MCM北美数学建模论文模版

TitleAbstract:Keywords:Team#4488Page2of9Contents1.Introduction...................................................................................................................................................31.1Whydoestollwaycollectstoll?………………………………………….…………………….31.2Tollmodes………………………………………………………………………………………………31.3Tollcollectionmethods……………………………………………………………………….……31.4Annoyanceintollplazas………………………………………….………….…………………….31.5Theoriginofthetollwayproblem……………………...……………………………………...31.6Queuingtheory…………………………………………………………………………………...…...42.TheDescriptionofProblem….............................................................................................................52.1Howdoweapproximatethewholecourseofpayingtoll?............................................52.2Howdowedefinetheoptimalconfiguration?........................…………….………….52.2.1Fromtheperspectiveofmotorist…………………………………….………………….52.2.2Fromtheperspectiveofthetollplaza…………………………………………………62.2.3Compromise…………………………………...……………………………………...………..62.3Overalloptimizationandlocaloptimization……………………………..……………….…62.4Thedifferencesinweightsandsizesofvehicles………………………………………..…72.5Whatifthereisnodataavailable?..............................................................................................73.Models……………...........................................................................................................................................73.1BasicModel.............................................................................................................................................73.1.1SymbolsandDefinitions………………………………..…...……………………………...73.1.2Assumptions……………………………………………………………….……..……………..83.1.3TheFoundationofModel………………………………………………………………….93.1.4SolutionandResult……………………………………………………………….………...113.1.5AnalysisoftheResult……………………………………………….………………………..……….….113.1.6StrengthandWeakness………………………………………………….…………….…..133.2ImprovedModel.................................................................................................143.2.1ExtraSymbols……………………………………..………………………...…………………......................143.2.2AdditionalAssumptions………………………………………………...…..…………………………..143.2.3TheFoundationofModel………………………………..…………………………………………….143.2.4SolutionandResult………………………………………….……………………………..……………...153.2.5AnalysisoftheResult…………………………………………….……………………..…………….….183.2.6StrengthandWeakness……………………………………………….……………….…..194.Conclusions..................................................................................................................................................194.1Conclusionsoftheproblem……………………………………..……………..194.2Methodsusedinourmodels…………………………………...……………………..…………194.3Applicationofourmodels…………………………………………………..………………..….195.FutureWork..............................................................................................................................................195.1Anothermodel………………………………………………………………………………………195.2Anotherlayoutoftollplaza………………………………………………………..……………235.3Thenewly-adoptedchargingmethods………………………………………..……………236.References...................................................................................................................................................237.Appendix......................................................................................................................................................23Programsandcodes………………………………………………………………..……………………24Team#4488Page3of9I.IntroductionInordertoindicatetheoriginofthetollwayproblems,thefollowingbackgroundisworthmentioning.1.11.21.31.41.51.6II.TheDescriptionoftheProblem2.1Howdoweapproximatethewholecourseofpayingtoll?2.2Howdowedefinetheoptimalconfiguration?1)Fromtheperspectiveofmotorist:2)Fromtheperspectiveofthetollplaza:3)Compromise:Team#4488Page4of92.3ThelocaloptimizationandtheoveralloptimizationVirtually:2.4Thedifferencesinweightsandsizesofvehicles2.5Whatifthereisnodataavailable?III.Models3.1BasicModel3.1.1Terms,DefinitionsandSymbolsThesignsanddefinitionsaremostlygeneratedfromqueuingtheory.3.1.2AssumptionsTeam#4488Page5of93.1.3TheFoundationofModel1)TheutilityfunctionThecostoftollplaza:Thelossofmotorist:Theweightofeachaspect:Compromise:2)TheintegerprogrammingAccordingtoqueuingtheory,wecancalculatethestatisticalpropertiesasfollows.3)TheoveralloptimizationandthelocaloptimizationTheoveralloptimization:Thelocaloptimization:Theoptimalnumberoftollbooths:3.1.4SolutionandResult1)Thesolutionoftheintegerprogramming:2)Results:3.1.5AnalysisoftheResultLocaloptimizationandoveralloptimization:Sensitivity:TheresultisquitesensitivetothechangeofthethreeparametersTrend:Comparison:3.1.6StrengthandWeaknessStrength:Indespiteofthis,themodelhasprovedthat.Moreover,wehavedrawnsomeusefulconclusionsabout.Themodelisfitfor,suchasWeakness:Thismodeljustappliesto.Aswehavestated,.That’sjustwhatweshoulddointheimprovedmodel.3.2ImprovedModelTeam#4488Page6of93.2.1ExtraSymbolsSignsanddefinitionsindicatedabovearestillvalid.Herearesomeextrasignsanddefinition