Optimal Spatiotemporal Pricing for Autonomous Mobility-on-Demand Systems: A Decomposition and Dynamic Programming Approach

Abstract

This paper studies the optimal spatiotemporal pricing of autonomous mobility-on-demand (AMoD) systems. We consider a platform that operates a fleet of autonomous vehicles (AVs) and determines the pricing, rebalancing, and fleet sizing strategies over the transportation network in response to demand fluctuations. A network flow model is formulated to characterize the evolution of system states over space and time. Fundamental elements in AMoD markets are captured, including demand elasticity, passenger waiting time, vehicle-passenger matching, proactive vehicle rebalancing, and dynamic fleet sizing. The platform's profit maximization problem is cast as a constrained optimal control problem, which is highly nonconvex due to the nonlinear demand model and passenger-vehicle matching model. An integrated decomposition and dynamic programming approach is developed to tackle this optimal control problem, where we first relax the problem through a change of variables, then separate the relaxed problem into a few smallscale subproblems via dual decomposition, and finally obtain the exact solution to each relaxed subproblem through dynamic programming. Despite the non-convexity, the proposed method establishes a theoretical upper bound to evaluate the optimality gap of the obtained solution. The proposed approach is validated with numerical studies using real data from New York City. We find that the platform adopts distinct operation strategies in core and non-core areas of the city because of the asymmetric demand pattern. Furthermore, we also find that low-demand areas are less resilient than high-demand ones when demand surges unexpectedly, because the operator prioritizes supporting high-demand areas at the sacrifice of service quality in lowdemand areas.