Introduction 5.2 Problem Formulation and Uniformization 5.3 Optimal ECR Policy 5.4 Suboptimal Policy Using a Dynamic Decomposition Procedure 5.4.1 Optimal Feedback Control for Two-Depot Systems 5.4.2 Dynamic Decomposition Procedure 5.4.3 Structural Properties of Dynamic Decomposition Policy 5.5 Numerical Examples 5.5.1 Structural Properties of ECR Policies in Two-Spoke-One-Hub Systems 5.5.2 Comparing DDP with the Optimal Policies in Three-Spoke-One-Hub Systems 5.5.3 Comparing DDP with a Heuristic Policy in a Many-Spoke-One-Hub Systems 5.6 Extension to Cases with External Supply and Demand 5.7 Summary and Notes References 6 Optimal ECR in General Inland Transportation Systems with Uncertainty: Periodic Review 6.1 Introduction 6.2 ECR in Inland Transportation Systems 6.3 ECR in Inland Transportation Systems with Transfer Ports 6.4 ECR in Intermodal Transportation Systems 6.5 Approximate Dynamic Programming Method 6.5.1 Generalized Stochastic Dynamic Programming Model 6.5.2 Approximate Dynamic Programming Algorithm 6.6 Simulation Methods and Parameterized Policies 6.7 Metaheuristic Optimization Methods 6.8 Stochastic Approximation Methods 6.9 Perturbation Analysis Methods 6.10 Ordinal Optimization Methods 6.11 Summary and Notes References 7 Conclusions 7.1 Conclusions and Managerial Insight for ECR 7.2 Limitations and Further Research References