共享单车分配策略建模与优化

摘要随着绿色环保理念的提倡与机动车交通堵塞等问题的日益凸显，共享单车正逐渐成为人们出行不可或缺的方式。随着用户增多，如何根据用户需求使共享单车的分配更加合理，发挥更大地经济和环保效益亟需解决。本文针对三种不同情况下对共享单车的分配进行建模与优化：共享单车单次分配、分配后及时回收剩余共享单车、共享单车和共享电动车单次分配后使用者按一定概率用多余共享单车弥补共享电动车的不足。在每种不同的情况下，首先根据随即动态规划与马尔可夫决策过程建立一般模型。其次，对一般模型建立相应的算法设计。然后带入数值算例求解模型的最优分配方案和最大期望利益。最后，对不同的参数进行敏感性分析，研究不同参数对最优值的影响。通过研究结果表明：在不同情况下建立的模型都能较好的完成车辆的分配以求最大效益。在单次分配共享单车模型下，各个中心点的单价会对结果造成比较明显的差异，单价上升最优值不小于变化前；在单次分配单车再回收模型下，不仅各个中心点的单价收益会对最优值产生影响，各个中心点的回收费用也会对其产生影响，回收费用变高最优值不高于变化前；在单次分配共享单车和共享电动车模型下，使用者用单车替换电动车的替换意愿概率也会影响最优值，替换意愿概率增大最优值随之增大。关键词：共享单车、随即动态规划、马尔可夫决策过程

AbstractWiththepromotionofgreenandenvironmentalprotectionconceptsandtheincreasinglyprominentproblemssuchastrafficcongestioncausedbymotorvehicles,sharedbikesaregraduallybecominganindispensablemodeoftransportationforpeople.Asthenumberofusersincreases,howtomakethedistributionofsharedbikesmorereasonableaccordingtouserneedsandachievegreatereconomicandenvironmentalbenefitsisanurgentissuetobesolved.Wemodelsandoptimizesthedistributionofsharedbikesunderthreedifferentscenarios:singledistributionofsharedbikes,timelyrecoveryofremainingsharedbikesafterdistribution,andsingledistributionofsharedbikesandsharedelectricbikes,whereusersmakeupfortheshortageofsharedelectricbikeswithextrasharedbikesatacertainprobability.Foreachdifferentscenario,ageneralmodelisfirstestablishedbasedonstochasticdynamicprogrammingandMarkovdecisionprocesses.Then,correspondingalgorithmdesignsaredevelopedforthegeneralmodels.Next,numericalexamplesareusedtosolvethemodelsandobtaintheoptimaldistributionschemesandmaximumexpectedbenefits.Finally,sensitivityanalysisisconductedondifferentparameterstostudytheirimpactontheoptimalvalues.Theresearchresultsshowthatthemodelsestablishedunderdifferentscenarioscaneffectivelycompletethedistributionofsharedbikestoachievemaximumbenefits.Inthesingledistributionmodelofsharedbikes,theunitpriceateachcenterpointwillcausesignificantdifferencesintheresults,andtheoptimalvaluewillnotbelessthanthatbeforethepriceincrease.Inthesingledistributionmodelofsharedbikeswithrecovery,notonlytheunitpriceateachcenterpointbutalsotherecoverycostwillaffecttheoptimalvalue,andtheoptimalvaluewillnotbehigherthanthatbeforetheincreaseinrecoverycost.Inthesingledistributionmodelofsharedbikesandsharedelectricbikes,thereplacementwillingnessprobabilityofusersusingsharedbikestoreplacesharedelectricbikeswillalsoaffecttheoptimalvalue,andtheoptimalvaluewillincreaseasthereplacementwillingnessprobabilityincreases.Keywords:bicyclesharing,StochasticDynamicProgramming,MarkovDecisionProcess参考文献王超然.共享单车出行需求预测及调度优化[D].兰州交通大学,2023.周瑜,张梦蝶.基于长短期记忆网络的共享单车真实需求预测方法[J].科学技术与工程,2025,25(01):394-403.张洪涛,甘佐贤.基于双向长短期记忆网络的共享单车需求预测与调度研究[C]//中国公路学会,中国航海学会,中国铁道学会,中国航空学会,中国汽车工程学会.2024世界交通运输大会(WTC2024)论文集（交通工程）.大连海事大学交通运输工程学院;,2024:276-282.张心雨.考虑需求动态变化的城市共享单车停放点选址优化研究[D].沈阳建筑大学,2024.陈梦瑶,张思奇,窦蕊,等.基于BP神经网络的共享单车需求预测研究[J].智能城市,2024,10(05):25-28.李连欣.基于深度强化学习的共享单车调度策略研究[D].武汉理工大学,2021.周柳慈.共享单车需求预测与动态调度优化研究[D].北方工业大学,2024.曾小杰,李海阔.一种基于网格划分的共享单车分配与调度模型[J].中国科技信息,2018,(07):90-92+15.马玉婷,张山山,鲍蓉.基于深度学习的共享单车需求预测及调度方法研究[J].软件,2024,45(06):28-30.LegrosB.Dynamicrepositioningstrategyinabike-sharingsystem;howtoprioritizeandhowtorebalanceabikestation[J].EuropeanJournalofOperationalResearch,2018,272(2):740-753.李晓丹,李冉,马迎辉.基于深度强化学习的共享单车调度优化方法[J].信息技术与信息化,2025,(01):193-196.王迪.分时段下共享单车供需再平衡问题研究[D].西华大学,2024.JieT,WeiW,JiangL.Asustainability-orientedoptimalallocationstrategyofsharingbicycles:EvidencefromofousageinShanghai[J].Resources,Conservation&Recycling,2020,153104510-104510.LiuR,XuJ,IrisÇ,etal.Dynamicrebalancingstrategiesfordocklessbike-sharingsystems[J].InternationalJournalofProductionEconomics,2025,285109634-109634.HamdyA.Taha、塔哈，运筹学导论：高级篇，北京：人民邮电出版社，2007.胡奇英，刘建庸，马尔可夫决策过程引论，西安电子科技大学出版社，西安，西安电子科技大学出版社，2000.附录表3-2电自556065707580859095100105550.01410.01000.00940.00940.00880.00650.01480.00250.01350.00270.0115600.01410.01250.00820.00410.00100.01180.00530.01000.00630.00880.0134650.00560.00260.00780.00310.00140.00200.00270.00950.00460.00580.0004700.01190.00190.00070.00700.00990.01280.01360.01450.00540.00500.0009750.01330.01150.00270.00920.00190.01210.00600.01370.00480.00460.0106800.00860.00110.00370.01490.00700.01040.00750.01290.01180.00370.0118850.00590.00940.00970.01370.01070.01040.01460.01180.00550.01010.0012900.00630.01470.01070.00980.00100.00010.00560.00640.00580.00200.0030950.01110.00820.00300.00570.00910.00750.00360.00900.00210.01470.00351000.00170.01340.01010.00390.01220.01430.01060.00800.00660.00140.00131050.00610.01110.00020.01190.01300.00220.00840.01430.00240.00080.00341100.00170.00720.00670.00770.00560.00160.01340.00650.00550.01420.0151表3-3电自556065707580859095100105550.01040.01250.00750.00560.00980.00530.00100.01040.00220.00720.0039600.00400.00480.00290.01050.00380.00370.00790.00200.00080.00870.0103650.01200.00110.00080.01040.00090.00940.00640.00800.01300.00810.0125700.00340.00600.00360.01270.00130.00430.01040.00990.00620.00320.0112750.01510.01530.00520.00270.00190.00920.00100.00200.01300.01170.0124800.01370.00750.00240.00690.01340.01400.00540.00460.00680.00560.0003850.00720.00070.01360.01230.00580.01490.01460.00490.01380.00890.0118900.00450.00830.01520.00740.01210.00950.00170.00580.00570.00170.0051950.00040.01090.01060.00520.00310.01520.01370.00790.01280.00370.01271000.00940.01110.01320.01560.01110.01010.00010.01230.00040.01550.00481050.01390.00400.01270.00030.01380.01080.00170.01530.01240.00020.00561100.00830.00760.00470.01430.00610.00890.00240.00410.00520.00030.0020表3-4电自556065707580859095100105550.01180.00630.00490.01380.00530.00220.00320.00490.01140.01180.0060600.01040.01330.01420.00110.00890.00030.01330.00800.00420.00050.0094650.00850.01210.00610.01410.01290.01060.00960.01380.00020.00470.0044700.01420.00310.00310.01420.01140.00730.01230.00360.00990.00980.0012750.00660.01010.00380.01000.00070.01000.00850.01450.00160.00880.0017800.00280.00540.01260.01160.00960.00370.00380.01420.00280.00030.0123850.01240.00820.01430.01300.01040.01160.00610.01430.00770.01360.0022900.01260.01390.00930.01040.01280.00370.00360.00960.00320.01180.0141950.00310.00700.00270.00510.00960.00080.01070.00620.00680.00270.01161000.00550.00130.01170.00790.00440.00700.01230.00140.00470.00670.00681050.00480.00240.01200.00380.01450.00800.00330.01070.00810.01370.00531100.00210.00420.00640.00400.00300.00510.01470.00630.00910.00380.0040表3-5电自556065707580859095100105550.00460.00230.01430.00220.00760.00360.00910.00820.00490.00700.0012600.00360.00860.01370.00270.00690.00940.00790.00210.00140.00260.0003650.00550.00450.00540.00660.00270.01180.00780.00980.01360.00850.0078700.00290.00290.00330.00200.00840.00590.01380.00690.00220.01510.0115750.01060.01320.00830.00800.01260.00360.01170.00360.01500.00080.0047800.00830.01040.00440.00870.01280.01350.01370.00620.00130.00930.0011850.00170.01320.00910.00160.01290.00980.00120.01300.00670.00430.0062900.00520.01230.00870.00240.00570.00490.01420.01410.01420.00490.0025950.00680.00410.01030.00980.00530.01480.01160.00780.00410.01350.01191000.00320.01060.01230.00500.00160.01260.00990.00160.00690.00900.00871050.00590.00400.01040.00460.00690.00870.00860.01070.00500.00710.00671100.01040.01060.01590.01330.01330.01320.00360.01360.00310.00760.0017表3-6电自5560657