美赛B题一等奖论文

2024年美赛B题一等奖论文Team#22362Pageof29Statisticaldataindicatethatthewatersuppliesofeachzonein2024arerespectivelyshownasthefollowingtable:Table4:thewatersuppliesofeachzonein2024ZoneABCDEFGOutput601.05523.27565.581370.641898.92473.83588.715.1.4Analysisofsupply-demandbalances:AccordingtothecalculationmethodofwaterdemandinAzone,waterdemandsofotherzonescanbecalculated,andtheresultsare:Table5AnalysisoffreshwatersupplyZoneOutputConsumptionD-valueA601.0455391537.53469563.52B523.2719044876.1035-352.83C565.5787098882.00135-316.42D1570.637961168.985791401.65E2602.9163242494.9068108.00F473.8310362703.47595-229.65G588.7133870.56585-281.85Theabovetableindicatesthat,amongthesevenzones,onlyzoneA、D、andEwouldhaveenoughwatersupplyin2025，andtheirredundantwaterquantityarerespectively63.52×108m3，401.65×108m3，108108m3.WhilezoneB、C、F、Gwouldbeinwatershortagein2025,andthequantityoftheirwatershortagearerespectively352.83×108m3，316.42×108m3，229.65×108m3，281.85×108m3.Thewatersupplyindicatesthatthewatershortagesituationofsomezonesisserious.Inordertosolvethewatercrisis,nationalwaterstrategyneedtobedeterminedtofacethechallenge.5.2.WaterstoragemodelInthefloodseasonofrainyyear,alargequantityofwatersupplyexceedsdemand.Excessrainwaterwouldbestoredintheintakearea,inordertobetakenadvantageofinthedryseason.Theexcesswaterisusuallystoredintwoways:groundwaterstoragethatmakesthemostofthehydrogeologicalconditionsandthepre-existinggroundwaterextractionwellsofthewater-starvedcitytoreplenishgroundwater;surfacewaterstoragethatmakesfulluseofthepre-existingreservoirsofwater-starvedcity,thebestofwhichsupplementsthesurfacewaterfromthesourceregionofthecity'swatersupply(whichcantakeadvantageofthepre-existingwatersupplysystem).Theundergroundreservoirisaspecialreservoir,builtwiththenaturalundergroundwaterstoragespace,playingtherolesofimpoundment、regulationandutilizinggroundwaterflow.Asshowninthefollowingfigure:Figure6:undergroundreservoirAccordingtothethicknessoftheaquifer,thedistributionareaandrockstoragecoefficient,itcanbecalculatedthatthemaximumregulationandstoragecapacityofundergroundreservoiras:𝑉𝑚𝑎𝑥=𝑆𝐴∆𝐻(6)Where:𝑉𝑚𝑎𝑥referstotheregulationandstoragecapacityofundergroundreservoirs(m3);isstoragecoefficientoftheundergroundwater-bearingmediuminreservoirstoragelayer,forthenopressurewater-bearingbody𝑆=𝜇+𝜇∗,forthepressurewater-bearingbody𝑆=𝜇∗,whereisgravityspecificyield(dimensionless),𝜇∗iselasticstoragecoefficient(dimensionless);isreservoirarea(km2);∆𝐻isthemaximumthicknesstheregulationandstoragelayer,thatis,thewaterleveldifferencevaluebetweentheextremehighwaterlevelandtheplanningregulationandstoragelayerbottominterface()(Zhengetal.2024).Superiorities：Undergroundreservoirtakingnaturalaquiferaswaterstoragespaces,soithasrelativelysimpleconstructionconditionsandlowerconstructioncosts;Undergroundreservoirshaslittleeffectonothergroundbuildings,relativelysafe,lowenvironmentalimpact;Groundwaterinreservoirregionshassmallerevaporationloss,easytoconserve;Itprovidesthebasisandconditionsforthejointschedulingofsurfacewaterandgroundwater,anditslowsdownthefloodpressure.Problems：Ithasrelativelargererrorstocalculatetheamountofresourcesofundergroundreservoirs;andithasalargerworkloadtosurvey,withhighercostsandlongerperiods〔Zhao2024〕.Consideringthattheundergroundreservoirjustsavesthelocalregion'swatersupply,ratherthanadditionalwatersource,itcanbeusedtosolvewatersupply-demandimbalanceissuesintheshortterm,sothatinthedryseasonoftheyear,theresidentscanusethewaterofthefloodseason.However,itisnotsuitableasalong-termwaterstrategytoresolvetheregionalwatersupply-demandimbalancesituation.5.3.MobilizationmodelBythefirstpredictionmodel,itcanbefoundthatthedistributionofwaterresourcesinChinaisextremelyimbalanced,withmoreWaterinSouthern,lessWaterinNorthern.AndthewaterresourcesareconcentratedintheYangtzeRiverbasin.Inordertosolvethewatershortageproblem,itisfeasibletotransferthewaterfromthewetareatothewater-poorareas,bytheredistributionofwaterresourcesthroughacanaloraqueduct.Statisticsshowthatthewatertransfercostsinthesouth-to-northwaterdiversionprojectcenterlineis2.6yuan/m3(Qiu2000).ThewatertransfercostsinwesternrouteofwaterdiversionfromSouthtoNorthis1yuan/m3(Tu2001),anditis3.4yuan/m3intheeastroute.Herethediversioncoststaketheaveragevalue(2.6+1+.4)÷=2.yuan/m3Abidebytheprincipleofcostminimization,thedeterminationofthewatertransferschemesneedlinearprogrammingtosolve.LinearprogrammingAsthefigureshows,inordertosimplifythetransferprocess,takeonebigcityineachzoneasacentralizedpointtostudytheirwatermobilization.Thosecentralizedpointturntoberespectively:A:Xining(+63.52)B:Hohhot(-352.83)C:Chengdu(-316.42)D:Wuhan(+401.65)E:Guangzhou(+108)F:Beijing(-229.65)G:Harbin(-281.85)Figure7:Mobilizationmodel①PointA、D、Earewatersupplypoints,B、C、F、Garewater-poorpoints.A+D+E=573.17B+C+F=898.9>573.17SoA、D、Edon’thaveenoughwatertomeetthequantityB、C、Fdemand.WhilethedistancebetweenGandwatersupplypointsisthefarthest，andthecostsisthelargest,soitcanbeignoredtotransferthefreshwatertoGzone.②.ItcanbeseenthatDzonemustsupplywatertoBorF〔D>C〕，inordertoavoidthecostscausedbyrouterepeat,whenEprovideswatertoB、F,itcanprovidewatertoDfirstly，thentoB、F.③.BecauseAzonehadlesswatersupply，andthedistancebetweenAandFisfatherthanDF,andthedistancebetweenAandCiscloserthanCDandCE,sotheroutineAFcanbeexcluded.SothefeasiblewatersupplylineincludesAC、AB、DB、DF、DC、EC、ED、〔ED+DB〕、〔ED+DF〕ItcanbesoughtbymeasuringtapethroughBaidumapthatED=838km，EC=1233km，DF=1056km，DB=1061km，AC=703km，AB=984km，CD=992km.IthasbeenassumedthatthewatersupplyamountfromAtoB、Cisrespectively:𝑥12、𝑥13，thewatersupplyamountfromDtoB、C、Fisrespectively:𝑥42、𝑥43、𝑥46，fromEtoB、C、Fisrespectively𝑥52、𝑥53、𝑥56.Transportationcostsoftheunitvolumeofwaterarea，thetransportationcostsareW.SotheDecisionobjective:minW=(703𝑥12+984𝑥13+992𝑥43+1061𝑥42+1056𝑥46+123353+1899𝑥52+1894)(7)Constraints(8)AftersolvingitbyLINGO，theoptimalsolutionhasbeenobtained：NamelythewatersupplyAtoBis63.52×108m3.DtoCis208.42×108m3.DtoFis193.23×108m3.EtoCallis108×108m3.SensitivityanalysisObtainingtheminimumvalueofthetotalcostofthediversionbythelingosoftware:588622.1a.Andthedataobtainedbythesensitivityanalysisareasfollows:Itcanbedrawnfromtheabovedatathatthereductionofthethirdandfourthrowsofdatawouldmakethetotalcostreducemore.100millionm3waterreductionofZoneDandZoneEwouldmakethetotalcostreduceto1056aand1297arespectively.Inaddition,100millionm3waterreductionofzoneCwouldmaketheincreaseof64ainthetotalcost.Tosumup,justconsideringtheeconomiccostofwaterdiversion,waterdiversioncanbechangedasthefollows:minimizingwaterdiversionofD、Ezoneorreducingitswatertransferdistance;astozoneC(Beijing,Tianjin,Shandong),themorethewaterdemandproportionoftheCzone(Beijing,Tianjin,Shandong),inthecaseofconstantwaterdemandofallzones,thelessthetotalcosts,whichisinlinewiththeactualsituation,inwhichthecostsofthesouth-to-northwaterdiversionprojectcenterlinearerespectivelylow.5.4.SeawaterdesalinationmodelSeawaterdesalinationtechnology,thatisusingseawaterdesalinationtoproducefreshwater,istheopensourceincrementaltechnology,whichrealizedtheutilizationofwaterresources,regardlessoftheimpactsoftime、spaceandclimate.Itcanprotectthedrinkingwaterneedsofcoastalresidents.Thedesalinationmethodsusednowadaysincludeseawaterfreezingmethod、electrodialysis、distillationandreverseosmosis.Thankstoitsadvantagesofsimpledevices,easymaintenanceandequipmentmodular,reverseosmosis,withtheapplicationofreverseosmosismembrane,occupiedthemarketquicklyandgraduallyreplacedistillationmethodtobecomethemostwidelyusedmethod.Thentakingreverseosmosisasanexampletocalculatetheexternalcostsofdesalination.Costanalysisofdesalination：Thecostsofdesalinatedwaterareproducedinvariousstages,includingtheeconomicandenvironmentalcosts,mainlythecostsoftheenergyconsumption,thecostsoftheeffluentdischargetotheenvironmentandthevalueconversionofusingseawater.Itscostanalysisisshownasfigure8:Figure8ExternalcostanalysisofseawaterdesalinationDesalinationprocessEnergycostsConcentratedbrinemissionscostsThecostofdesalinationtap-waterusersSewagetreatmenSewagecostSeawaterSewage5.4.1.Analysisofenergyconsumptioncosts：Energyconsumptioncostiscalculatedinaccordancewiththequantityoftheresourcesconsumedbyunitelectricity,whichisgeneratedbygeneralcoal-firedpowergeneration(Chen2024).Theformulais：𝐶1=𝑅×∑𝑃𝑖𝑄𝑖(9)WhereRiselectricityconsumptionPertonofdesalinationwater(kW*h);Piisthepricesofresource(yuan);Qiindicatesthattheresourcesquantityconsumedbyunitofelectricityisi(g/kWh).5.4.2.Analysisofenvironmentalcosts：Whenthesewagechargesiscalculatedbypollutionequivalent,accordingtothetypeandquantityoftheemissionpollutants,chargedstandardofeachpollutionequivalentis0.7Yuan.Foreachoutfall,thetypenumberofpollutantswhicharechargedofsewagefees,indecreasingorderofpollutionequivalentamount,uptonotmorethan3.PollutionequivalentamountofsomecertainpollutantNis：Environmentalcostsofunitutilization:(11)Where𝜔𝑖istheconcentrationofpollutanti,whichisproducedaftertheusageofdesalinatedwater,(mg/L)；𝑄𝑎istheamountofsewageconvertedbyunitfreshwater；istheconcentrationofpollutantiinthefreshwater,(mg/L)；𝐷𝑖isthepollutionequivalentvalueofpollutanti,(kg).Amongisthetotalamountofsewageemitted；𝑄2isthetotalwaterconsumption.Inthesimilarway，theexternalimpactofconcentratedbrineemissionsonthemarineenvironment,canalsobecalculatedbymethodofestimatingsewagecharges,ofwhichtheformulais:(12)Therefore，thecostsofdesalinationcanbecalculatedas:𝐶=𝐶1+𝐶2+𝐶3(13)where𝐶iisthecostoffactori.Example:solvingofthedesalinationexternalcosts：〔takingdesalinationofQingdaoBaifaprojectasanexample〕1.Calculationontheenergyexternalcosts：Thedailyproductionofthisplantis100,000m3desalinatedwater,andenergyconsumptionpertonofwateris3.8kWh/m3.Resourcesconsumedbyunitelectricity,whichisgeneratedbygeneralcoal-firedpower,areshowninTable2.Table2：Resourcesconsumedbyunitofcombustionpowergeneratedelectricity〔g/kWh〕resourceironorerawcoalchalkcopperorecrudeoilPrice/(Yuan/t)400672306005500Coalacquisitionstage0.3112.360.1630.0270.017coaltransportation0.062.280.0440.0070.58productionstages2.491491.2950.1422.1250total2.861505.9350.3492.1590.597Notation:Takestandardcoalconsumptionofcoal-firedpoweras350g/kWh,andtheresourceconsumptionofcoalminingandtransportationstagesiscalculatedbytheNational122departmentsinput-outputtablein2024.Externalcostsofitsresourcescanbecalculatedaccordingtotheformula：𝐶1=𝑅×∑𝑃𝑖𝑄𝑖=.8×(2.861×400+505.95×672+0.49×0+2.159×600+0.597×5500)÷106=1.1(yuan).CalculationontheEnvironmentalexternalcosts,thedataareshownasthefllows:Table3pollutantcontentsandtheirpollutionequivalentvalue(2024)pollutantContentsinthereverseosmosisbrine/(mg/L)Contentsafterusage/(mg/L)pollutionequivalentvalue/kg1280432501NH4−N0.02300.8Tp0.970.970.25ThetotalwateramountQingdaousedin2024is943millionm3，anditswastewateremissionsamountis381.56milliontons，then(2024): 8156Thenitcanbeestimatedthattheenvironmentalcostsofuseddesalinatedwater：Environmentalcostsofconcentratedbrineemissioncanbecalculatedaccordingtotable4:Table4：Thechemicalcomponents’natureofpollutantsMeasuringItemsOriginalseawater〔μmol/L〕Concentratedbrine〔μmol/〕Pollutionequivalentvalue(kg)Mn4.358.040.2u0.742.140.1NH4−N4.4829.530.8Takingthecurrenttechnologylevelintoaccount,theefficiencyofthedesalinationprocessingisapproximatelyamong40%to50%.DailyseawaterrequirementofBaiFaprojectis260000t.Itproduces100000tfreshwatereveryday,withtheemissionconcentratedbrine160000teveryday,sothequantityofemissionsconcentratedbrineforproducingunitdesalinatedwaterQis1.6.Thereforetheenvironmentalcostsofbrineemissionsare:𝐶=𝐶1+𝐶2+𝐶3+𝐶4=1.1+0.101+0.072=1.49yuan5.5.SewagetreatmentmodelAnotherideatoincreasetheavailablefreshwaterisrecycle.Aftertreatmentofthesewagetreatmentplant,reusethewastewaterthatmeetsthenationalemissionstandards.CostAnalysis：ThecostofprocessinganditscomponentsFormunicipalwastewatertreatmentplant,domesticwastewateristhemainsewagesource.Andnowadays,itsprocessinghasbeenrelativelymature,ofwhichthecoretechnologyisbiologicalactivatedsludgeprocess.𝑋=𝑋1+𝑋2+𝑋3+𝑋4+𝑋5+𝑋6(14)Whereisthemonthprocessingcostofthesewagetreatmentplant;𝑋1isdepreciationcost;2ispersonnelcost;𝑋3ispowercost;𝑋4ismaintenancecost;𝑋5isagentcost;𝑋6isothercosts,whichcanbeestimatedas5%ofthepreviousfivecosts.AnalysisofProcessingcostTakesewagetreatmentplantwiththehandlingcapacityof30,000t/dofNorthChinaasanexampleforanalysis.a.Depreciationcharges𝐗𝟏Depreciationisameasuretorecovertheinvestment,whichmeansextractingacertainamountoffundsasarecoveryofinvestmentattheendoftheyear.Accordingtothecalculationmethodoftheannuity,withoutextraconsiderationoffinancialexpense,thedepreciationextractedeveryyearis(Jin2024)𝑋1=𝑍×(1−𝑖)/(12×𝑛)(15)WhereZistotalinvestmentamount(×104yuan);iisthediscountrate〔%〕,whichiscalculatedgenerallybasedontheloaninterestrate;nisdepreciationlife〔year〕.Assumethatthetotalinvestmentamountis3000×104yuan,theloaninterestrateis5%,depreciationlifeis20years,thenthedepreciationeverymouthis:X1=Z(1-i)/(12n)=118750(Yuan)MonthprocessingcostDepreciationcostX1personnelcost𝑋2Powercost𝑋3Maintenancecost𝑋4Agentcost𝑋5Othercost𝑋6StationelectricityX7=K720μP=85680TankelectricityX8=0.5×η×P×24×0=135000X4=70000yuanX5=27000yuanX1=118750(yuan)X6=5%(X1+X2+X3+X4+X5)=23821yuanemployees25withmonthlywage1600，X2=25×1600=40000MonthprocessingcostX=500251yuan，costpertonX÷(0×0000)=0.56yuanFigure9:sewagetreatmentcostb.Powercosts𝐗𝟑i.PumpingstationelectricitybillsX7：𝑋7=720×𝐾×𝜇×𝑃(16)Where:X7ispumpingstationelectricitybill,Yuan;iselectricitybillsperkilowattperhour,Yuan/(kWh);istheutilizationefficiencyofthepump,kW;isthepowerofthepump,kW;720istheruntimeofpumppermonth.Forthe30000t/dsewagetreatmentplant,thepowerof4liftpumpsis4×60kW=240kW,thepowerof5sludgeandrefluxpumpsis5×20kW=100kW,andelectriccharges0.5Yuan/(kWh),theutilizationefficiencyofthepumpis0.7,thenthepumpingstationelectricitybillsonemouthis:X7=85680(yuan).ii.aerationtankelectricfees𝑋8：Thepowerofaerationequipmentisamong450~550kW,takingthemiddlevalue500kW.Theutilizationefficiencyofthepumpisabout75%.Monthlyelectricitybillsis:𝑋8=500×0.5×0.75×720=15000(Yuan)。powercostis:𝑋6=𝑋7+𝑋8=220680(Yuan)(17)c.Maintenancecost𝐗𝟒Maintenancefeesandinstrumentcalibrationfeesaregenerallyaccruedannual5%oftheamountofinvestmentinequipment.Equipmentoverhaulcostsandpipelinemaintenancefeesaregenerallyonlyonetimeamongafewyears,withtheannualprovisionfor2%oftheamountofinvestmentinequipment.Theinvestmentinequipmentisgenerallyabout1200×104yuan.Inaccordancewiththesituationthatoneequipmentoverhauleveryfiveyears,themonthlymaintenancefeeis:𝑋4=70000(yuan)d.Pharmacyfees𝑿𝟓Pharmacyfeesincludedvariouschemicalreagents,flocculantsanddisinfectionfees.Theoperatingcostsofsewagedisinfectionis0.025yuan/t.Thedosageofchemicalreagentsandflocculantisrelativelysmall,andthepharmaceuticalfeesforprocessingsewageis0.03yuan/t,sothepharmacyfeeseverymonthis:𝑋5=27000Yuan.Soprocessingcosteverymouth:𝑋=𝑋1+𝑋2+𝑋3+𝑋4+𝑋5+𝑋6=500251(yuan)Processingcostpertonis:𝑋÷(0×0000)=0.56(yuan).WaterStrategyThepredictionmodelhasconfirmedthewatershortageareasandwetareasin2025.Inordertosolvethewatershortageproblem,fourwatersupplyschemeswereintroduced:storage,movement,seawaterdesalinationandsewagetreatmentTodeterminethebestwaterstrategy,itisnecessarytoevaluatethestrengthsandweaknessesofthosefourschemes,beforethepermutationandcombinationofthem.Becauseundergroundreservoirsjustsavetheregionalwater,ratherthanprovideadditionalwater,itcanjustsolvewaterdemand-supplyimbalancesintheshortterm,sothatinthedryseasonoftheyearcanalsousethewaterofthefloodseason,butisnotsuitableasalong-termwaterstrategy.Therefore,itisfeasibletoevaluatethemobilization、desalinationandsewagetreatmentbyanalytichierarchyprocessmodelsfirstly.5.6.AHPmodelTheTheaimlayerTheProportionofeachmethodtoWaterStrategy〔A〕Economic(B1)EnvironmentB(2)PhysicalB(3)SocietyB(4)PrincipalLayerTransfer(C1)Sewagetreatment(C2)Desalination(C3)ProjectLayerFigure10:analytichierarchyprocessmodesTheweighingresultisasfollow:A B1 B2 B3 B4 B1C1 C2 C3 B1 1 3/2 9/8 5/4 C11 3 2 B2 2/3 1 2 7/5 C21/31 3/2B3 8/9 1/2 1 3 C31/22/31 B4 4/5 5/7 1/3 1 B2C1 C2 C3 B3C1 C2 C3 B4C1 C2 C3C11 3/27/5 C11 3 7/4 C11 3 2C22/31 1/2 C21/31 1/2 C21/31 3/2C35/72 1 C34/72 1 C31/22/31Afterthestandardizationofeigenvector,thevectorofweighingcanbeacquiredby:Wi1n naijnj1aklk1 (18)CoherenceCheck:Firstly，calculatetheC.I.〔consistencyindex〕CImaxnn1(19)Secondly,calculateR.I.〔randomindex〕:n=3,R.I.=0.90n=4,R.I.=0.58Thirdly，calculateC.R.〔consistencyratio〕CI.CRRI.(20)WhenCR<0.1,theconsistencyofjudgmentmatrixisacceptable,otherwise,itshouldbecorrected.UsingMatlab,theweightvectorandtestresultscanbegottenasfollows:B2 weight B3 weight B4 weightC1 0.3752 C1 0.3726 C1 0.4215C2 0.2531 C2 0.2768 C2 0.2917C30.3717C30.3506C30.2868λ3.07λ3.04λ3.02CR0.06CR0.05CR0.05Accordingtoabovetables,theresultscanbeobtainedasfollow:MethodWeightImportancesequence(HightoLow)Mobilization0.46831Desalination0.32842Sewagetreatment0.20333Whendeterminethebestwaterstrategy,itshouldmobilizethewaterfirstly,namelytheredistributionofwaterresources.Itcanbefoundfromthemobilizationmodel:Czonesolveditswatershortage;Bzoneneedmorewater52.8−63.52=289.31108m3，Fzoneneedmorewater229.65−193.23=36.42×108m3，Gzoneneedmorewater281.85×108m3.Implementationofdesalinationneedsoffshoreenvironment.Basedontheprincipleoflocalconditions,Fzoneshouldadoptdesalinationstrategy.Bzonebelongstoinland，soitshouldadoptsewagetreatmentstrategy.Gzonehassomepartsoffshore,soitwouldbebettertoadoptjointstrategiesofdesalinationandsewagetreatment.CostsAnalysisNowadays,thedailyaverageprocessingcapacityofdesalinatoris1.0×105m3,whilethesewagetreatmentplantis8.0×104m3,asthefollowingtableshows：Poor-waterzonesWatershortage×108m3AmountofdesalinationplantsAmountofsewagetreatmentplantscosts/108yuanB289.310990147.5F36.42100054.3G281.8550903161.6Thewaterstrategycostsofeachzone：ZoneMobilizationcosts/108yuanDesalinationcosts/108yuanSewagetreatmentcosts/×108yuanTotal/108yuanB146.10147.5293.6C727.800727.8F444.454.30498.7G027.2134.4161.6Total/108yuan1318.354.3 147.51520.1Theresultsshowthat,inordertosolvethewatershortage,Fzoneneedstobuildatleast100desalinatorsinShandong、Tianjinbefore2025,withthecosts54.3×108yuan;Bzoneneedstobuildatleast990desalinatorsbefore2025,withthecosts147.5×108yuan。Gzoneneedstobuildatleast50desalinatorsinLiaoningbefore2025,and903sewagetreatmentplantsbefore2025,withtherespectivecosts27.2×108yuan、134.4×108yuan.5.7.Modelforintra-regionaloptimalallocationofwaterInadditiontoreplenishingthewatershortage,theoptimalwaterstrategyalsoneedstoensurethattheincreasedfreshwaterresourceswithinthezonecouldbringthemaximumeconomicbenefits.Thefamilieswithinthezoneareseenasminimumunits.Alongwiththeincreaseintheamountoffreshwaterallocated,othermeansofproductionwouldbefullyutilized,andtheeconomicefficiencywouldincrease.However,whentheallocationamountisincreasedtoacertaindegree,theeconomicefficiencywoulddecreasebecausetheincreasedwatercostsandthedecreasedproductivitygrowth.Tosimplifythemodel,assumethattheeconomicbenefits,Jandwaterconsumption,qsatisfythequadraticfunction.Asthefigureshown.Set𝐽=𝑎𝑞2+𝑏𝑞,a0,qisthewaterconsumptionamount,Jisactualbenefits.Whenwaterconsumptionq=0，theeconomicbenefitsJ=0；Whenwaterconsumptionq=Q，themaximumeconomicbenefitsJ=J‘.Solvingequations,thenitcanbegotten:Figure11:JandqFigure11:JandqThentheincreasedeconomicbenefitswiththewaterallocationof∆qare:∆𝐽=(𝑞+∆𝑞)2+𝑏(𝑞+∆𝑞)−(𝑎𝑞2+𝑏𝑞)=𝑎∆𝑞2+(2𝑎𝑞+𝑏)∆𝑞(21)Assumethatthereareunits(families)withinthezone,thentheincreasedtotalbenefitsafterintroducingwaterQare:(22)𝑄=∑𝑖∆𝑞𝑖(23)Themaximumeconomicbenefits,namelythelargest.Sothisquestioncanbeconvertedintoanother,namely,when𝑄=∑𝑖∆𝑞𝑖，seekthemaximumvalueHmaxonthebasisof𝐻=∑[𝑎∆𝑞𝑖2+(2𝑎𝑞+𝑏)∆𝑞𝑖]ThisproblemcanbesolvedbyusingtheLagrangemultipliermethodtoobtainitsextremevalue：Make𝐾=∑[𝑎∆𝑞𝑖2+(2𝑎𝑞+𝑏)∆𝑞𝑖]+𝛾∑𝑖∆𝑞𝑖(24)𝐾′=0,then∆qiisoptimumsolutionInactualsituation,waterconsumptionunits,whichrefertofamilies,areoftennotabletograsptheoptimalwaterconsumptionQ.Thenitisnecessarytoaddupthepastwaterusagesituationstodeterminethebestrangeofwaterconsumption.6.Thenon-technicalpositionpaperAmongthesevenzones,onlyzoneA,D,Ewouldhaveenoughwatersupplyin2025,theirredundantwaterquantityisrespectively63.52，401.65，108×108m3.whilezoneB,C,F,Gwouldbeinwatershortagein2025,theirwatershortageisrespectively352.83，316.42，229.65，281.85×108m3.Thesolutionsare：ForCzone，itisnecessarytobuildCD、CEtworoutes，andtransferwaterfromDzone208.42in2025，fromEzone108，withthetotalcosts72.78billionyuan.ForFzone，itisnecessarytobuildrouteFD，andtransferwaterfromDzone193.23in2025withthecosts444.4.Anditisnecessarytobuildatleast100desalinatorsinShandong、Tianjinbefore2025,withthecosts5.43billionyuan.ForBzone，itisnecessarytobuildrouteAB，andtransferwaterfromAzone63.52in2025withthecosts146.1.Anditisnecessarytobuildatleast990desalinatorsbefore2025,withthecosts14.75billionyuan.ForGzone,itisnecessarytobuildatleast50desalinatorsinLiaoningbefore2025,and903sewagetreatmentplantsbefore2025,withtherespectivecosts2.72billionyuan、13.44billionyuan.Forthewholecountry,itisnecessarytoreplenishwaterresourcesoftheundergroundreservoirs.Inordertoprotecttheundergroundstoragespace,apartfromlandsubsidence,goodstorageworkmustbedone.Fortheregionalfreshwaterallocation,alotofstatisticalworkneedstobedone.Anditisnecessarytodeterminetheoptimumwaterconsumptiontoachievemaximumproductionefficiency.Feasibilityanalysis:Fromreality,theroutesofthewaterdiversionschemesdeterminedbymodelsinthisarticlearesomeroutesoftheSouth-to-northproject.AndthesolutionsofC、Fzonearecost-effectiveandpractical.Itisimpracticaltobuild990desalinatorsinBand903sewagetreatmentplantsinG.Becauseofthelowpriceoftreatedwater,sewagetreatmentplantscanonlygainprofitsafterformingacertainscale.Nowadays,mostofthedomesticsewagetreatmentplantsoperateunderthestatesupportandgrants.Soaccordingtothecurrentsewagetreatmentlevel,itisunwisetobuildmorethan900sewagetreatmentplants.SothewatershortageprobleminzoneB、FDisveryserious,anditisverydifficulttosolvethewatershortageprobleminaccordancewiththecurrentleveloftechnology.Therefore，forB、Fzone，theproblemscan’tbesolvedbytheabovemeasures.Thegovernmentshouldincreaseinvestmentindesalinationandsewagetreatment,andreduceoperatingcosts,improveproductionefficiency.Inadditiontoincreasingtheavailablefreshwater,thegovernmentalsoshouldtrytoreducethedemandforfreshwater、increasewaterprices、popularizeagriculturalirrigationdriptechnologyanddevelopnewenergytoreducedependenceonwaterresourcesandsoon.Ontheotherhand,thegovernmentshouldimprovethenationalwater-savingawareness.Ther