{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T09:28:45Z","timestamp":1771666125654,"version":"3.50.1"},"reference-count":28,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T00:00:00Z","timestamp":1728345600000},"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":["52302395"],"award-info":[{"award-number":["52302395"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013139","name":"Humanities and Social Science Fund of Ministry of Education of China","doi-asserted-by":"publisher","award":["23YJAZH122"],"award-info":[{"award-number":["23YJAZH122"]}],"id":[{"id":"10.13039\/501100013139","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>Faced with the land use heterogeneity and trip distribution non-equilibrium along the corridor connecting urban district and rural area, the operation characteristics of the all-stop bus, the express bus and the shuttle bus running on the transportation corridor should be given full consideration, as well as the tradeoff between passenger trip cost and bus operation cost during the peak-hour period. In order to realize the reliable decision of bus resources configuration for urban-rural public transportation, a bi-objective programming model of multi-modal urban-rural bus operation scheme is established, where the decision variables include the departure frequency of different bus modals, the terminals of shuttle buses, and the stop scheme of express buses, under the constraints of departure interval, passenger volume, vehicle occupancy, section capacity usage and modal competition. To validate the feasibility of proposed optimization model, an urban-rural bus corridor from Rural Jasmine Ecological Park in Hanjiang District to West Xiangyang Bridge in Songqiao Town was chosen as a study case, and the operation organization scheme of three bus modals were solved by the mathematical solver Lingo using mixed integer programming. Meanwhile, the scheme differences under different subobjective weights were discussed, taking into account the uncertain passenger demand and operation supply. The result shows that the increase of passenger trip cost weight will increase the departure frequency of all three bus modals, while the increase of operation cost weight will decrease the total operating vehicles, but the stop frequency at middle stations for express buses will increase accordingly. Compared to the current operation scheme, the optimized scheme can greatly enhance the section capacity usage at a slight sacrifice of passenger trip time with fewer bus vehicles.<\/jats:p>","DOI":"10.1371\/journal.pone.0309096","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T17:27:32Z","timestamp":1728408452000},"page":"e0309096","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Collaborative optimization of multi-modal transport solutions for urban-rural bus routes"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2285-3093","authenticated-orcid":true,"given":"Jun","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingyi","family":"Qin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinliang","family":"Shao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiajun","family":"Shen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Lv","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,10,8]]},"reference":[{"issue":"3","key":"pone.0309096.ref001","first-page":"141","article-title":"Integrated optimization for timetabling and vehicle scheduling of zone urban and rural bus","volume":"19","author":"X Jiang","year":"2019","journal-title":"Journal of Transportation Systems Engineering and Information Technology"},{"key":"pone.0309096.ref002","doi-asserted-by":"crossref","first-page":"48","DOI":"10.3141\/2218-06","article-title":"Joint optimization of bus size, headway, and slack time for efficient timed transfer","volume":"2218","author":"M Chowdhury","year":"2011","journal-title":"Transportation Research Record"},{"key":"pone.0309096.ref003","first-page":"1","article-title":"Integrated optimization for commuting customized bus stop planning, routing design, and timetable development with passenger spatial-temporal accessibility","volume":"99","author":"X Chen","year":"2021","journal-title":"IEEE Transactions on Intelligent Transportation Systems"},{"key":"pone.0309096.ref004","article-title":"Effects on operating costs of adjusting bus departure times during peak-hour traffic in Sweden.","volume":"2023100","author":"EL Eriksson","year":"2023","journal-title":"Research in Transportation Economics"},{"issue":"11","key":"pone.0309096.ref005","first-page":"1663","article-title":"Optimization of buses\u2019 flexible departure intervals considering crowdedness state. 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