Pricing and Optimization in Shared Vehicle Systems: An Approximation Framework

Optimizing shared vehicle systems (bike-/scooter-/car-/ride-sharing) are more challenging compared with traditional resource allocation settings because of the presence of complex network 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 such models to design pricing and other control policies is computationally difficult because the resulting optimization problems are high dimensional and nonconvex. To this end, we develop a rigorous approximation framework for shared vehicle systems, providing a unified approach for a wide range of controls (pricing, matching, rebalancing), objective functions (throughput, revenue, welfare), and system constraints (travel times, welfare benchmarks, posted-price constraints). Our approach is based on the analysis of natural convex relaxations and obtains as special cases existing approximate optimal policies for limited settings, asymptotic optimality results, and heuristic policies. The resulting guarantees are nonasymptotic and parametric and provide operational insights into the design of real-world systems. In particular, for any shared vehicle system with n stations and m vehicles, our framework obtains an approximation ratio of $1+(n-1)/m$, which is particularly meaningful when m/n, the average number of vehicles per station, is large, as is often the case in practice.