Capacity allocation

1. Capacityallocation Lecture 4

2. Capacity allocation • How many low-fare seats (hotel rooms, rental cars) to allow to be booked while facing the possibility of future high-fare demand • Airlines, rental car companies, hotels, cruise lines, freight transportation, made-to-order manufacturing

3. The two-class problem • The basic model: all the discount bookings occur any full-fare passengers seek to book • Maximizing revenue/taking into account incremental costs and ancilliary contribution/taking into account sunk costs

4. Determinethediscountbookinglimit • Tradeoff between setting it too high or too low (dilution vs. spoilage) • ***7.1

9. B=60->61 • PlaneC=100 • *Dd=50 • *Df=45; Df=55 • *86% • **Dd=65 • **Df=30 • **14%..*6.5% • ***Dd=65 • ***Df=45 • ***14%..*93.5% • =6.5%*190+93.5%*(190-200)=3 • =86%*0+14%*3=0.42 • =86%*0+14%*(6.5%*190+93.5%*(190-200)) • =14%*(6.5%*190+93.5%*(190-200))=>6.5%*190+93.5%*(190-200) • =190—93.5%*200=> Pd—93.5%*Pf>0=>Pd/Pf>93.5%;190/200=95% • 50%*10000+50%*20000=

10. Discountbookinglimitforanairplanewith 150 seatsis 80 seats. • Theairplaneisbeingsubstitutedforonewith 100 seats. • Whatisthediscountbookinglimitnow?

15. Kui pd/pf = 0.5, siis paneme me täishinnaga müüki alati mü=66 piletit, olenemata sellest kui suur on full demand standardhälve

16. Kui diskonteeritud piletid on väga kallid, siis mida riskantsem on täishinnaga piletite müük, seda vähem me täishinnale pileteid protectime

17. Kui diskonteeritud piletid on väga odavad, siis mida riskantsem on täishinnaga piletite müük, seda rohkem me täishinnale pileteid protectime

19. Relationtothenewsvendorproblem, 1882 • Overage and underagecosts • O=20 • U=5 • Withrespecttothehighpriceclass • O=pd • U=pf-pd

22. UsingLittlewood’s (1972) rule • Thealgorithmforsetting b: • Set b to 0; set pd=190; set pf=200->pd/pf=95% • Set b=b+1 (e.g. remainder = 99, if PlaneCapacity=100) • Checkwhether1-Ff(C-b) > 95%– probability, thatthereis too muchfulldemand, isover 95% • If no, gobacktoincreasing b • Otherwisestop at previous b

26. Dynamicprogramming, Bellman’sprinciple

27. ExpectedMarginalSeatRevenue (EMSR) Heuristics, thecasewiththreepriceclasses, heuristicEMSRa • Littlewoodlookupforthedistributionof P1: • P3/P1 • Littlewoodlookupforthedistributionof P2: • P3/P2 • Bookinglimit b3= PlaneC minus thetwoquantitiescomputedabove • Thecaseswithmoreclassesanalogous – e.g. firstcalculate b4, then b3, then b2

28. HeuristicEMSRb, thistime, forexample, forfourclasses • Firstof all, wewantthebookinglimit b4 • Fortheclassesaboveit, calculate a following „weightedaverage“ class • AvgNew=Avg3+Avg2+Avg1 • StdevNew=sqrt(Stdev3^2+Stdev2^2+Stdev1^2) • priceNew=price3*Avg3 /AvgNew + price2*Avg2/AvgNew + price1*Avg1/AvgNew • Do a Littlewoodlookup on price4/priceNew on a distributiongivenbyAvgNew and StdevNewtodeterming b4 • Proceedanalogouslyfor b3, then b2

29. ComparisonofEMSRa, EMSRb and dynamicprogramming, see Belobaba 1992

30. Demanddependence • Demandineachfareclassisindependentofdemandintheotherfareclasses • E.g. no cannibalization – opening a discountclass, has no effect on full-faredemand • Also, no buy-up/sell-up – closing a discountfareclassdoesnotleadtoincreaseddemandinhigherfareclasses

31. Two-classcapacityallocationwithdemanddependence • Insteadof=pd/pf, wehavethemodifiedformula=1/(1-alfa)*(pd/pf-alfa) • to look upusingLittlewood’srule, • alfa beingthefractionofcustomers, whowillswitchtofullprice, afterbeingdenied a discountedticket

32. Modified EMSR Heuristics, Belobaba and Weatherford 1996 • Allowsbuy-uptothenexthighestclassonly • ModifiedEMSRa – usemodifiedformulaforthecalculationofthenextlevelonly, originalformulafor all theclassesabovethat • ModifiedEMSRb – usemodifiedformulawithrespectto „weightedaverage“ classcreatedforEMSRb (createthisclassintheoriginalway) • Though, they are „heuristicsgrafted on toanotherheuristic“

33. Measuringtheeffectivenessofrevenuemanagement • Totalrevenueopportunity • No revenuemanagement • RevenueOpportunityMetric • Example: • ROM = ($45 000 – $35 000)/($50 000 - $35 000) • =67% • But, ROM forflightswithverylowdemandwillalwaysbecloseto 100% • And, see Fig7.5 above, iffull-faredemandishigh, butuncertain, ROM willbelower, thanwhenfull-faredemandishigh, butmorecertain (lowstdev) • Thus, astheseexamples show, changesin ROM, mightalsobeduetochangesintheunderlyingfactorsofdemand, ratherthanduetochangesintheeffectivenessofrevenuemanagement

34. LECTURE 4 ENDS HERE

35. Tacticalrevenuemanagement • Calculates and periodicallyupdatesthebookinglimits • Resources • Unitsofcapacity (flightdeparture, hotel room night, rentalcarday) • Products • Customers are seekingtopurchasethose (a seat on Flight 130 from St. Louis to Cleveland on Monday, June 30 – singleresource; A two-nightstay at theSheraton Cleveland, arriving on March 19 and departing on March 21 – tworesources) • Fareclasses • A combinationof a price and a setofrestrictions on whocanpurchase and when (e.g. group and regionalpricing)

37. Thefactthat RM operatesfareclasses, doesnotchangemuchfromcustomersview – hestill sees onlythelowestavailablefare • Sinceairlinesstillrespondtotheoffers made bythecompetition, RM supplementsratherthanreplacespricing

38. Capacityallocation • Howmanyseats (hotelrooms, rentalcars) toallowlow-farecustomerstobook – giventhepossiblefuturehigh-faredemand • Two-classproblem • Discountcustomers • Full-farecustomers • BASIC MODEL – all discountbookingshappenbeforefull-farebookings • Wemaximizeexpectedrevenue – incrementalcosts and ancillarycontribution are zero • Inrealitycompaniesshouldmaximizeexpectedtotalcontribution