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1、BumpingforDollars:TheAirlineOverbookingProblem351BumpingforDollars:TheAirlineOverbookingProblemJohnD.BowmanCoreyR.HoumardAdamS.DickeyWakeForestUniversityWinston-Salem,NCAdvisor:FrederickH.ChenIntroductionWeconstructamodelthatexpressestheexpectedreven
2、ueforaflightintermsofthenumberofreservations,thecapacityoftheplane,thepriceofaticket,thevalueofavoucher,andtheprobabilityofapersonshowingupfortheflight.Whenvaluesaresuppliedforeveryvariablebutthefirst,thefunctioncanbemaximizedtoyieldanoptimalbookingthat
3、maximizesexpectedrevenue.Weapplythemodeltothreesituations:asingleflight,twoflightsinachainofflights,andmultipleflightsinachainofflights.Weconcludethatfewerflightswillincreasethevalueofthepenaltyorvoucherandthusdecreasetheoptimalnumberofreservations.Heighte
4、nedsecurityalsolowerstheoptimalnumberofreservations.Anincreaseinpassengers’feardecreasestheprob-abilitythatapersonwillshowupforaflightandthusincreasestheoptimalnumberofreservations.Finally,thelossofbillionsofdollarinrevenuehasnoeffectontheoptimalvalue
5、ofreservations.Wemodeltheprobabilityofagivennumberofpeopleshowingupasabinomialdistribution.Weexpresstheaverageexpectedrevenueofaflightintermsofthenumberofbookingsmade.StartingwiththeSingle-Flightcase,wederiveamodelandrevenuefunctionforaflightunaffected
6、bypreviousflights.Fromthissituation,weexpandthemodeltotheTwo-Flightcase,inwhichtheearlierflightaffectsthenumberofpeoplewhoshowupforthelaterflight.Wegeneralizethemodelevenfurthertothenumberofpeopleshowingupdependingonmanypreviousflights.TheUMAPJournal351–
7、365.cCopyright2002byCOMAP,Inc.Allrightsreserved.Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abs
8、tractingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.352TheUMAPJournal23.3(2002)TheModelIneachoftheth
