2016美赛E题参考答案

Team#52766ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber52766ProblemChosenEForofficeuseonlyF1________________F2________________F3________________F4________________2016MCM/ICMSummarySheetInordertopredictthewaterscarcityandoptimizetheconfigurationreasonably,weanalyzethesituationofwaterscarcitybyestablishingamathematicalmodel,andproposethefeasiblesuggestionsonoptimization.Alltheworkisbasedonthesufficientdatawecollect.Firstly,thelocalsituationofwaterscarcityisestimatedbyintroducingthewaterlackingrateindex.Secondly,thelocalwaterconsumptionispredictedfrompersonalliving,industry,agricultureandecology.Meanwhile,thelocalwaterconsumptionispredictedthroughestablishingacompoundmodelwhichbasedonanimprovedLogisticModelandthestatisticalregressionanalysis.Thirdly,theGrayPredictionMetabolismModelisusedforpredictingtheamountoflocalwatersupply.Atlast,wecomprehensivelyanalyzetheexperimentalresults,andpredicttheabilityofwatersupplyinthislocalarea.Toverifytheavailabilityofthemodel,wechoosetheNorthChinaastheobjectofstudy.Weconcludethatthisareaisseriouslyscarcebefore2010onthebasisofmassdata.Thewaterscarcitywillsteadilyremitandreachbalancein2025.ThisisduetoChinahasfinishedtheSouth-to-NorthWaterDiversionandtheNorthChinagainslargewaterresourcesfromoutside.Theresultscallinsidewiththetruth,sothemodelisreliable.ThenwetrytooptimizethewatersupplyinganddemandingstructureintheNorthChina,sothatitcanrealizetheinternalself-sufficiency.Weuseanalytichierarchyprocess(AHP)toassessthefourschemesofwaterstorage,watertransfer,wastewatertreatmentanddesalinationfromfouraspectsoftimeliness,sustainability,economic,environmentalbenefits,soamorescientificwatersupplyingsystemisdeveloped.Finally,bymeansofadjustingtheindustrialstructure,optimizingthemodeofagriculturalirrigationandimprovingthewaterconservationawarenessofcitizens,weproposeawaterresourcesallocationmodeltooptimizethewatersupplysystemintheNorthChina.Inthisway,thewaterscarcityintheNorthChinacanbesolvedfiveyearsaheadoftheoriginalschedule.KeywordsWaterscarcity;waterlackingrateindex;improvedLogisticModel;GrayPredictionMetabolismModel;statisticalregression;analytichierarchyprocess(AHP)Team#52766Contents1INTRODUCTION&BACKGROUNDS.....................................................................................................12PROBLEMANALYSIS...........................................................................................................................12.1ProblemRestatement..................................................................................................................12.2Problemsolving..........................................................................................................................23ASSUMPTIONS....................................................................................................................................24NOTATIONS.........................................................................................................................................35BASICMODEL.....................................................................................................................................35.1Modelofthewaterconsumption................................................................................................35.1.1CompoundpopulationModelbasedonLogisticModel.....................................................................45.1.2ModelofIndustrialwaterconsumption...............................................................................................55.1.3Modeloftotalwaterconsumptionofaregion.....................................................................................65.2ModeloftheGrayMetabolismModelGM(1,1).......................................................................65.2.1PrincipleofcommonGrayGM(1,1)Model......................................................................................65.2.2PrincipleofGrayMetabolismModelGM(1,1)[2]..............................................................................85.2.3Accuracytesting..................................................................................................................................85.3Modelofwatersupplycapacityofaregion...............................................................................95.4Strengths&Weakness..............................................................................................................106CHOOSEAREGIONTOANALYZE........................................................................................................106.1Briefintroduction.....................................................................................................................106.2Physicalscarcity:.....................................................................................................................116.3Economicalscarcity:................................................................................................................127PRED