美赛E题参考答案Word格式.docx

美赛E题参考答案Word格式.docx

《美赛E题参考答案Word格式.docx》由会员分享，可在线阅读，更多相关《美赛E题参考答案Word格式.docx（42页珍藏版）》请在冰豆网上搜索。

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