Optimal and Near-Optimal ECR Policies in Hub-and-Spoke Systems: Continuous Review

Abstract

This chapter considers the ECR problem in a hub-and-spoke transportation system over an infinite time horizon. Similar to the methodology in Chap. 4, we take the perspective of continuous review and discrete state to formulate an event-driven Markov decision model. The empty repositioning decisions are made at each epoch when the system state changes. To overcome the computational complexity of the stochastic dynamic programming model, we propose a dynamic decomposition procedure, whose computational complexity is linear in the number of spokes and can be calculated offline. The requirement for online calculation and data communication is very low. We analyze the structures of the dynamic decomposition policy and show that the dynamic decomposition policy has the same asymptotic behaviors as the optimal ECR policy. The proposed dynamic decomposition procedure can be applied to both discounted cost and long-run average cost cases. Numerical experiments demonstrate the effectiveness of the dynamic decomposition policy and its robustness against the assumption of the distribution types in terms of the laden container arrivals and the empty container transfer times. The model is then extended to the cases with external supply and demand of empty containers at all depots, where empty containers may exit and enter the two-depot shuttle system randomly.