Optimization problem of bike-sharing system rebalancing based on dynamic pricing

Bike-Sharing Systems (BSS) help address first- and last-mile travel challenges. As a limited public resource, the current pricing mechanism fails to fully exploit the service potential of bike-sharing or adequately capture heterogeneous user price sensitivity. We propose a Dynamic pricing-based Stochastic Demand-Response Optimization (DSDRO) method to address this gap. The method balances service fairness under varying demand stickiness while maximizing enterprise resource utilization. The DSDRO framework leverages spatiotemporal patterns in bike-sharing demand data and introduces a dynamic pricing model that differentiates user demand stickiness. This model is embedded in a two-stage allocation-rebalancing formulation. An improved Particle Swarm Optimization algorithm enhanced with Large-scale Neighborhood Search (PSO-LNS) is designed to solve the model, yielding the optimal bike allocation and dispatch routes at each node. Numerical experiments based on real operational data validate the proposed approach. Compared to a traditional genetic algorithm baseline, DSDRO increases expected revenue by 15.51% and net profit by 24.18% under identical resource conditions. An ablation study shows that dynamic pricing alone increases revenue by over 300% relative to fixed pricing, while the LNS component reduces rebalancing cost by 76.21% relative to pure PSO. Algorithm stability is confirmed through 10 independent runs, with all performance metrics exhibiting a coefficient of variation below 5%. These results suggest that DSDRO shows promise in improving the utilization of bike-sharing resources, though further validation across diverse operational contexts is needed before broader conclusions can be drawn.