{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T12:16:06Z","timestamp":1785327366860,"version":"3.55.0"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,30]],"date-time":"2021-01-30T00:00:00Z","timestamp":1611964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012228","name":"Shenzhen Municipal Development and Reform Commission","doi-asserted-by":"publisher","award":["SDRC [2016]172]."],"award-info":[{"award-number":["SDRC [2016]172]."]}],"id":[{"id":"10.13039\/501100012228","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The imbalanced distribution of shared bikes in the dockless bike-sharing system (a typical example of the resource-sharing system), which may lead to potential customer churn and lost profit, gradually becomes a vital problem for bike-sharing firms and their users. To resolve the problem, we first formulate the bike-sharing system as a Markovian queueing network with higher-demand nodes and lower-demand nodes, which can provide steady-state probabilities of having a certain number of bikes at one node. A model reduction method is then designed to reduce the complexity of the proposed model. Subsequently, we adopt an operator-based relocation strategy to optimize the reduced network. The objective of the optimization model is to maximize the total profit and act as a decision-making tool for operators to determine the optimal relocation frequency. The results reveal that it is possible for most of the shared bikes to gather at one low-demand node eventually in the long run under the influence of the various arrival rates at different nodes. However, the decrease of the number of bikes at the high-demand nodes is more sensitive to the unequal demands, especially when the size of the network and the number of bikes in the system are large. It may cause a significant loss for operators, to which they should pay attention. Meanwhile, different estimated values of parameters related with revenue and cost affect the optimization results differently.<\/jats:p>","DOI":"10.3390\/a14020047","type":"journal-article","created":{"date-parts":[[2021,1,30]],"date-time":"2021-01-30T06:22:20Z","timestamp":1611987740000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modeling and Optimization in Resource Sharing Systems: Application to Bike-Sharing with Unequal Demands"],"prefix":"10.3390","volume":"14","author":[{"given":"Xiaoting","family":"Mo","sequence":"first","affiliation":[{"name":"Intelligent Transportation and Logistics Systems Laboratory, Tsinghua-Berkeley Shenzhen Institute, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6011-3179","authenticated-orcid":false,"given":"Xinglu","family":"Liu","sequence":"additional","affiliation":[{"name":"Intelligent Transportation and Logistics Systems Laboratory, Tsinghua-Berkeley Shenzhen Institute, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7202-1922","authenticated-orcid":false,"given":"Wai Kin (Victor)","family":"Chan","sequence":"additional","affiliation":[{"name":"Intelligent Transportation and Logistics Systems Laboratory, Tsinghua-Berkeley Shenzhen Institute, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1287\/inte.2019.1005","article-title":"Analytics and bikes: Riding tandem with motivate to improve mobility","volume":"49","author":"Freund","year":"2019","journal-title":"INFORMS J. 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