航空公司的售票营销策略

应用统计学案例3，学时：36小时，案例规模：中类型：选编来源：StatisticsForBusinessAndEconomics,DavidR.AndersonSouth-WesternThomsonLearning,1998Estimatingthechancesof“Noshows”andIsOverbookingWorthit?TransamericanAirlineshasopenedanewdailyflightfromChicagotoBoise,Idaho.Itissopopularthatits75seatshaveallbeenreservedinitsfirst20flightsUnfortunately,ineachflightsomeofthepassengersfailedtoshowup.Sothattheplaneleftwithsomeemptyseatsandlostrevenue.Thenumberof“noshows”variedfrom2onthebestflightto11ontheworstflight.Herearethedetails:Numberof“NoShows”xFrequency234567891011140425110220FlightsToreducethenumberofemptyseats,theairlinecansellmorethan75reservations,ofcourse.Butthatintroducesanewriskofoverbooking,ifmorethan75peopleshowupwithreservations.Inordertoproperlybalanceitsrisks,theairlineneedstoestimatethechancesofvariousnoshows”.Wethereforeimaginecollectingdataformanyflights(undersimilarconditions)sothattherelativefrequencieswouldsettledowntoprobabilitiesp(x).Letusestimateoneoftheseprobabilities-forexample,thechanceofexactly3“noshows”,p(3).a.Toestimatethislong-runrelativefrequencyp(3).Theshortrunrelativefrequencyinthetableaboveis4/20=0.20.Doyouthinkthisestimateistoohigh,ortoolow?Why?b.GraphtherelativefrequencydistributionofXfromthetableabove.Sketchasmoothcurvethroughit-acrudeprobabilityofp(3)?c.Foramorerefinedmodel,letpdenotetheproportionofpassengerwhoare“noshows”,Thenassumethataflightconsistsofn=75randomlychosenpassengers.SothatXhasbinomialdistribution.Toestimatep.howmanypassengersweretherealtogetherinthe20flights?Andhowmany“noshows”?Sowhatisyourestimateofp?d.Nowestimatep(3)usingthebinomialdistribution.Graphitalongsideyouotherestimatesforcomparison.e.Transamericanthereforeplannedto“overbook”,makingreservationsforn=78passengers.Assumingtheyformarandomsamplefromthewholepopulationofpassengers,whatischanceofanoverloadcrisis,thatis,morethan75actuallyshowingupfortheflight?f.Transamericanalsoconsideredtheriskierplanofmakingreservationsforn=80passengers.Usingthebinomialformula,acomputerprintedoutthefollowingscheduleofhowmanypassengerswouldshowup(y):yP(y)yP(y)8079787776capacity75740.000.010.030.070.110.150.17737271706968670.150.120.080.050.030.020.01Nowwhatisthechanceofanoverloadcrisis?g.Todeterminewhethertheoverbookinginbwasworthit,variouscostshavetobeconsidered.Thesimplestcoststoquotearetheconceptuallossesinrevenue,incurredbyfailingtoachievetheopportunityofaplaneideallyloadedwithexactlyy=75passengersshowingup.Called“OpportunityLosses”inmanagementscience,theyarethesameideaas“OpportunityCosts”ineconomics.OpportunityLosses:i.Ify75,eachemptyseatcosts$200inlostrevenue.ii.Ify75,eachextrapassengerwhogetsturnedawaycosts$400,becauseofa“doubleyourmoneyback”guarantee.Whatistheexpectedopportunityloss(EOL)forbookingn=80?h.WhatistheEOLfortheconservativebookingn=75?(Hint,Whatistheexpectednumberwhodon,tshow?Howmuchdoeseachcost?)i.Whichisthebetterpolicy,bookingn=75orn=80?Overthe365flightsinayear,abouthowmuchwouldtheygainfromusingthebetterpolicy(insteadoftheother)?*j.UsingMinitaborsimilarsoftwear,verifythatthebetterpolicyiniisverybestofall.(HintForn=80,usetheBINOMIALorPDFcommandtogeneratethetablegiveninb.Alsotabulatetheopportunitylosses,soyoucanfinallycomputetheEOLforn=80,andsoverifyyouranswertog.Nowitiseasytorepeatthis.forn=79.thenn=78,etc,toverifythereisnobettern.)