Robust Repositioning for Vehicle Sharing

Abstract

Problem definition: In this paper, we study the fleet problem for a free-float vehicle sharing system, aiming to dynamically match the vehicle supply and travel demand at the lowest total cost of and lost sales. Academic/Practical relevance: Besides the analytical results on the optimal policy, the proposed optimization framework is applicable to practical problems by its computational efficiency as well as the capability to handle temporally dependent demands. Methodology: We first formulate the problem as a stochastic dynamic program. To solve for a multi-region system, we deploy the distributionally robust optimization (DRO) approach that can incorporate demand temporal dependence, motivated by real data. We first propose a myopic two-stage DRO model that serves both as an illustration of the DRO framework as well as a benchmark for the later multi-stage model. We then develop a computationally efficient multi-stage DRO model with enhanced linear decision rule (ELDR). Results: Under a 2-region system, we find that a simple reposition up-to and down-to policy to be optimal, when the demands are temporally independent. Such structure is also preserved by our ELDR solution. We also provide new analytical insights by proving the optimality of ELDR in solving single-period DRO problem. We then show that the numerical performance of ELDR solution is close to the exact optimal solution from the dynamic program. Managerial implications: In a real-world case study of car2go, we quantify the value of repositioning and compare with several benchmarks to demonstrate that the ELDR solutions are computationally scalable and in general result in lower cost with less frequent repositioning. We also explore several managerial implications and extensions from the experiments.