Optimal Control and Station Relocation of Vehicle-Sharing Systems With Distributed Dynamic Pricing

This paper addresses an optimal control problem for one-way car-sharing systems under dynamic pricing. One-way car-sharing service allows customers to return vehicles to any available station. Although this service provides great convenience to customers, it has a serious drawback such that vehicles can be unevenly parked and some stations can be unavailable. To solve this problem, dynamic pricing is promising to distribute car parking, with which customers change their origins and destinations by walking according to prices. First, we develop a model of this system by using differential equations, including stochastic processes which represent uncertain human behavior such as the demand shift. Next, we design a uniform, distributed dynamic pricing policy by solving the optimization problem to minimize the unevenness of the vehicles. Then, we show that the effectiveness of the dynamic pricing depends on the network topology of stations. So, we propose an optimization method to relocate stations for effective dynamic pricing with PSO (Particle Swarm Optimization). Finally, numerical examples demonstrate the effectiveness of the developed methods.