美赛E题参考答案Word格式.docx
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52766
ProblemChosen
E
F1
F2
F3
F4
2016MCM/ICM
SummarySheet
Inordertopredictthewaterscarcityandoptimizetheconfigurationreasonably,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.
Keywords
Waterscarcity;
waterlackingrateindex;
improvedLogisticModel;
GrayPredictionMetabolismModel;
statisticalregression;
analytichierarchyprocess(AHP)
Contents
1Introduction&
Backgrounds1
2ProblemAnalysis1
2.1ProblemRestatement1
2.2Problemsolving2
3Assumptions2
4Notations3
5Basicmodel3
5.1Modelofthewaterconsumption3
5.1.1CompoundpopulationModelbasedonLogisticModel4
5.1.2ModelofIndustrialwaterconsumption5
5.1.3Modeloftotalwaterconsumptionofaregion6
5.2ModeloftheGrayMetabolismModelGM(1,1)6
5.2.1PrincipleofcommonGrayGM(1,1)Model6
5.2.2PrincipleofGrayMetabolismModelGM(1,1)[2]8
5.2.3Accuracytesting8
5.3Modelofwatersupplycapacityofaregion9
5.4Strengths&
Weakness9
6Choosearegiontoanalyze10
6.1Briefintroduction10
6.2Physicalscarcity:
11
6.3Economicalscarcity:
12
7PredictionmodelfortheNorthChina12
7.1ModelofwaterconsumptioninNorthChina.12
7.2WatersupplymodelintheNorthChina17
7.3ThecomprehensiveevaluationtothefuturewaterresourcesintheNorthChina18
7.4StrengthsandWeaknesses21
8OptimizationofwaterresourcesAllocation21
8.1Optimizationofwatersupplyallocation21
8.1.1Constructthemodelofhierarchicalstructure21
8.1.2Constructionofcomparisonmatrixoftarget-criterionlayer.22
8.1.3Constructionofcomparisonmatrixcriterion-targetlayer23
8.1.4Totalsortsofhierarchyandconsistencycheck27
8.1.5Interpretationofresult28
8.2Optimizationofwaterconsumptionallocation29
8.2.1Constructionofwaterresourcesallocationmodel29
8.2.2Mainconstraintequations30
8.2.3ModelSolution31
Conclusions33
Furtherdiscussions34
Reference34
Appendix35
StrategyofConqueringThirst
Backgrounds
Aneffectiveplanofsolvingthewaterscarcityproblemiscrucialtohumansociety.AccordingtotheUnitedNations,todaymorethanonebillionpeoplelackaccesstosafe,cleandrinkingwater,andjust10countriesshare60percentoftheworld’snatural,renewablewaterresources;
what’smore,waterusehasbeengrowingattwicetherateofpopulationoverthelastcentury.Amodelofwaterscarcityoftheworldshowstheserioussituation.(SeeFigure1)
Figure1:
themapoftheworld’swaterscarcity
Atthesametime,oursocietalandeconomicgrowthislargelydrivenbytheproductiveuseofwater.Actually,theworldtripleditswateruseinthelast50yearsalone.O