Designing dynamic pricing for bike-sharing systems via differentiable agent-based simulation

Abstract

Abstract Bike-sharing systems are emerging in various cities as new eco-friendly transportation systems. In these systems, spatiotemporally varying user trip demand leads to imbalances in inventory at bicycle stations, resulting in additional relocation costs. Therefore, user trip demand must be managed through optimal dynamic pricing for these systems. However, optimal pricing design is challenging because these systems involve users with diverse backgrounds and probabilistic choices. To address this problem, we develop a differentiable agent-based simulation to rapidly design dynamic pricing in bike-sharing systems. We first validate our approach through experiments involving 25 bicycle stations and five time slots, yielding 100 parameters. In this small-scale synthetic scenario, our approach achieves a 73–78% reduction in loss and more than a 100-fold reduction in the number of simulation runs required for convergence compared to differential evolution and finite-difference-based gradient descent. We further validate our approach on a synthetic scenario involving 289 bicycle stations, resulting in 1,156 parameters. While we do not compare against conventional methods due to computational limitations, we observe that the number of simulation runs required by our approach does not increase with the number of optimized parameters. To illustrate the applicability of our method to real-world trip demand, we conduct simulation experiments using NYC Citi Bike data, where user behavior is specified heuristically. The results show that, in simulation, the estimated dynamic pricing can induce balanced inventories without any manual relocation. Additionally, we observe that the cost of discounts required to induce inventory balance can be reduced by choosing appropriate initial pricing parameters, even though this cost is not included in the optimization objective.