Pricing and Optimization in shared vehicle systems
We develop a general framework for data-driven pricing and optimization in shared vehicle systems (such as bike-sharing, car-sharing, and ride-sharing). Our approach is the first to provide efficient algorithms with rigorous approximation guarantees for a wide range of different controls (pricing, rebalancing, matching), objective functions (throughput, revenue, welfare), and a variety of constraints (Ramsey pricing, discrete prices, rebalancing budget). Compared to traditional problems in revenue management, pricing in shared vehicle systems is more challenging due to network externalities, wherein prices and rebalancing decisions in any location affect the future supply throughout the network. To capture the system dynamics, we use a closed queueing model which tracks the position of all vehicles in the network; arriving demand can be modulated through pricing, while supply (vehicles) can be controlled through rebalancing. In this setting, we provide a general data-driven optimization framework which uses a convex program to find pricing and control policies with good approximation guarantees. Our guarantees are obtained by first describing vehicle-sharing system using Markovian models with product-form distributions, projecting the models to an infinite-supply setting, deriving optimal policies in this limit, and then bounding the performance of these policies in the finite-vehicle system. Our infinite-to-finite reduction technique may be of independent interest for other stochastic optimization problems.