2016年美赛C题清华大学获奖论文

ForofficeuseonlyT1T2T3T4TeamControlNumber50193ProblemChosenCForofficeuseonlyF1F2F3F42016MCM/ICMSummarySheetAnEducationalDonationMechanismBasedOnDataInsightSummaryRecentyears,BigDatahasbecomeincreasinglypopularandtheguidanceofbigdataisrequiredinmanyfields,includingcharitablefield.Inourpaper,weconstructanewROIevaluationsystemforcharitableorganizationusingdataminingmethodstoprocessdata,andsucceedindetermininganoptimalinvestmentstrategyforGoodgrantFoundation.First,weoperateonthedata.Wedodatascreeningaccordingtotheintegrityandre-dundancyoftheinformation,deletingdatawithinformationlessthanthethreshold,andmergingdifferentattributesusinglinearfittingandPCA.Forthereservedattributesandschools,wedodataimputationtofillthemissingdatabasedonK-meansClustering.Thenwenormalizeallthedatatomakethemcomparableinthefollowinganalysis.Second,weconstructaROIevaluationcriteria,whichisaratioofoutputandinputmul-tiplyinganadjustmentcoefficient,named“urgency”.Theratioreflectsthebenefitsinrelatedtothecost,whileurgencyreflectsthedemandformoneywhichisanimportantfactorshouldbeconsideredbycharitableorganization.WeusePCAtoselectattributes,lettingsalary,educationqualityandsomeotherstorepresentoutput,tuitiontorepresentinputandFederalloan,debtandsomeotherstorepresenturgency.Then,AHPisusedtomeasuretheimportancebetweendifferentfactorsandallocateweights.Third,weputforwardtwokindsofmodel,basicmodelforoneyearandtimeseriesmodelforfiveyear.SeeingtheROIasbenefitsfrominvestment,weintroducethefluctuationofoutputas“risk”,imitatingtheconceptofModernPortfolioTheoryinthefinancialsectortosolvetheproblems.Inthebasicmodel,wedevelopaMixedIntegerLinearPro-grammingAlgorithmandsucceedinfinding14schoolsfortheinvestment.Further,weconsiderthetimefactorandimprovethemodelintoatimeseriesmodel,usingMILPandGreyPredictiontodeterminethelong-terminvestmentstrategy.16schoolsarechosenwithdifferenttimedurationanddifferentamountsofmoney.Finally,wemakesensitivityanalysisforourmodel,changingtheamountofschools,therestrictionformoney,whetherallocatingthemoneyequallyornotandsoontoanalyzethedifferentresultsoftheoutputandtofindthebetterparametersforidealresults.Tosumup,ourmodelisafeasibleandreasonablemodelwithtechnicalanddatasupport.Becauseofthesubjectivity,thismodelcanbeusedflexiblyafterdatatraining.Team#50193Page2of22Contents1Introduction31.1Background.................................31.2OverviewofOurWork...........................31.3Assumptions................................42DataProcessing52.1DataScreening...............................52.2Dataimputation...............................62.3DataNormalization.............................83ROIEvaluationSystem93.1ConceptofROI...............................93.2UsingGreyTheorytopredictROI.....................124ModelConstruction134.1DefinitionofRisk..............................144.2BasicModel.................................144.3Resultsofbasicmodel...........................154.4Timeseriesmodel..............................174.5Resultsoftimeseriesmodel........................175Sensitiveanalysisandvalidation185.1Risk-Return.................................185.2Schoolnumber...............................185.3Policyofdistribution............................196FutureWork207Conclusion217.1Strengths..................................217.2weaknesses.................................21Team#50193Page3of221Introduction1.1BackgroundIfitwereadecadeago,youwouldnotimagethatthepageviewof”Facebook”canbemorethanmillionsinoneminute;youwouldnotimagethatwhenyouopen”googlemaps”,allthetravelinformationisalreadyinthepalmofyourhand;youwouldnotimagethatthroughdataminingyoucangainaninsightintothedevelopmenttrendofanenterprisetoguideyourinvestment.Nowadaysbigdatahaspenetratedintoourworkandlives,andhasbroughtsuchhugechanges.Inturn,ithasbecomeparticularlyimportantforustofindusefulinformationfromthemassofdatatoguideourworkandlife.Asaspecialcolumnfrom”NewYorkTimes”inFeb.,2012says,BigDataErahascome.Inthecommercial,economicandotherareas,informationwillincreasinglybemadebasedondataandanalysis,ratherthanbasedonexperienceandintuition.Alsothefieldofcharityisinthesamecase.Inthepast,itismoredifficulttogivemoneyawayintelligentlythantoearnitinthefirstplace.[1]Wedonotknowhowtodothecharitablegivingrationally,thus,thecalculationofROIisalsooutofthequestion.Butnownewandfasterinformationcouldmakecharitablegivingmoreeffectiveandefficient.Moreover,itprovidesapossibilitytolinkcharitablegivingissueswiththeinvestmentissuesinthefinancialsector.ThisarticleisaboutacharitabledonationissueofuniversitiesintheU.S.Weaimtodesignameasuresystemofthereturnoninvestmentbasedonlargequantitiesofdatathroughdataminingmethods.Tosolvetheproblem,wewillusethePortfolioTheory,LinearProgramming,GreyTheoryandsomeothermethodstodeterminetheoptimalstrategyintermsofdimensionoftime.1.2OverviewofOurWorkFirst,wefindafewkeypointsinthisquestion:Thevolumeofdataislargeandofdifferenttypes.Howtodothenormalizationofthedata.Amongthemassivedata,therearemanymissingdatainthefiles,whichcontainslessinformationandnoteasytodobatchprocessing.Howtoclassifythelar