Optimal empty vehicle redistribution for hub-and-spoke transportation systems

This article considers the empty vehicle redistribution problem in a hub-and-spoke transportation system, with random demands and stochastic transportation times. An event-driven model is formulated, which yields the implicit optimal control policy. Based on the analytical results for two-depot systems, a dynamic decomposition procedure is presented which produces a near-optimal policy with linear computational complexity in terms of the number of spokes. The resulting policy has the same asymptotic behavior as that of the optimal policy. It is found that the threshold-type control policy is not usually optimal in such systems. The results are illustrated through small-scale numerical examples. Through simulation the robustness of the dynamic decomposition policy is tested using a variety of scenarios: more spokes, more vehicles, different combinations of distribution types for the empty vehicle travel times and loaded vehicle arrivals. This shows that the dynamic decomposition policy is significantly better than a heuristics policy in all scenarios and appears to be robust to the assumptions of the distribution types.