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

Abstract

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 nearoptimal 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.

On determining optimal fleet size and vehicle transfer policy for a car rental company

“…They demonstrate that the optimal vehicle transfer policy has the following properties: first, either do not transfer or if transfer then use the fastest mode only; second, the timing of transferring vehicles is triggered by a threshold policy. On the basis of this work, Song and Carter [19] extended the model to a hub-and-spoke transportation system and presented a decomposition procedure to solve the problem.…”

A novel approach for designing rental vehicle repositioning strategies

“…Song and Earl (2008) considered the problem of determining optimal control policies for empty vehicle repositioning and fleet sizing in a two-depot service system with uncertainties in loaded vehicle arrival at depots and repositioning times for empty vehicles in the fleet using discrete-time Markov decision process. Song and Carter (2008) consider the empty vehicle redistribution problem in a hub-and-spoke transportation system with random demands and stochastic transportation times. Li and Tao (2010) determined the optimal fleet size and vehicle transfer policy for a rental car company that serves two cities.…”

Optimization of empty container movements in intermodal transport

“…Optimal repositioning policies minimizing the expected discount cost or the long-run average costs are determined. Song and Carter (2008) extend this work to a hub-and-spoke transportation system using a dynamic decomposition procedure, while Song and Dong (2008) study a threshold control policy for empty container management in cyclic shipping routes. The optimal control policy for a two-port service system without short term container leasing is determined by .…”