Fleet Repositioning for Vehicle Sharing Systems: the Optimality of Balanced Myopic Policy

We consider the fleet repositioning problem for a free-floating vehicle sharing system. The objective is to decide on the vehicle distribution dynamically in the network in order to maximize the long-run average social welfare, i.e., to match the vehicle supply and travel demand at the least total cost of repositioning and lost sales. We formulate the problem as a Markov decision process by considering an ex ante vehicle distribution decision in each period. Interestingly, we show that a balanced myopic policy is optimal, i.e., it is optimal to maintain the vehicle distribution which best matches the vehicle supply and trip demand. We also extend our results to systems with seasonal demand. The optimality of the (generalized) balanced myopic policy overcomes the curse of dimensionality. Our results suggest a simple and effective solution procedure for fleet repositioning, and shed light on how to design effective heuristics. We also quantify the operational value of the balanced myopic policy through a case study of a real-world vehicle sharing system.