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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
