2016数学建模美赛一等奖论文.pdf

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1、TeamControlNumberForofficeuseonlyForofficeuseonly52888T1________________F1________________T2________________F2________________T3________________ProblemChosenF3________________T4________________F4________________AMathematicalContestinModeling(MCM/ICM)SummaryS

2、heetSummaryIt’spleasanttogohometotakeabathwiththeevenlymaintainedtemperatureofhotwaterthroughoutthebathtub.Thisbeautifulidea,however,cannotbealwaysrealizedbytheconstantlyfallingwatertemperature.Therefore,peopleshouldcontinuallyaddhotwatertokeepthetemperature

3、evenandascloseaspossibletotheinitialtemperaturewithoutwastingtoomuchwater.Thispaperproposesapartialdifferentialequationoftheheatconductionofthebathwatertemperature,andanobjectprogrammingmodel.BasedontheAnalyticHierarchyProcess(AHP)andTechniqueforOrderPrefere

4、ncebySimilaritytoIdealSolution(TOPSIS),thispaperillustratesthebeststrategythepersoninthebathtubcanadopttosatisfyhisdesires.First,aspatiotemporalpartialdifferentialequationmodeloftheheatconductionofthetemperatureofthebathwaterisbuilt.Accordingtothepriority,an

5、objectprogrammingmodelisestablished,whichtakesthedeviationoftemperaturethroughoutthebathtub,thedeviationoftemperaturewiththeinitialcondition,waterconsumption,andthetimesofswitchingfaucetasthefourobjectives.Toensurethetoppriorityobjective—homogenizationoftemp

6、erature,thediscretizationmethodofthePartialDifferentialEquationmodel(PDE)andtheanalyticalanalysisareconducted.Thesimulationandanalyticalresultsallimplythatthetopprioritystrategyis:Thepropermotionsofthepersonmakingthetemperaturewell-distributedthroughouttheba

7、thtub.Therefore,thePartialDifferentialEquationmodel(PDE)canbesimplifiedtotheordinarydifferentialequationmodel.Second,theweightsfortheremainingthreeobjectivesaredeterminedbasedonthetoleranceoftemperatureandthehobbyofthepersonbyapplyingAnalyticHierarchyProcess

8、(AHP)andTechniqueforOrderPreferencebySimilaritytoIdealSolution(TOPSIS).Therefore,theevaluationmodelofthesynthesisscoreofthestrategyisproposedtodeterminethebestonethepersoninthebathtubcanadopt.Fo