RevenueManagement

andDynamicPricing:

PartIE.AndrewBoydChiefScientistandSeniorVP,ScienceandResearchPROSRevenueManagementaboyd@OutlineConceptExampleComponentsReal-TimeTransactionProcessingExtracting,Transforming,andLoadingDataForecastingOptimizationDecisionSupportNon-TraditionalApplicationsFurtherReadingandSpecialInterestGroupsRevenueManagement

andDynamicPricingRevenueManagementinConceptWhatisRevenueManagement?BeganintheairlineindustrySeatsonanaircraftdividedintodifferentproductsbasedondifferentrestrictions$1000Yclassproduct:canbepurchasedatanytime,norestrictions,fullyrefundable$200Qclassproduct:Requires3weekadvancedpurchase,Saturdaynightstay,penaltiesforchangingticketafterpurchaseQuestion:Howmuchinventorytomakeavailableineachclassateachpointinthesalescycle?WhatisRevenueManagement?RevenueManagement:ThescienceofmaximizingprofitsthroughmarketdemandforecastingandthemathematicaloptimizationofpricingandinventoryRelatednames:YieldManagement(original)RevenueOptimizationDemandManagementDemandChainManagementRudimentsStrategic/Tactical:MarketingMarketsegmentationProductdefinitionPricingframeworkDistributionstrategyOperational:RevenueManagementForecastingdemandbywillingness-to-payDynamicchangestopriceandavailableinventoryIndustryPopularityWasbornofabusinessproblemandspeakstoabusinessproblemAddressestherevenuesideoftheequation,notthecostside2–10%revenueimprovementscommonIndustryAccolades“Nowwecanbealotsmarter.Revenuemanagementisallofourprofit,andmore.” BillBrunger,VicePresidentContinentalAirlines“PROSproductshavebeenakeyfactorinSouthwest'sprofitperformance.”KeithTaylor,VicePresidentSouthwestAirlinesAnalystAccolades“RevenuePricingOptimizationrepresentthenextwaveofsoftwareascompaniesseektoleveragetheirERPandCRMsolutions.”–ScottPhillips,MerrillLynch“Oneofthemostexcitinginevitabilitiesaheadis‘yieldmanagement.’”–BobAustrian,BancofAmericaSecurities“RevenueOptimizationwillbecomeacompetitivestrategyinnearlyallindustries.”–AMRResearchAcademicAccolades“Anareaofparticularinteresttooperationsresearchexpertstoday,accordingtoTrick,isrevenuemanagement.”InformationWeek,July12,2002.Dr.TrickisaProfessoratCMU

andPresidentofINFORMS.AcademicAccoladesAswemoveintoanewmillennium,dynamicpricinghasbecometherule.“Yieldmanagement,”saysMr.Varian,“iswhereit’sat.”“ToHalVarianthePriceisAlwaysRight,”strategy+business,Q12000.Dr.VarianisDeanoftheSchoolofInformationManagementandSystemsatUCBerkeley,andwasrecentlynamedoneofthe25mostinfluentialpeopleineBusinessbyBusinessWeek(May14,2001)ApplicationAreasTraditionalAirlineHotelExtendedStayHotelCarRentalRailTourOperatorsCargoCruiseNon-TraditionalEnergyBroadcastHealthcareManufacturingApparelRestaurantsGolfMore…DynamicPricingThedistinctionbetweenrevenuemanagementanddynamicpricingisnotaltogetherclearArefareclassesdifferentproducts,ordifferentpricesforthesameproduct?RevenuemanagementtendstofocusoninventoryavailabilityratherthanpriceRealityisthatrevenuemanagementanddynamicpricingareinextricablylinkedTraditionalRevenueManagementNon-traditionalrevenuemanagementanddynamicpricingapplicationareashavenotevolvedtothepointofstandardindustrypracticesTraditionalrevenuemanagementhas,andwefocusprimarilyontraditionalapplicationsinthispresentationRevenueManagement

andDynamicPricingManagingAirlineInventoryAirlineInventoryAmid-sizecarriermighthave1000dailydepartureswithanaverageof200seatsperflightlegEWRSEALAXIAHATLORDAirlineInventory200seatsperflightleg200x1000=200,000seatspernetworkday365networkdaysmaintainedininventory365x200,000=73millionseatsininventoryatanygiventimeThemechanicsofmanagingfinalinventoryrepresentsachallengesimplyduetovolumeAirlineInventoryRevenuemanagementprovidesanalyticalcapabilitiesthatdriverevenuemaximizingdecisionsonwhatinventoryshouldbesoldandatwhatpriceForecastingtodeterminedemandanditswillingness-to-payEstablishinganoptimalmixoffareproductsFareProductMixShoulda$1200SEA-IAH-ATLMclassitinerarybeavailable?A$2000Yclassitinerary?EWRSEALAXIAHATLORDFareProductMixShoulda$600IAH-ATL-EWRBclassitinerarybeavailable?An$800Mclassitinerary?EWRSEALAXIAHATLORDFareProductMixOptimizationputsinplaceinventorycontrolsthatallowthehighestpayingcollectionofcustomerstobechosenWhenitmakeseconomicsense,fareclasseswillbeclosedsoastosaveroomforhigherpayingcustomersthatareyettocomeRevenueManagement

andDynamicPricingComponentsTheReal-TimeTransactionProcessorRealTimeTransactionProcessor(RESSystem)RequestsforInventoryTheRevenueManagementSystemRevenueManagementSystemForecastingOptimizationExtract,Transform,andLoadTransactionDataRealTimeTransactionProcessor(RESSystem)RequestsforInventoryAnalystsRevenueManagementSystemForecastingOptimizationExtract,Transform,andLoadTransactionDataRealTimeTransactionProcessor(RESSystem)RequestsforInventoryAnalystDecisionSupportTheRevenueManagementProcessRevenueManagementSystemForecastingOptimizationExtract,Transform,andLoadTransactionDataRealTimeTransactionProcessor(RESSystem)RequestsforInventoryAnalystDecisionSupportReal-TimeTransactionProcessorTheoptimizationparametersrequiredbythereal-timetransactionprocessorandsuppliedbytherevenuemanagementsystemconstitutetheinventory

control

mechanismReal-TimeTransactionProcessorDFWEWRYAvailMAvailBAvailQAvail11060200DFW-EWR:$1000Y$650M$450B$300QReal-TimeTransactionProcessorNestedleg/classavailabilityisthepredominantinventorycontrolmechanismintheairlineindustryDFWEWRYAvailMAvailBAvailQAvail11060200DFW-EWR:$1000Y$650M$450B$300QMClassBooking10959Real-TimeTransactionProcessorAfareclassmustbeopenonbothflightlegsifthefareclassistobeopenonthetwo-legitinerarySATDFWEWRYClassMClassBClassQClass501000YClassMClassBClassQClass11060200Extract,Transform,andLoadTransactionDataComplicationsVolumePerformancerequirementsNewproductsModifiedproductsPurchasemodificationsExtract,Transform,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?Smallnumbers/levelofdetailUnobserveddemandandunconstrainingElementsofdemand:purchases,cancellations,noshows,goshowsDemandmodel…theprocessbywhichconsumersmakeproductdecisionsDemandcorrelationanddistributionalassumptionsSeasonalityDemandModelsandForecastingHolidaysandrecurringeventsSpecialeventsPromotionsandmajorpriceinitiativesCompetitiveactionsOptimizationOptimizationissuesConvertibleinventoryMovableinventory/capacitymodificationsOverbooking/oversaleofphysicalinventoryUpgrade/upwardsubstitutableinventoryProductmix/competitionforresources/networkeffectsDecisionSupportRevenueManagement

andDynamicPricingNon-TraditionalApplicationsTwoNon-TraditionalApplicationsBroadcastBusinessprocessessurroundingthepurchaseandfulfillmentofadvertisingtimerequiremodificationoftraditionalrevenuemanagementmodelsHealthcareBusinessprocessessurroundingpatientadmissionsrequirere-conceptualizationoftherevenuemanagementprocessNewAreasContractsandlongtermcommitmentsofinventoryCustomerlevelrevenuemanagementIntegratingsalesandinventorymanagementAlliancesandcooperativeagreementsRevenueManagement

andDynamicPricingFurtherReadingandSpecialInterestGroupsFurtherReadingForanentrypointintotraditionalrevenuemanagementJefferyMcGillandGarrettvanRyzin,“RevenueManagement:ResearchOverviewandProspects,”TransportationScience,33(2),1999E.AndrewBoydandIoanaBilegan,“RevenueManagementande-Commerce,”underreview,2002SpecialInterestGroupsINFORMSRevenueManagementSection/Pages/MAIN.htmAnnualmeetingheldinJuneatColumbiaUniversityAGIFORSReservationsandYieldManagementStudyGroup

FollowlinktoStudyGroupsAnnualmeetingheldintheSpringRevenueManagement

andDynamicPricing:

PartIIE.AndrewBoydChiefScientistandSeniorVP,ScienceandResearchPROSRevenueManagementaboyd@OutlineSingleFlightLegLeg/ClassControlBidPriceControlNetwork(O&D)ControlControlMechanismsModelsRevenueManagement

andDynamicPricingSingleFlightLegLeg/ClassControlDFWEWRYAvailMAvailBAvailQAvail11060200DFW-EWR:$1000Y$650M$450B$300QAtafixedpointintime,whataretheoptimalnestedinventoryavailabilitylimits?AMathematicalModelGiven:FareforeachfareclassDistributionoftotaldemand-to-comebyclassDemandassumedindependentDetermine:OptimalnestedbookinglimitsNote:Cancellationstypicallytreatedthroughseparateoptimizationmodeltodetermineoverbooking

levelsAMathematicalModelWheninventoryispartitionedratherthannested,thesolutionissimplePartitioninventorysothattheexpectedmarginalrevenuegeneratedofthelastseatassignedtoeachfareclassisequal(forsufficientlyprofitablefareclasses)AMathematicalModelNestedinventorymakestheproblemsignificantlymoredifficultduetothefactthatdemandforonefareclassimpactstheavailabilityforotherfareclassesTheproblemisill-posedwithoutmakingexplicitassumptionsaboutarrivalorderEarlymodelsassumedlow-before-highfareclassarrivalsAMathematicalModelThereexistsasubstantialbodyofliteratureonmethodsforgeneratingoptimalnestedbookingclasslimitsMathematicsbasicallyconsistsofworkingthroughthedetailsofconditioningonthenumberofarrivalsinthelowervaluefareclassesAnheuristicknownasEMSRbthatmimicstheoptimalmethodshascometodominateinpracticeAnAlternativeModelThelow-before-higharrivalassumptionwasaddressedbyassumingdemandarrivesbyfareclassaccordingtoindependentstochasticprocesses(typicallynon-homogeneousPoisson)Sincemanypractitionersconceptualizedemandas

totaldemand-to-come,modelsbasedonstochasticprocessesfrequentlycauseconfusionALegDPFormulationWithPoissonarrivals,anaturalsolutionmethodologyisdynamicprogrammingStagespace:timepriortodepartureStatespacewithineachstage:numberofbookingsStatetransitionscorrespondtoeventssuchasarrivalsandcancellations…TT-1T-2T-310nn+1n+2n+3…SeatsRemainingTimetoDepartureCancellationNoEvent/RejectedArrivalAcceptedArrival………………ALegDPFormulationV(t,n):Expectedreturninstaget,staten

whenmakingoptimaldecisionsV(t,n)=maxu[p0(0+V(t-1,n)) Noevent

(1-p0)

c(0+V(t-1,n-1))+ Cancel

(1-p0)

(fi<u)

i(0+V(t-1,n))

Arrival/Reject

(1-p0)

(fiu)

i(fi+V(t-1,n+1))] Arrival/Acceptu(t,n):Optimalpricepointformaking accept/rejectdecisionswheneventin

staget,statenisabookingrequestALegDPFormulationDPhastheinterestingcharacteristicthatitcalculatesV(t,n)forall(t,n)pairsProvidesvaluableinformationfordecisionmakingPresentscomputationalchallengesThisnaturallysuggestsanalternativecontrolmechanismtonestedfareclassavailabilityBidpricecontrol882591639492847884768473200……8823916194908820915891878817200………nn+1n+2n+3SeatsRemainingTT-1T-2T-310TimetoDeparture………………8480V(t,n)=

ExpectedRevenue882591639492…nn+1n+2n+3SeatsRemainingT…8480V(t,n)=

ExpectedRevenueV(t,n+1)–V(t,n)=

MarginalExpectedRevenue345338330…T…352nn+1n+2n+3SeatsRemainingBidPriceControl:Withn+1seatsremaining,acceptonlyarrivalswithfaresinexcessof345345338330…T…352BidPriceControlLikenestedbookinglimits,thereexistsasubstantialliteratureondynamicprogrammingmethodsforbidpricecontrolWhilebidpricecontrolissimpleandmathematicallyoptimal(foritsmodelingassumptions),ithasnotyetbeenbroadlyacceptedintheairlineindustrySubstantialchangestotheunderlyingbusinessprocessesBidPriceControlSolutionsfromdynamicprogrammingcanalsobeconvertedtonestedbookinglimits,butthistechniquehasnotbeenbroadlyadoptedinpracticeBidpricecontrolcanbeimplementedwithroughlythesamenumberofcontrolparameters(bidprices)asnestedfareclassavailabilityRevenueManagement

andDynamicPricingNetwork(O&D)ControlControlMechanismsNetworkControlNetworkcontrolrecognizesthatpassengersflowonmultipleflightlegsAnissueofglobalversuslocaloptimizationProblemiscomplicatedformanyreasonsForecastsofmanysmallnumbersDataLegacybusinesspracticesInventoryControlMechanismTheinventorycontrolmechanismcanhaveasubstantialimpactonRevenueMarketinganddistributionChangestoRESsystemChangestocontractsanddistributionchannelsExample:

LimitationsofLeg/ClassControlSATDFWEWRSupply:1seatontheSAT-DFWleg1seatontheDFW-EWRlegDemand:1$300SAT-DFWYpassenger1$1200SAT-DFW-EWRYpassenger$1200Y$300YExample:

LimitationsofLeg/ClassControlOptimalleg/classavailabilityistoleaveoneseatavailableinYclassoneachlegSATDFWEWRYClassMClassBClassQClass1000YClassMClassBClassQClass1000Example:

LimitationsofLeg/ClassControlSATDFWEWR$1200Y$300YWithleg/classcontrol,thereisnowaytoclose

SAT-DFWYwhileleavingSAT-DFW-EWRYopenSupply:1seatontheSAT-DFWleg1seatontheDFW-EWRlegDemand:1$300SAT-DFWYpassenger1$1200SAT-DFW-EWRYpassengerLimitationsofLeg/ClassControlThelimitationsofleg/classavailabilityasacontrolmechanismlargelyeliminaterevenueimprovementsfromanythingmoresophisticatedthanleg/classoptimizationForthisreason,carriersthatadoptO&DcontrolalsoadoptanewinventorycontrolmechanismRequirestremendouseffortandexpensetoworkaroundthelegacyinventoryenvironmentAlternativeControlMechanismsWhiletherearemanypotentialinventorycontrolmechanismsotherthanleg/classcontrol,twohavecometopredominateO&DrevenuemanagementapplicationsVirtualnestingBidpriceNotethattheconceptofitinerary/fareclass(ODIF)inventorylevelcontrolisimpracticalVirtualNestingAprimalcontrolmechanismsimilarinflavortoleg/classcontrolAsmallsetofvirtualinventorybucketsaredeterminedforeachlegNestedinventorylevelsareestablishedforeachbucketEachleginanODIFismappedtoaleginventorybucketandanODIFisavailableforsaleifinventoryisavailableineachlegbucketVirtualNestingSAT-DFW-EWRYmapstovirtualbucket3onlegSAT-DFWandvirtualbucket1onlegDFW-EWRTotalavailabilityof10forSAT-DFW-EWRYSATDFWEWRBucket1Bucket2Bucket3Bucket410060100Bucket1Bucket2Bucket3Bucket440000VirtualNestingSAT-DFWYmapstovirtualbucket4onlegSAT-DFWSAT-DFWYisclosedSATDFWEWRBucket1Bucket2Bucket3Bucket410060100Bucket1Bucket2Bucket3Bucket440000BidPriceControlAdualcontrolmechanismAbidpriceisestablishedforeachflightlegAnODIFisopenforsaleifthefareexceedsthesumofthebidpricesonthelegsthatareusedBidPriceControlSATDFWEWR$1200YBidPrice=$400BidPrice=$600SAT-DFW-EWRYisopenforsalebecause

$1200$400+$600

BidPriceControlSATDFWEWRBidPrice=$400BidPrice=$600$300YSAT-DFWYisclosedforsalebecause

$300<$400BidPriceControlSATDFWEWRIntermediatecontrolbetweenoptimizationpointsisachievedbyhavingadifferentbidpriceforeach

seatsoldininventory654321$664$647$632$619$610$600SeatBidPrice654321$434$425$417$410$405$400SeatBidPriceBidPriceControlSATDFWEWRAfteraseatissoldthebidpriceincreases,reflectingthereducedinventoryavailability654321$664$647$632$619$610$600SeatBidPrice654321$434$425$417$410$405$400SeatBidPriceVirtualNestingAdvantagesVerygoodrevenueperformanceComputationallytractableRelativelysmallnumberofcontrolparametersComprehensibletousersAcceptedindustrypracticeDisadvantagesNotdirectlyapplicabletomulti-dimensionalresourcedomainsProperoperationrequiresconstantremappingofODIFstovirtualbucketsBidPriceControlAdvantagesExcellentrevenueperformanceComputationallytractableComprehensibletousersBroaderusethanrevenuemanagementapplicationsPlacesamonetaryvalueonunitinventoryDisadvantagesGrowinguseracceptance,buthasnotreached

thesamelevelasprimalmethodsRevenueManagement

andDynamicPricingNetwork(O&D)ControlModelsAModelThedemandallocationmodel(alsoknownasthedemand-to-comemodel)hasbeenproposedforuseinrevenuemanagementapplications,butistypicallynotemployedForallofitslimitations,thedemandallocationmodelbringstolightmanyoftheimportantissuesinrevenuemanagementDemandAllocationModelMax

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I=setofODIFsE=setofflightlegsce=capacityofflightedi=demandforODIFiri=ODIFirevenueI(e)=ODIFsusingflightexi=demandallocatedtoODIFiLeg/ClassControlMax

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Thevariablesxicanberolleduptogenerateleg/classavailabilityVirtualNestingMax

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ThedualvariableseassociatedwiththecapacityconstraintscanbeusedasbidpricesNetworkAlgorithms:

Leg/ClassControlNetworkalgorithmsforgeneratingnestedleg/classavailabilityarenottypicallyusedLimitationsofthecontrolmechanismandfarestructureeliminatemuchofthevalueNetworkAlgorithms:

VirtualNestingControlOptimizationconsistsofdeterminingtheODIFtoleg/bucketmapping,andthencalculatingnestedleg/bucketinventorylevelsBestmappingsprorateODIFfarestolegs,andthengroupsimilarproratedfaresintothesamebucketThebestprorationmethodsdependondemandforecastsandrealizedbookings,andchangedynamicallythroughoutthebookingcycleWithODIFsmappedtobuckets,nestedbucketinventorylevelsarecalculatedusingthenestedleg/bucketalgorithmofchoiceNetworkAlgorithms:

BidPriceControlBidpricesarenormallygenerateddirectlyorindirectlyfromthedualsolutionofanetworkoptimizationmodelResourceAllocationModelObservationsA200legnetworkmayhave10,000activeODIFs,leadingtoanetworkoptimizationproblemwith10,000columnsand10,200rowsWith20,000passengers,theaveragenumberofpassengersperODIFis2Typically,20%oftheODIFswillcarry80%ofthetraffic,withalargenumberofODIFscarryingontheorderof.01orfewerpassengersper

networkdayResourceAllocationModelMax

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ManysmallnumbersLevelofDetailProblemThelevelofdetailproblemremainsapracticalconsiderationwhensettingupanyrevenuemanag