建模美赛B题.docx
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建模美赛B题.docx
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建模美赛B题
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2014
MathematicalContestinModeling(MCM/ICM)SummarySheet
(Attachacopyofthispagetoyoursolutionpaper.)
ResearchonChoosingtheBestCollegeCoachesBasedonDataEnvelopmentAnalysis
Summary
Inordertogettherankofcoachesindifferentsportsandlookforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury,inthispaper,webuildacomprehensiveevaluationmodelforchoosingthebestcollegecoachesbasedondataenvelopmentanalysis.Intheestablishedmodel,wechoosethelengthofcoachingcareer,thenumberofparticipationintheNCAAGames,andthenumberofcoachingsessionastheinputindexes,andchoosethevictoryratioofgames,thenumberofvictorysessionandthenumberofequivalentchampionastheoutputindexes.Inaddition,eachcoachisregardedasadecisionmakingunit(DMU).
Firstofall,withtheexampleofbasketballcoaches,therelativelyexcellentbasketballcoachesareevaluatedbytheestablishedmodel.ByusingLINGOsoftware,thetop5coachesareobtainedasfollows:
JoeB.Hall,JohnWooden,JohnCalipari,AdolphRuppandHankIba.
Secondly,theyear1938ischosenasatimesetaparttodividethetimelineintotwoparts.Andthen,basketballcoachesarestilltakenasanexampletoevaluatethetop5coachesusedtheconstructedmodelinthosetwoparts,respectively.Theevaluatedresultsareshownas:
DocMeanwell,FrancisSchmidt,RalphJones,E.J.Mather,HarryFisherbefore1938,andJoeB.Hall,JohnWooden,JohnCalipari,AdolphRuppandHankIbaafter1938.Theseresultsareaccordantwiththosebestcoachesthatwereuniversallyacknowledgedbypublic.Itsuggeststhatthemodelisvalidandeffective.Asaconsequence,itcanbeappliedingeneralacrossbothgendersandallpossiblesports.
Thirdly,justthesameasbasketballcoaches,footballandfieldhockeycoachesarealsostudiedbyusingthemodel.Afterthecalculation,thetop5coachesoffootball’sresultsareasfollows:
PhillipFulmer,TomOsborne,DanDevine,BobbyBowdenandPatDye,andfieldhockey’sareFredShero,MikeBabcock,ClaudeJulien,JoelQuennevilleandKenHitchcock.
Finally,althoughthetop5coachesineachof3differentsportshavebeenchosen,theabove-mentionedmodelfailedtosortthesecoaches.Therefore,thesuper-efficiencyDEAmodelisintroducedtosolvetheproblem.Thismodelnotonlycanevaluatethebettercoachesbutalsocanrankthem.Asaresult,wecanchoosethe“bestalltimecollegecoach”fromallthecoacheseasily.
Typeasummaryofyourresultsonthispage.Donotinclude
thenameofyourschool,advisor,orteammembersonthispage.
ResearchonChoosingtheBestCollegeCoachesBasedonDataEnvelopmentAnalysis
Summary
Inordertogettherankofcoachesindifferentsportsandlookforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury,inthispaper,webuildacomprehensiveevaluationmodelforchoosingthebestcollegecoachesbasedondataenvelopmentanalysis.Intheestablishedmodel,wechoosethelengthofcoachingcareer,thenumberofparticipationintheNCAAGames,andthenumberofcoachingsessionastheinputindexes,andchoosethevictoryratioofgames,thenumberofvictorysessionandthenumberofequivalentchampionastheoutputindexes.Inaddition,eachcoachisregardedasadecisionmakingunit(DMU).
Firstofall,withtheexampleofbasketballcoaches,therelativelyexcellentbasketballcoachesareevaluatedbytheestablishedmodel.ByusingLINGOsoftware,thetop5coachesareobtainedasfollows:
JoeB.Hall,JohnWooden,JohnCalipari,AdolphRuppandHankIba.
Secondly,theyear1938ischosenasatimesetaparttodividethetimelineintotwoparts.Andthen,basketballcoachesarestilltakenasanexampletoevaluatethetop5coachesusedtheconstructedmodelinthosetwoparts,respectively.Theevaluatedresultsareshownas:
DocMeanwell,FrancisSchmidt,RalphJones,E.J.Mather,HarryFisherbefore1938,andJoeB.Hall,JohnWooden,JohnCalipari,AdolphRuppandHankIbaafter1938.Theseresultsareaccordantwiththosebestcoachesthatwereuniversallyacknowledgedbypublic.Itsuggeststhatthemodelisvalidandeffective.Asaconsequence,itcanbeappliedingeneralacrossbothgendersandallpossiblesports.
Thirdly,justthesameasbasketballcoaches,footballandfieldhockeycoachesarealsostudiedbyusingthemodel.Afterthecalculation,thetop5coachesoffootball’sresultsareasfollows:
PhillipFulmer,TomOsborne,DanDevine,BobbyBowdenandPatDye,andfieldhockey’sareFredShero,MikeBabcock,ClaudeJulien,JoelQuennevilleandKenHitchcock.
Finally,althoughthetop5coachesineachof3differentsportshavebeenchosen,theabove-mentionedmodelfailedtosortthesecoaches.Therefore,thesuper-efficiencyDEAmodelisintroducedtosolvetheproblem.Thismodelnotonlycanevaluatethebettercoachesbutalsocanrankthem.Asaresult,wecanchoosethe“bestalltimecollegecoach”fromallthecoacheseasily.
Keywords:
collegecoach;dataenvelopmentanalysis;decisionmakingunit;comprehensiveevaluation
Contents
1.Introduction...................................................................................................................................................4
2.TheDescriptionofProblem….............................................................................................................4
3.Models……………...........................................................................................................................................5
3.1SymbolsandDefinitions………………………………..…...……………………………........5
3.2GeneralAssumptions……………………………………………………………….……..…....6
3.3AnalysisoftheProblem…………………………………………………………………........6
3.4TheFoundationofModel……………………………………………………………….…..6
3.5SolutionandResult……………………………………………….………………………..............................8
3.6sensitivityanalysis………………………………………………….…………….…...............17
3.7AnalysisoftheResult...................................................................................19
3.8StrengthandWeakness……………………………………..………………………...................................19
4.ImprovedModel.......................................................................................................................................20
4.1super-efficiencyDEAmodel…………………………………...……………………................20
4.2SolutionandResult…………………………………………………..………………..…...............21
4.3StrengthandWeakness…………………………………………………..………………..….........25
5.Conclusions...................................................................................................................................................25
5.1Conclusionsoftheproblem…………………………………………………………………....,.25
5.2Methodsusedinourmodels………………………………………………………..……….......26
5.3Applicationsofourmodels………………………………………..…………….........................26
6.ThearticleforSportsIllustrated...................................................................................................26
7.References......................................................................................................................................................28
I.Introduction
Atpresent,thescientificevaluationindexsystemsrelatedtocollegecoachabilitiesarelimited,andtheevaluationofcoachabilitiesaremostlydeterminedbythesportsteams’gameresults,anditlacksofsystematic,scientificandaccurateevaluationwithlargesubjectivityandone-sidedness,thusitcannotobjectivelyreflecttheactualtraininglevelofcoaches.Inrecentyears,thereappearmanynewperformanceevaluationmethods,whichmostlyconsidertheintegrityoftheevaluationsystem.Thustheyovercomealotofweaknessesthatpurelybasedontheevaluationofgameresults.However,itisfollowedbythecomplexityofevaluationprocessandindexsystem,aswellasthegreatincreaseoftheimplementationcost.Dataenvelopmentanalysisisanon-parametrictechniqueforevaluatingtherelativeefficiencyofasetofhomogeneousdecision-makingunits(DMUs)withmultipleinputsandmultipleoutputsbyusingaratiooftheweightedsumofoutputstotheweightedsumofinputs.Therefore,itnotonlysimplifiesthenumberofindexes,butalsoavoidstheinterferenceofsubjectiveconsciousness,thusmakestheevaluationsystemmorejustandscientific.
BasedontheinvestigationandresearchoftheUScollegebasketballcoachforthepreviouscentury,thispaperaimsatestablishingascientificandobjectiveevaluationindexsystemtoassesstheircoachingabilitiescomprehensively.Itprovidesreferencefortherelatingsportsmanagementdepartmenttoevaluatecoachesandcontinuouslyoptimizetheircoachingabilities.Forthispurpose,theDEAissuccessfullyintroducedintothisarticletoestablishacomprehensiveevaluationmodelforchoosingthebestcollegecoaches.Itmakestheassessmentofthecoachesindifferenttimelinehorizon,differentgenderanddifferentsportstotestifythevalidityandtheeffectivenessofthisapproach.
II.TheDescriptionoftheProblem
Inordertofindoutthe“bestalltimecollegecoach”forthepreviouscentury,acomprehensiveevaluationmodelisneededtosetup.Therefore,asetofscientificandobjectiveevaluationindexsystemshouldbeestablished,whichshouldmeetthefollowingprinciplesorrequirements:
Theprincipleofsufficiencyandcomprehensiveness
Theindexsystem
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