公交车的调度问题.doc

公交车调度的最优方案摘要公共交通系统是城市交通的重要组成部分，做好公交车的调度对于改进市民出行状况、提高公交公司的经济和社会效益，都具有十分重要的意义。发车时刻表是公共交通管理系统中的一个重要组成部分。一个好的发车时刻表应体现乘客和公交公司双方利益的均衡，而编制发车时刻表的关键是确定发车的时间间隔。对于乘客来说，发车时间间隔越短，乘客的等车时间越少，而且不显拥挤；另一方面，公交公司希望发车间隔长些，这样满载率就会提高，投入运营的车子总数和发车总次数就会减少，有利于降低成本。根据本文兼顾公司与乘客的利益，建立了公交车辆行车时刻表优化模型。本文采用线性规划的方法，根据首站的人数和在该时间段车上的人数的峰值确定所必须的总车数，然后根据乘客的候车时间和公交公司的利润综合比较确定每一时间段派出的车辆数，最后根据首尾两站的公交总数进行合理的调配，算出一天需要派出79辆公交车。关键词：车辆调度 线性规划 行车时刻表 候车时间1、问题重述以考虑一条公交线路上公交车的调度问题为例，本方案设计数据如下表1、表2是来自我国一座特大城市某条公交线路的客流调查和运营资料。该条公交线路上行方向共14站，下行方向共13站，表1、表2给出的是典型的一个工作日两个运行方向各站上下车的乘客数量统计。现知公交公司配给该线路同一型号的大客车，每辆标准载客100 人，据统计客车在该线路上运行的平均速度为20公里/小时。且运营调度要求，乘客候车时间一般不要超过10分钟，早高峰时一般不要超过5分钟，车辆满载率不应超过 120%，一般也不要低于50%。现根据这些资料和要求，为该线路设计一个便于操作的全天（工作日）的公交车调度方案，即用尽可能少的车来运送乘客，同时不能让乘客等待时间过长，也不能超载；包括两个起点站的发车时刻表；一共需要多少辆车；这个方案以怎样的程度照顾到了乘客和公交公司双方的利益。我们的目标就是根据所提供的这些统计资料，对该调度问题建立起一个明确、完整的数学模型之后，再根据实际问题的要求，提出一个数据采集方案，以设计出一个更好的公交调度方案。表1某路公交汽车各时组每站上下车人数统计表 上行方向：A13开往A0站名A13A12A11A10A9A8A7A6A5A4A3A2A1A0站间距(公里)1.60.510.732.041.262.2911.20.411.030.535:00-6:00上3716052437690488385264545110下08913204845813218242585576:00-7:00上1990376333256589594315622510176308307680下0991051642395885428004072083002889216157:00-8:00上3626634528447948868523958904259465454990下0205227272461105810971793801469560636187114598:00-9:00上2064322305235477549271486439157275234600下010612316930063462197144024533940811327599:00-10:00上118620516614728130417232426778143162360下0817512018140741155125013618723377448310:00-11:00上92315112010821521411921220175123112260下052558113629928044217810515316753238511:00-12:00上95718115713325426413525326074138117300下054588413132129142019611915915353434012:00-13:00上87314114010821520412923222165103112260下046497111126325638916411113414848833313:00-14:00上779141103841861851032111736610897230下03941701032211972971378511311638426314:00-15:00上6251041088216218090185170497585200下036394778189176339139809712038323915:00-16:00上635124988215218080185150498585200下0363957882091963391298010711035322916:00-17:00上1493299240199396404210428390120208197490下0808513519445044173133515725525180055717:00-18:00上2011379311230497479296586508140250259610下0110118171257694573957390253293378122879318:00-19:00上69112410789167165108201194539382220下04548801082372313901508913112542833619:00-20:00上3506455469185508889274847110下0222334631161081968348646620413920:00-21:00上304504336727540776022383790下01617243880841435934464716011721:00-22:00上209373226535529475216282760下0141421337863125623040411289222:00-23:00上193325535513210下03358181727127993221表2某路公交汽车各时组每站上下车人数统计表 下行方向：A0开往A13站名A0A2A3A4A5A6A7A8A9A10A11A12A13站间距(公里)1.5610.441.20.972.291.320.7310.51.625:00-6:00上22342443331100下02116775342396:00-7:00上795143167841511881091371304553160下070404018420519514793109751082717:00-8:00上2328380427224420455272343331126138450下02941561577107808495453744442653739588:00-9:00上2706374492224404532333345354120153460下026615814975682785652936742823737611679:00-10:00上15562042741252353081622031987699270下01571008041051149833619927613621955610:00-11:00上902147183821552061201501435059180下010359592463463201911471859615443811:00-12:00上847130132671271501081041074148150下09448481992382561751221436812834612:00-13:00上70690118661051449295883440120下0704040174215205127103119659826113:00-14:00上7709712659102133971021043643130下0754343166210209136901276011530914:00-15:00上839133156691301651011181204249150下08448482192382461551121537811834615:00-16:00上1110170189791691941411521665464190下0110736325330734121513616710214442516:00-17:00上183726033014630540422927725395122340下01759610645961754940126630416226978417:00-18:00上3020474587248468649388432452157205560下03301931947379341016606416494278448124918:00-19:00上1966350399204328471289335342122132400下0223129150635787690505304423246320101019:00-20:00上939130165881381871241431474856170下011359592663062902011471558615439820:00-21:00上6401071266911215387102943643130下075434318623021914690127709531921:00-22:00上636110128561051448295983440120下07341421902431921321071236710129022:00-23:00上2944351244658354142151750下0352020871089269476033491362、问题分析根据题目所给的已知条件，由时间段计算车辆会有重复的车辆，除第一段时间外其余的时间段必须要减去重复的车辆，重复的车辆数为本段时间16分钟以后的发车数。由时间段人数的最大值，确定所需的车辆数，而A13站作为首站也会确定最少的车辆数，根据线性约束条件确定最少的车辆数，在保证顾客等车一般不要超过10分钟，早高峰时一般不要超过5分钟的基础上，合理地进行调配。然后根据公交公司和顾客的满意度确定合理的时刻安排表。3、模型假设与符号说明模型假设：1、在工作日内乘客到达车站等车的人数均匀分布在该时段；2、不考虑公交车在各站的停车时间；3、不考虑其他情况对公交车的影响，假设公交车以20公里/每小时的速度匀速行驶；4、每个时间段的发车间隔时间是确定的且平均；5、每个时间段内整点开始发该时段第一班车；6、在早高峰时段每辆车都满载（120人）；7、上行车辆从A0开到A13后转为下行车从A13开回A0；8、公交车行驶过程中不存在阻塞现象，且公交车之间依次进行，不存在超车现象；9、公交车按发车时刻表顺次发车，准时到达每个站点； 符号说明：符号说明：符号说明表示乘车人数的峰值表示每一时段出现的总车数表示相邻两时间段重复出现的车次总数表示每一时间段新派出来的车表示运行一天的利润表示票价表示空车运输的费用表示公交车里单位人的费用4、模型建立与模型求解上行时刻安排表的线性约束方程式 （1）下行时刻安排表的线性约束方程式 （2）经济效益模型： （3）当值足够大的时候，当然也不会是最大，接近满载时，确定合适的和由确定，重复的车辆： （4）每个时间段安排发出的车辆： （5）综合上行和下行的公交，进行调度。 时间段上车人数/下车人数差值峰值每车载5000人每车载120人需要增加车辆（辆）每辆车的时间间隔（分钟）5:00-6:00103546557070114.02辆5.8辆6106:00-7:00644452761738351370.26辆29.275辆262.37:00-8:00107131090915426756135.12辆56.3辆391.58:00-9:00587462471169424784.94辆35.3辆311.939:00-10:0034713889751269753.94辆17.98辆10610:00-11:0025992865485194438.88辆16.2辆10611:00-12:0029532860578184036.8辆15.3辆96.612:00-13:0025692563584177835.56辆14.8辆96.613:00-14:0022592066777162432.48辆13.5辆87.514:00-15:0019351962750165833.16辆13.8辆96.615:00-16:0019251972703162132.42辆13.5辆87.516:00-17:0046334471865283656.7辆23.6辆193.1517:00-18:0060076215657363772.74辆30.3辆183.3318:00-19:0020962398355155431.18辆12.95辆61019:00-20:001051116624081916.38辆6.825辆61020:00-21:0086386523865013辆5.41辆32021:00-22:0061774111451310.25辆4.275辆32022:00-23:0057171053210.64辆4.43辆160上行车5:00:005:10:005:20:005:30:005:40:005:50:006:00:006:02:186:04:366:06:546:09:126:11:306:13:486:16:066:18:246:20:426:23:006:25:186:27:366:29:546:32:126:34:306:36:486:39:066:41:246:43:426:46:006:48:186:50:366:52:546:55:126:57:306:59:487:00:007:01:307:03:007:04:307:06:007:07:307:09:007:10:307:12:007:13:307:15:007:16:307:18:007:19:307:21:007:22:307:24:007:25:307:27:007:28:307:30:007:31:307:33:007:34:307:36:007:37:307:39:007:40:307:42:007:43:307:45:007:46:307:48:007:49:307:51:007:52:307:54:007:55:307:57:007:58:308:00:008:01:568:03:528:05:488:07:448:09:408:11:368:13:328:15:288:17:248:19:208:21:168:23:128:25:088:27:048:29:008:30:568:32:528:34:488:36:448:38:408:40:368:42:328:44:288:46:248:48:208:50:168:52:128:54:088:56:048:58:008:59:569:00:009:06:009:12:009:18:009:24:009:30:009:36:009:42:009:48:009:54:0010:00:0010:06:0010:12:0010:18:0010:24:0010:30:0010:36:0010:42:0010:48:0010:54:0011:00:0011:06:3611:13:1211:19:4811:26:2411:33:0011:39:3611:46:1211:52:4811:59:2412:00:0012:06:3612:13:1212:19:4812:26:2412:33:0012:39:3612:46:1212:52:4812:59:2413:00:0013:07:3013:15:0013:22:3013:30:0013:37:3013:45:0013:52:3014:00:0014:06:3614:13:1214:19:4814:26:2414:33:0014:39:3614:46:1214:52:4814:59:2415:00:0015:07:3015:15:0015:22:3015:30:0015:37:3015:45:0015:52:3016:00:0016:0316:06:1816:0916:12:3616:1516:18:5416:2216:25:1216:2817:00:0017:03:2017:06:4017:10:0017:13:2017:16:4017:20:0017:23:2017:26:4017:30:0017:33:2017:36:4017:40:0017:43:2017:46:4017:50:0017:53:2017:56:4018:00:0018:10:0018:20:0018:30:0018:40:0018:50:0019:00:0019:10:0019:20:0019:30:0019:40:0019:50:0020:00:0020:20:0020:40:0021:00:0021:20:0021:40:0022:00:00下行车差值指的是该时间段上车人数与下车人数的差，峰值指的是该时间段同一时间在车上的最大人数。首先要保证A0，A2，A3，A4,车站的人能全部上车，对必要的车辆数照成制约。时间段上车人数/下车人数差值峰值每车载5000人每车载120人需要增加车辆（辆）每辆车的时间间隔（分钟）5:00-6:0050500270.54辆0.225辆1606:00-7:0020181537481101320.26辆8.44辆96.77:00-8:005489590565323364.66辆26.9辆27-6=212.868:00-9:006083611632328865.76辆27.4辆28-15=132.739:00-10:003467347821185437.08辆15.45辆16-9=7510:00-11:0022152344-108111422.28辆9.28辆10-5=56.711:00-12:0018761865-9787817.56辆7.3辆8-4=27.512:00-13:0015901517-2469313.86辆5.775辆6-1=58.5713:00-14:00168215837586717.34辆7.2辆8-4=48.5714:00-15:0019371845167109221.8辆9.1辆10-3=77.515:00-16:0025072336338146929.38辆12.24辆13-4=9616:00-17:0042924188442253450.68辆21.12辆22-6=163.7517:00-18:0071366895683405481.08辆33.78辆34-11=232.1418:00-19:0049785422239310062辆25.8辆26-18=8319:00-20:0021822234187133026.6辆11.08辆12-5=77.520:00-21:001582164312696819.36辆8.07辆9-5=21021:00-22:00154016016590018辆7.5辆8-1=78.5722:00-23:00671756-204028.04辆3.35辆4155:00:006:00:006:06:426:13:246:20:066:26:486:33:306:40:126:46:546:53:367:00:007:02:527:05:447:08:367:11:287:14:207:17:127:20:047:22:567:25:487:28:407:31:327:34:247:37:167:40:087:43:007:45:527:48:447:51:367:54:287:57:208:00:008:02:448:05:288:08:128:10:568:13:408:16:248:19:088:21:528:24:368:27:208:30:048:32:488:35:328:38:168:41:008:43:448:46:288:49:128:51:568:54:408:57:249:00:009:05:009:10:009:15:009:20:009:25:009:30:009:35:009:40:009:45:009:50:009:55:0010:00:0010:06:4210:13:2410:20:0610:26:4810:33:3010:40:1210:46:5410:53:3611:00:0011:07:3011:15:0011:22:3011:30:0011:37:3011:45:0011:52:3012:00:0012:08:3512:17:1012:25:4512:34:2012:42:5512:51:3013:00:0013:08:3513:17:1013:25:4513:34:2013:42:5513:51:3014:00:0014:07:3514:15:1014:22:4514:30:2014:37:5514:45:3014:53:0515:00:0015:06:0015:12:0015:18:0015:24:0015:30:0015:36:0015:42:0015:48:0015:54:0016:00:0016:03:4516:07:3016:11:1516:15:0016:18:4516:22:3016:26:1516:30:0016:33:4516:37:3016:41:1516:45:0016:48:4516:52:3016:56:1517:00:0017:02:0817:04:1617:06:2417:08:3217:10:4017:12:4817:14:5617:17:0417:19:1217:21:2017:23:2817:25:3617:27:4417:29:5217:32:0017:34:0817:36:1617:38:2417:40:3217:42:4017:44:4817:46:5617:49:0417:51:1217:53:2017:55:2817:57:3617:59:4418:00:0018:03:0018:06:0018:09:0018:12:0018:15:0018:18:0018:21:0018:24:0018:27:0018:30:0018:33:0018:36:0018:39:0018:42:0018:45:0018:48:0018:51:0018:54:0018:57:0019:00:0019:07:3519:15:1019:22:4519:30:2019:37:5519:45:3019:53:0520:00:0020:10:0020:20:0020:30:0020:40:0020:50:0021:00:0021:08:3521:17:1021:25:4521:34:2021:42:5521:51:3022:00:0022:15:0022:30:0022:45:00上行车安排表5:00:005:10:005:20:005:30:005:40:005:50:00C1C2C3C4C5C66:00:006:02:186:04:366:06:546:09:126:11:306:13:486:16:06S1C7C8C9C10C11C12C136:18:246:20:426:23:006:25:186:27:366:29:546:32:126:34:30C14C15C16C17C18C19C20C216:36:486:39:066:41:246:43:426:46:006:48:186:50:366:52:54C22C23C24C25C26C27C28C296:55:126:57:306:59:48C30C31C327:00:007:01:307:03:007:04:307:06:007:07:307:09:007:10:30C1C2C3C4C33C34C35C367:12:007:13:307:15:007:16:307:18:007:19:307:21:007:22:30C5C37C38C39S2C40C41C427:24:007:25:307:27:007:28:307:30:007:31:307:33:007:34:30C43C6C44C45C46S3C47C487:36:007:37:307:39:007:40:307:42:007:43:307:45:007:46:30C49S4C50C51C52C53C54C557:48:007:49:307:51:007:52:307:54:007:55:307:57:007:58:30C56C57C58C59C60C61C62C638:00:008:01:568:03:528:05:488:07:448:09:408:11:368:13:32S1C7C8C9C10C11C12C138:15:288:17:248:19:208:21:168:23:128:25:088:27:048:29:00C14C15C16C17C18C19C20C648:30:568:32:528:34:488:36:448:38:408:40:368:42:328:44:28C21C22C65C23C24C66C25C678:46:248:48:208:50:168:52:128:54:088:56:048:58:008:59:56C68C69C70C71C72C73C74C759:00:009:06:009:12:009:18:009:24:009:30:009:36:009:42:00C26C27C28C29C30C31C32C19:48:009:54:00C2C310:00:0010:06:0010:12:0010:18:0010:24:0010:30:0010:36:0010:42:00C4C33C34C35C36C37C38C3910:48:0010:54:00C40C4111:00:0011:06:3611:13:1211:19:4811:26:2411:33:0011:39:3611:46:12C42C43C6C44C45C46S3C4711:52:4811:59:24C48C4912:00:0012:06:3612:13:1212:19:4812:26:2412:33:0012:39:3612:46:12S4C50C51C52C53C54C55C5612:52:4812:59:24C57C5813:00:0013:07:3013:15:0013:22:3013:30:0013:37:3013:45:0013:52:30C59C60C61C62C63S1C7C814:00:0014:06:3614:13:1214:19:4814:26:2414:33:0014:39:3614:46:12C9C10C11C12C13C14C15C1614:52:4814:59:24C17C1815:00:0015:07:3015:15:0015:22:3015:30:0015:37:3015:45:0015:52:30C19C20C64C21C22C65C23C2416:00:0016:0316:06:1816:0916:12:3616:1516:18:5416:22C66C25C67C68C69C70C71C7216:25:1216:28C73C7417:00:0017:03:2017:06:4017:10:0017:13:2017:16:4017:20:0017:23:20C75C26C27C28