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数学中国国际赛论文参考模版
第二届“认证杯”数学中国
数学建模国际赛
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第二届“认证杯”数学中国
数学建模国际赛
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TITLE
Abstract:
Keywords:
Contents
1.Introduction...................................................................................................................................................3
1.1Whydoestollwaycollectstoll?
………………………………………….…………………….3
1.2Tollmodes………………………………………………………………………………………………3
1.3Tollcollectionmethods……………………………………………………………………….……3
1.4Annoyanceintollplazas………………………………………….………….…………………….3
1.5Theoriginofthetollwayproblem……………………...……………………………………...3
1.6Queuingtheory…………………………………………………………………………………...…...4
2.TheDescriptionofProblem….............................................................................................................5
2.1Howdoweapproximatethewholecourseofpayingtoll?
............................................5
2.2Howdowedefinetheoptimalconfiguration?
........................…………….………….5
2.2.1Fromtheperspectiveofmotorist…………………………………….………………….5
2.2.2Fromtheperspectiveofthetollplaza…………………………………………………6
2.2.3Compromise…………………………………...……………………………………...………..6
2.3Overalloptimizationandlocaloptimization……………………………..……………….…6
2.4Thedifferencesinweightsandsizesofvehicles………………………………………..…7
2.5Whatifthereisnodataavailable?
..............................................................................................7
3.Models……………...........................................................................................................................................7
3.1BasicModel.............................................................................................................................................7
3.1.1SymbolsandDefinitions………………………………..…...……………………………...7
3.1.2Assumptions……………………………………………………………….……..……………..8
3.1.3TheFoundationofModel………………………………………………………………….9
3.1.4SolutionandResult……………………………………………………………….………...11
3.1.5AnalysisoftheResult……………………………………………….………………………..……….….11
3.1.6StrengthandWeakness………………………………………………….…………….…..13
3.2ImprovedModel.................................................................................................14
3.2.1ExtraSymbols……………………………………..………………………...…………………......................14
3.2.2AdditionalAssumptions………………………………………………...…..…………………………..14
3.2.3TheFoundationofModel………………………………..…………………………………………….14
3.2.4SolutionandResult………………………………………….……………………………..……………...15
3.2.5AnalysisoftheResult…………………………………………….……………………..…………….….18
3.2.6StrengthandWeakness……………………………………………….……………….…..19
4.Conclusions..................................................................................................................................................19
4.1Conclusionsoftheproblem……………………………………..……………..19
4.2Methodsusedinourmodels…………………………………...……………………..…………19
4.3Applicationofourmodels…………………………………………………..………………..….19
5.FutureWork..............................................................................................................................................19
5.1Anothermodel………………………………………………………………………………………19
5.2Anotherlayoutoftollplaza………………………………………………………..……………23
5.3Thenewly-adoptedchargingmethods………………………………………..……………23
6.References...................................................................................................................................................23
7.Appendix......................................................................................................................................................23
Programsandcodes………………………………………………………………..……………………24
I.Introduction
Inordertoindicatetheoriginofthetollwayproblems,thefollowingbackgroundisworthmentioning.
1.1
1.2
1.3
1.4
1.5
1.6
II.TheDescriptionoftheProblem
2.1Howdoweapproximatethewholecourseofpayingtoll?
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2.2Howdowedefinetheoptimalconfiguration?
1）Fromtheperspectiveofmotorist:
2）Fromtheperspectiveofthetollplaza:
3）Compromise:
2.3Thelocaloptimizationandtheoveralloptimization
●
●
●Virtually:
2.4Thedifferencesinweightsandsizesofvehicles
2.5Whatifthereisnodataavailable?
III.Models
3.1BasicModel
3.1.1Terms,DefinitionsandSymbols
Thesignsanddefinitionsaremostlygeneratedfromqueuingtheory.
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3.1.2Assumptions
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3.1.3TheFoundationofModel
1）Theutilityfunction
●Thecostoftollplaza:
●Thelossofmotorist:
●Theweightofeachaspect:
●Compromise:
2）Theintegerprogramming
Accordingtoqueuingtheory,wecancalculatethestatisticalpropertiesasfollows.
3）Theoveralloptimizationandthelocaloptimization
●Theoveralloptimization:
●Thelocaloptimization:
●Theoptimalnumberoftollbooths:
3.1.4SolutionandResult
1）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.
3.2ImprovedModel
3.2.1ExtraSymbols
Signsanddefinitionsindicatedabovearestillvalid.Herearesomeextrasignsanddefinitions.
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3.2.2AdditionalAssumptions
●
●
●AssumptionsconcerningtheanteriorprocessarethesameastheBasicModel.
3.2.3TheFoundationofModel
1）Howdowedeterminetheoptimalnumber?
AswehaveconcludedfromtheBasicModel,
3.2.4SolutionandResult
1）Simulationalgorithm
Basedontheanalysisabove,wedesignoursimulationarithmeticasfollows.
●Step1:
●Step2:
●Step3:
●Step4:
●Step5:
●Step6:
●Step7:
●Step8:
●Step9:
2）Flowchart
Thefigurebelowistheflowchartofthesimulation.
3）Solution
3.2.5AnalysisoftheResult
3.2.6StrengthandWeakness
●Strength:
TheImprovedModelaimstomakeupfortheneglectof.TheresultseemstodeclarethatthismodelismorereasonablethantheBasicModelandmuchmoreeffectivethantheexistingdesign.
●Weakness:
.Thusthemodelisstillanapproximateonalargescale.Thishasdoomedtolimittheapplicationsofit.
IV.Conclusions
4.1Conclusionsoftheproblem
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●
●
4.2Methodsusedinourmodels
●
●
●
4.3Applicationsofourmodels
●
●
●
V.FutureWork
5.1Anothermodel
5.1.1Thelimitationsofqueuingtheory
5.1.2
5.1.3
5.1.4
1）
●
●
●
●
2）
●
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●
3）
●
●
●
4）
5.2Anotherlayoutoftollplaza
5.3Thenewly-adoptedchargingmethods
VI.References
[1]
[2]
[3]
[4]
VII.Appendix
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