962012年美国高中生数学建模竞赛特等奖论文

1题目：HowMuchGasShouldIBuyThisWeek?题目来源：2012年第十五届美国高中生数学建模竞赛（HiMCM）B题获奖等级：特等奖，并授予INFORMS奖论文作者：深圳中学2014届毕业生李依琛、王喆沛、林桂兴、李卓尔指导老师：深圳中学张文涛AbstractGasolineisthebleedthatsurgesincessantlywithinthemusculargroundofcity;gasolineisthefeastthatlurestheappetiteofdrivers.“Tofillornotfill?”Thatisthequestionflusteringthousandsofcarowners.Thispaperwillguideyoutopredictthegasolinepricesofthecomingweekwiththecurrentlyavailabledatawithrespecttoswiftchangesofoilprices.Doyouholdanyinterestinwhatpatternoffillingupthegastankcanleadtoalowercostintotal?ByapplyingtheTimeseriesanalysismethod,thispaperinfersthepriceintheimminentweek.Furthermore,weinnovativelyutilizetheaveragepricesofthecontinuoustwoweekstopredictthenexttwoweek’saverageprice;similarly,employthefour-week-longaveragepricestoforecasttheaveragepriceoffourweekslater.Byadoptingthedataobtainedfrom2011andthecomparisonindifferentaspects,wecanobtainthegaspricepredictionmodel：𝐺𝑡+1=0.0398+1.6002𝑔𝑡+−0.7842𝑔𝑡−1+0.1207𝑔𝑡−2+0.4147𝑔𝑡−0.5107𝑔𝑡−1+0.1703𝑔𝑡−2+𝜀.Thispredictedresultof2012accordingtothismodelisfairlyideal.Basedonthepredictionmodel,Wealsoestablishthemodelforhowtofillgasoline.Withthesemodels,wehadcalculatedthelowestcostoffillingupin2012whentraveling100milesaweekis637.24dollarswiththehelpofMATLAB,whilethelowestcostwhentraveling200milesaweekis1283.5dollars.Thesetwovaluesareveryclosetotheidealvalueofcostonthebasisofthehistoricalfigure,whichare635.24dollarsand1253.5dollarsrespectively.Also,wehavecomeupwiththeschemeofgasfulfillmentrespectively.Byanalyzingtheschemesofgasfilling,wecandiscoverthatwhenyoupredictthefuturegasolinepricegoingup,thebeststrategyistofillthetankassoonaspossible,inordertolowerthegasfare.Onthecontrary,whenthepredictedpricetendstodecrease,itiswiserandmoreeconomicforpeopletopostponethefilling,whichencouragespeopletopurchaseahalftankofgasolineonlyifthetankisalmostempty.Forotherdifferentpatternforeveryweek’s“mileagedriven”,wecalculatethechangingpointofstrategies-changedis133.33miles.Eventually,wewillapplythemodels-totheanalysisoftheNewYorkCity.Theresultofpredictionisgoodenoughtomatchtheactualdataapproximately.However,thetotalgascostofNewYorkisalittlehigherthanthatoftheaveragecostnationally,whichmightberelatedtothehigherconsumerpriceindexinthecity.Duetothelimitoftime,wearenotabletoinvestigatefurthertheparticularfactors.Keywords:gasolinepriceTimeseriesanalysisforecastlowestcostMATLAB2CatalogueAbstract---------------------------------------------------------------------------------------1Restatement--------------------------------------------------------------------------------------21.Assumption----------------------------------------------------------------------------------42.DefinitionsofVariablesandModels-----------------------------------------------------42.1Modelsforthepredictionofgasolinepriceinthesubsequentweek------------42.2TheModelofoilpricenexttwoweeksandfourweeks--------------------------52.3Modelforrefueldecision-------------------------------------------------------------52.3.1DecisionModelforconsumerwhodrives100milesperweek-------------62.3.2DecisionModelforconsumerwhodrives200milesperweek-------------73.TrainandTestModelby2011dataset---------------------------------------------------83.1DeterminethealltheparametersinEquation②fromthe2011dataset-------83.2TesttheForecastModelofgasolinepricebythedatasetofgasolinepricein2012-------------------------------------------------------------------------------------103.3Calculating𝜀--------------------------------------------------------------------------123.4TestDecisionModelsofbuyinggasolinebydatasetof2012-------------------143.4.1100milesperweek---------------------------------------------------------------143.4.2200milesperweek---------------------------------------------------------------143.4.3SecondTestfortheDecisionofbuyinggasoline-----------------------------154.TheupperboundwillchangetheDecisionofbuyinggasoline---------------------155.AnanalysisofNewYorkCity-----------------------------------------------------------165.1ThemainfactorthatwillaffectthegasolinepriceinNewYorkCity----------165.2TestModelswithNewYorkdata----------------------------------------------------185.3Theanalysisofresult------------------------------------------------------------------196.Summery&Advantageanddisadvantage-----------------------------------------------197.Report----------------------------------------------------------------------------------------208.Appendix------------------------------------------------------------------------------------21Appendix1(mainMATLABprograms)------------------------------------------------21Appendix2(outcomeandgraph)--------------------------------------------------------343RestatementTheworldmarketisfluctuatingswiftlynow.Asthemostimportantlimitedenergy,oilismuchaccountedofcarsownersanddealer.Wearerequiredtomakeagas-buyingplanwhichrelatestothepriceofgasoline,thevolumeoftank,thedistancethatconsumerdrivesperweek,thedatafromEIAandtheinfluenceofothereventsinordertohelpdriverstosav