{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T18:39:16Z","timestamp":1776364756655,"version":"3.51.2"},"reference-count":33,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T00:00:00Z","timestamp":1776297600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52302389"],"award-info":[{"award-number":["52302389"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52262046"],"award-info":[{"award-number":["52262046"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Gansu Provincial Science and Technology Plan-Basic. Research Program Project","award":["25JRRA221"],"award-info":[{"award-number":["25JRRA221"]}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1371\/journal.pone.0347218","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T17:39:10Z","timestamp":1776361150000},"page":"e0347218","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimization problem of bike-sharing system rebalancing based on dynamic 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