Pricing and Optimization in Shared Vehicle Systems: An Approximation Framework

Abstract

<jats:p> The optimal management of shared vehicle systems, such as bike-, scooter-, car-, or ride-sharing, is more challenging compared with traditional resource allocation settings because of the presence of spatial externalities—changes in the demand/supply at any location affect future supply throughout the system within short timescales. These externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze such systems. However, using Markovian models to design pricing and other control policies is computationally difficult because the resulting optimization problems are high dimensional and nonconvex. In our work, we design a framework that provides near-optimal policies, for a range of possible controls, that are based on applying the possible controls to achieve spatial balance on average. The optimality gap of these policies improves as the ratio between supply and the number of locations increases and asymptotically goes to zero. </jats:p>