Learning While Repositioning in On-Demand Vehicle Sharing Networks
76 Pages Posted: 26 Jun 2022 Last revised: 26 Mar 2024
Date Written: December 18, 2022
Abstract
We consider the vehicle repositioning problem for a one-way on-demand vehicle sharing service with a fixed number of rental units distributed across the network. Due to uncertainty in both customer arrivals and vehicle returns, the service provider needs to periodically reposition the vehicles to match the supply with the demand while minimizing the total costs of repositioning labor and lost sales. The optimal repositioning policy under a general $n$-location network is intractable without knowing the optimal value function. We define the best base-stock repositioning policy as a generalization of the popular inventory control policy to the vehicle repositioning problem, and we establish its asymptotic optimality in two different limiting regimes under general network structures. We then study learning methods to dynamically reposition vehicles to find the best base-stock policy with censored demand. We develop an online gradient-based repositioning algorithm using only censored demand and prove that it achieves an optimal regret of $O\left(T^{\frac{1}{2}}\right)$ under a mild cost structure assumption. Our online algorithm is based on a careful decomposition of cumulative costs and constructing a linear programming problem and its dual for computing the gradient. More broadly, our analysis elucidates the challenges and offers new insights into learning with censored data in networks. Numerical experiments illustrate the effective performance of our proposed approach.
Keywords: censored demand, vehicle sharing, vehicle repositioning, online learning, regret analysis
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