{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T17:41:21Z","timestamp":1760722881822,"version":"build-2065373602"},"reference-count":36,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["52302443"],"award-info":[{"award-number":["52302443"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100017611","name":"Social Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2023R059"],"award-info":[{"award-number":["2023R059"]}],"id":[{"id":"10.13039\/501100017611","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>The distribution of shared bikes is different from that of other goods. There are some demand stations which need a large number of shared bikes, such as bus stations, subway exits and business districts. The demand of these stations cannot be met in a single delivery, so the demand can be split into batches for distribution. Therefore, shared bikes need to be delivered from distribution centers to demand stations. However, these delivery vehicles generate carbon emissions during the process, which has an impact on environment. Thus, shared bikes distribution vehicle route selection with considering carbon emission under demand splitting is an important problem. The paper established a model for distribution vehicle route selection of shared bikes considering carbon emission which aims at minimization the sum of carbon emission cost and delivery cost, under demand splitting of the stations and delivery vehicles with load limit. Then an approximation algorithm <jats:italic>GA<\/jats:italic> is designed to solve it. The time complexity of <jats:italic>GA<\/jats:italic> was proved, and the upper and lower bounds of the approximate ratio of <jats:italic>GA<\/jats:italic> are discussed. Finally, an empirical example was facilitated by examining real shared bikes stations in the Yanta district of Xi\u2019an, China, to verify the effectiveness of the model and algorithm. The approximation ratio of <jats:italic>GA<\/jats:italic> is 3.52 which shows that the approximate performance of the algorithm in the example is good. The results and conclusions yield a theoretical basis for decision-makers to optimize the delivery of shared bikes.<\/jats:p>","DOI":"10.1371\/journal.pone.0333781","type":"journal-article","created":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T17:27:31Z","timestamp":1760722051000},"page":"e0333781","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Shared bikes distribution vehicle routing problem with split delivery considering carbon 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