最新美赛格式参考summary sheet精品名师资料.docx

最新美赛格式参考summary sheet精品名师资料.docx

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最新美赛格式参考summarysheet精品名师资料

最新美赛格式参考（summarysheet）精品名师资料

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2011MathematicalContestinModeling（MCM）SummarySheet

AssessingtheProspectsofElectricVehicles

Summary

Withthegrowingscarcityofpetroleumthroughouttheworld,increasedconcernovertheenvironmentalimpactofthepetroleum-basedtransportationinfrastructurehasledtogreatinterestinanelectrictransportationinfrastructure.Butuncertaintyinhowenvironmentallyandeconomicallysoundareelectricvehiclesstillexists,andthattheirwidespreaduseisfeasibleandpracticalisstilluncertain.Ourpaperaimstoquantifytheeffectsoftheelectricvehiclesontheenvironment,society,economy,health,andmodeltheamountandthetypeofelectricitygenerationtogetthemostbenefitstotheenvironment,society,business,andindividuals.

InModel1,weestablishanevaluationmodelnamedAnalyticHierarchyProcess（AHP）tocomparetheenvironmental,social,economic,andhealthimpactsofelectriccarsandfuelcarsquantitatively.Therearefourparameters,includingenergyconsumption,thegreenhouseeffect,emissionsofharmfulsubstancesandnoisepollution,whichinfluencetheenvironment.Ofcourse,weconductthesimilarworktoanalyzetheinfluentialparametersofsociety,economyandhealth.Intermoftheweights,weconcludethatingeneralelectriccarsarebetterthanfuelcars.

InModel2,usingdata,weadoptlogisticregressiontopredicttheproportionofelectricvehiclesinthefutureonthreepremiseswhichincludethebaselineoilprice,thehighoilpriceandOperator-Subsidizedpremise.Astimegoes,theproportionofelectricvehiclesisincreasinglybiggerandtheamountofenergysavingsisincreasinglybigger.By2030,theproportionofelectricvehiclesinautomarketis86%.Thenusethesamemodeltoconcludethattheamountofoilsavingislarge.

Similarly,weconcludethattheamountofelectricitygenerationisalsoincreasingwithtimegoing.

InModel3,weestablishafunctiontoexpressthetotalbenefitsthatenvironment,society,businessandindividualscanget.Certainly,indifferentcircumstancesandareas,thechoiceofthetypeofelectricitygenerationwilldiffer.Sowediscussunderseveralcircumstanceshowthefunctionwillchange.

Keywords:

AnalyticHierarchyProcess（AHP）Logisticregression

Content

1.Introduction..............................................................................................................................................2

2.Models……………........................................................................................................................................2

2.1Model.

..................................................................................................................................................2

2.1.1TheintroductionofAHP………………………………..…...…………………………….....3

2.1.2Assumptions……………………………………………………………….……..……………….4

2.1.3TheFoundationofModel…………………………………………………………………….4

2.1.4SolutionandResult……………………………………………………………….……….........10

2.1.5AnalysisoftheResult……………………………………………….………………………..……….………10

2.2Model

………………………………………………….…………….……………………………….11

2.2.1Forecastthepenetrationratesofelectricvehicles...........................................12

2.2.2AdditionalAssumptions………………………………………………...…..………………………………..132.2.3Theimpactsofwidespreaduseofelectricvehicle…………………………13

2.2.4Summary…………………………………………………………………………………………………………..14

AnalysisoftheResult……………………………………………………..16

2.3Model

………………………………………………………………………17

3.ConclusionsandDiscussions………..……………………………………………………………17

3.1Conclusionsoftheproblem……………………………………..……………..18

3.2StrengthsandWeakness……………………………………….....……………………..…………18

3.3FutureWork…………………………………………………..…………………………………..….18

4.References...................................................................................................................................................18

I.Introduction

Theimprovementsinbatterytechnologyoverthepasttwodecades,inparticulartheadvancesinLithium-ion（Li-ion）batterytechnologyaswellasautomotivetechnologicaladvancesusheredinbyhybridvehicles,havemadeitpossibletodesignandmanufactureelectricvehicleswithbetterperformancethantheirgasoline-poweredcounterparts.Since2003,whentheToyotaPriuswasthefirstmass-producedhybridgasoline-electriccarandintroducedworldwide,andG-Wizelectriccarbecametheworld'sbestsellingEV,electricvehicleshasdevelopedrapidly.TheNissanLeafwasdebutedinDecember2010andothermajorautocompanieshaveelectriccarsindevelopment.Meanwhilevariousnationsaroundtheworldarebuildingpilotnetworksofchargingstationstorechargethem.

Thoughtheprospectofelectricvehiclesissplendidaccordingtomarketanalysts,governmentsandmanufacturers,electricvehiclesshareaminimal proportionofautomarketandthehistoricaldataofthemaboutproductiononwhichtocalculateispoor.Andnowadaysheavyandlong-rangetransportationandshippingishardtoachievetechnically.Inordertoassesstheprospectofelectricvehicles,wechooseelectriccars,especiallyinAmerica,asatypicalparametertoextrapolatetheeffectsofelectricvehicles.

Electricvehicleshavevariousadvantageswhichcanreducegasconsumption,weakenthegreenhouseeffect,protectenvironmentandsoon.However,peopledon’tknowwhetherthewidespreaduseofelectricvehiclesactuallysavefossilfuelsorwemerelybetradingoneuseoffossilfuelforanothergiventhatelectricityiscurrentlymostlyproducedbyburningfossilfuels.Peopledon’tanalyzewhetherornottheneededgrowthofthesealternatesourcesofelectricityislikelyandpossible.

Ourpaperaimstoassesstheimpactsofelectriccarsonenvironment,society,economyandhealth,and,intermsofdata,predicttheproportionofelectricvehiclesintheU.S.inthefuture.Meantime,promotethepredictionmodeltoestimatetheamountofoiltheworldwouldsavebywidelyusingelectriccars.Then,establishingamodeloftheamountandtypeofelectricitygenerationtoproducethelargestnumberofbenefitsoftheenvironment,society,businessandindividuals.

II.Models

2.1Model

Thereisasystematicmethodforcomparingalistofobjectivesoralternatives.Whenusedinthesystemsassessingprocess,AHPcanbeapowerfultoolforcomparingalternativedesignconcepts

Soweconsidertheaspectsofsociety,economy,environmentandhealthasobjectives,andthatwearetryingtoestablishanormalizedsetofweightstobeusedwhencomparingalternativesusingtheseobjectives.Welistthefactorswhichinvolveinsociety,environment,economyandhealth.

2.1.1TheintroductionofAHP

Stepsofdeterminingtheweighs:

1）Formapair-wisecomparisonmatrixA,wherethenumberintheithrowandjthcolumngivestherelativeimportanceofOiascomparedwithOj.

Usea1–9scale,with

–aij=1ifthetwoobjectivesareequalinimportance

–aij=3ifOiisweaklymoreimportantthanOj

–aij=5ifOiisstronglymoreimportantthanOj

–aij=7ifOiisverystronglymoreimportantthanOj

–aij=9ifOiisabsolutelymoreimportantthanOj

2）Thuswemightarriveatthefollowingmatrix:

3）Tonormalizetheweights,computethesumofeachcolumnandthendivideeachcolumnbythecorrespondingsum

4）Usinganoverbartodenotenormalization

5）ThenextstepistocomputetheaveragevaluesofeachrowandusetheseastheweightsintheObjectiveHierarchy.

6）Thenwecangettheweights.TheseweightswouldbeusedinsummingthemeasuresasrequiredintheevaluationoftheObjectiveHierarchy

Notes:

1）

2）Themaximumeigenvalue,λmaxofAisapositiverealnumber.

TheoperatingstepsofAHPconsistencycheck:

1.ComputetheConsistentIndex:

.

2.Find thecorresponding averagerandomIndex:

Table1TheAHPIndexTable

theorderofthematrix

1

2

3

4

5

6

R.I.

0

0

0.52

0.89

1.12

1.26

theorderofthematrix

7

8

9

10

11

12

R.I.

1.36

1.41

1.46

1.49

1.52

1.54

3.ComputetheConsistentRadio:

When

wecanconsiderComparisonMatrixasAcceptable consistency.

2.1.2Assumptions

●Electricvehicles andfuel vehicles arein astateof widelyused

●All electricvehicles andall fuelvehicles havesimilar properties

●Electricvehicleshavesimilarperformance,andfuelcarshavesimilarperformance.

2.1.3TheFoundationofModel

1）Wepassedthereferencepreviousstudiesandpapers,judgingthatweshouldestablishanAHPmodeltoreflecttheeffectsonenvironment,society,economyandhealthwhentheelectricvehiclesarewidelyused.So,inthismodel,weregardrespectivelyenvironment,society,economyandhealthasobjectives.Inaddition,weanalyzeandlisttherelateelementsaccordingtotheobjectivesasfollows.

Figure1EnvironmentHierarchical Structure

Accordingto thedata andinformation  wecangain theimpactofeachofthese factorsonenvironment,andgive theabovefactors theorderofsignificance.

A1>A3>A2>A4

Accordingtotheimportance,wecangetComparisonMatrixO1-A.

Table2ComparisonMatrixO1-A

O1

A1

A2

A3

A4

ω11

λmax=4.1145

C.I.=0.0382

C.R.=0.0429

A1

1

4

2

5

0.4869

A2

1/4

1

1/3

3

0.1395

A3

1/2

3

1

4

0.3031

A4

1/5

1/3

1/4

1

0.0705

Accordingto thedata andinformation （from）,wegetsomeresultsasfollows:

Forthe criteria ofthe A1, weget value3indicatingthatelectricvehicles is