THE PASSENGER-MIX PROBLEM IN THE SCHEDULED AIRLINES

INTERFACES Vol. 12, No.3, June 1982 Copyright 1982, The institute of Management Sciences 0092-2102/82/1203/0073$0 I. 25 THE PASSENGER-MIX PROBLEM IN THE SCHEDULED AIRLINES Fred Glover Management Science and informati Systems, College of Business and Administrati, University of Colorado, Boulder, Colorado 80309 Randy Glover Management Science Software Systems, 1040 Lehigh, Boulder, Colorado 80303 Joe Lorenzo Vice President, Frti,~ r Airlines, Inc., Denver, Colorado 80207 Claude McMillan Divisi of Informati Science Research, University of Colorado, Box 419, Boulder. Colorado 80309 ABSTRACT. Deregulati ha ~ opened up many opportunities and challenges in the transportati industry - opportunities to increase profits and challenges to keep from being outflanked by competiti. A goal of particular interest to the sc heduled airlines is to set prices more adaptively and to ~ h ange them more rapidly. A difficult problem arises when many passengers with different itineraries compete for a limited number of seats a single-flight segment. The proble 11 is complicated by the existence of different fare classes, many flight segments, and different demands across time. For any given set of prices, flight-segment capacities, and passenger-carrying demand, there is some number of passengers at each fare class each flight segment that will optimize reve nue. Knowledge of such an optimum can be used nn ly in pricing analysis but also in setting policies to influence the passenger fare-class mix so that the optimum will be more nearly achieved in actual practice. We describe a method for identifying the optimum fare-class mix and the design of a system for that purpose which we built and implemented for Frtier Airlines. The recogniti and formulati of the problem has become even more important as the number of aircraft in the sky has been reduce and the competiti for a limited number of seats has become more intense. I Prior to deregulati, compl~ tltl amg carriers was limited by the Civil Aerautics Board (CAB) in two of the three major areas of airline marketing - route authority and pricing -leaving ly the amount of capacity (number of flights ) to be made available by anye carrier over anye route up to individual carrier management judgment. Competiti, therefore, was limited to frills (fancy meals) and flights (departures every hour). Pricing policies were generally viewed and analyzed from an industry standpoint because the CAB would not permit any carrier to offer a lower fare that was unecomic for the industry as a whole. Thus even though a particular fare might benefit a particular carrier at the expense of another carrier, the CAB would not permit the offering of the proposed fare without an extremely strg justificati TRANSPORTATION; AIR INTERFACES June 1982 73

showing clearly that the fare would benefit the general public. The carriers who stood to lose revenue as a result of the lower fare would argue in rebuttal that their loss of revenue would have to be offset by a gencral fare increase in all fares, thereby harming the general public by requiring them to pay a higher fare and in effect subsidizing those few passengers who would benefit from the lower fare proposed by their competitor. With the advent of deregulati, caitiers suddenly found themselves facing new forms of competiti. New, low-cost, nuni carriers sprung up in major ma"kets offering transportati at unrestricted fares priced from 30 to 75% below exi:,ting fares. Smaller regial carriers whose route structure had been limited by the CA.B to short-haul, feeder-type operatis hubbed around a single major airport such as Denver or St. Louis began to expand into other major cities and compete with the large trunk carriers whose route structures had been designed by the CAB to carry passengers over the lger distances between the major hub cities. In additi to expanding their services to large cities beyd their old route structures, the regial airlines realized that they could also compete effectively for a p0l1i of the lg-haul pool of traffic that had historically traveled the trunk carriers' lg-haul nstop flights by offering lower fares their muitistop or cnecting flights. Since the individual airlines were no lger limited to an industry orientati with regard to their pricing policies, true price competiti expanded dramatically. The rewards associated with filling seats (that would otherwise be empty) with low-fare passengers that an airline would otherwise not have carried must be balanced against the risks of displacing higher-fare passengers that would otherwise have been carried. The problem is complicated by (a) the existence of a multitude of prices (f-lres) with varying degrees of restrictis limiting the availability of all but the highest priced seat; (b) numerous flights operated by a number of airlines over various routings, anye of which (or combinati of two or more) can be used by passengers to get to theil' destinatis; and finally, (c) varying degrees of demand for the seats anye airline's flight segment over time, depending up the number of city pairs that can be reasably serviced by the particular flight, the seas of the year. d~ty of week, time of day, quality of service offered (nstop, e-stop, cnecti) for a particular passenger's routing vis-a-vis alternative flights either of the same or competitive caitiers. The Passenger Mix PNblem The problem faced by the airlines then may be termed the "pricing and passenger mix" problem. The problem has relevance not ly for airlines but also for other segments of the carrier industry. One might substitute the term" load mix" in alternative settings; e.g., for a trucking company or steamship company that has :l set of regularly scheduled routes and which faces decisis of the type elaborated below. With the eliminati of certain government restrictis, airlines now have more opportunity to explore different pricing and routing optis and to seek for each the best mix of passengers [Murphy, 1980]. The determinati of this mix provides two major outcomes: (1) it ~nables the airline to structure its reservati system more effectively, setting appropriate limits and priorities governing the number of 74 INTERFACES June 1982

passengers at different fare classes traveling different flights; (2) it allows different price/route scenarios to be evaluated in csiderati of the profit generated from the best passenger mix, relative to a given scenario. The passenger mix problem may therefore be viewed as serving both a "tactical" (reservati mitoring) objective and a " strategic" (price/route setting) objective. To meet these objectives, a computer-based system embodying a cvenient, user-friendly model and a highly efficient soluti method is needed. A system that fails to exhibit these characteristics will not ly incur undesirable costs in terms of human and computer resources but will also seriously inhibit scenario analysis and respsiveness to changing cditis [Dembo and Mulvey, 1976; Glover and Klingman, 1978; Glover, McMillan, and Taylor, 1977]. This paper describes the development of a system based a network-related model that meets the dual criteria of cvenience and efficiency, a system implemented for Frtier Airlines. We will first provide a descripti of the passenger pricing and passenger mix problem and some Jf its practical implicatis, and then develop the network-related model by reference to a simplified illustrati. Finally, we will describe supporting software features that provide additial user cvenience and report preliminary computatial experience. Features of the Pricing and Passenger Mix Problem The profitability of a passenger to the carrier depends the length of the trip and the fare class he travels. While revenue per mile is generally less for passengers traveling lg distances, the total revenue to the carrier is greater for those passengers. Associated with each passenger a given flight segment is an opportunity cost, in that each passenger a given flight segment occupies a seat that might have ge to another passenger traveling a more profitable itinerary or at a more profitable fare class. Thus a flight which cnects terminals A, B, and C (in that order), a local passenger traveling ly from B to C occupil!s a seat that might have ge to a passenger traveling A to C, a through trave.:er. The traveler from B to C may therefore be respsible for an empty seat segment A to B of that flight or some segment of another flight involved in the passenger itinerary (PI) which includes segment B to C. On each segment of each flight in a carrier's network there may be many PI's, passengers traveling from many different origins to many different destinatis and in different fare classes. Given a forecast of the demand for PI's anye day at the various fare classes and over the carrier' s entire network, there exists a theoretically optimal mix of PI's at the various fare classes. The oplmal mix is that mix of passenger itineraries and associated fare classes which maximizes the carrier's total revenue that day. The optimal mix of PI's can be expressed in terms of the best number of PI's in various fare classes each segment of each flight; that is, the optimal occupancy of the available seats each segment of each flight. Much of the planning de at the operat is level in the scheduled airlines focuses PI's and the demand for them at the various fare classes. Marketing managers endeavor to design fare class structures, in associati with PI's, so as to increase occupancy and thus increase revenue. It is a complex business in that fare class modificati and the offering of special discounts may result in "spill" and "diversi. " INTERFACES June 1982 75

is the movement of passengers to other Divep,i occur, whcn jlas~cnger the fare takes offered to stimulate increased occupancy, either the less revenue for the carner restrict;s such of time between the Carriers also try ctrol. " This is de carrier has some measure of and diversi and for traffic may be vanous fare classes, what PI and associated fare-class mix, each segment of will maximize revenue for that ' The answer to that the carrier to determine the optimal reservati amg the various fare each segment of each The cost associated with each passenger each of each his PI and fare class and the demand for all other PI's and classes his the of each ctext of the entire is then Model Formulati We formulated the as a minimum cosl network flow side cstraints. In the network segment:; of and another set fare classes. Flow :m the former a segment, and passengers each PI each The formulati is illustrated in 76 JUrle 1982

FIGURE I. PASSENGER C APACITY AND LOADING SHOWN AS ARC FLOWS. TO NODE A 'BACK ARCS', FOR PI A TO B, ONE FOR Y ~ CLASS AND ONE FOR N CLASS Y=60 AIRCRAFT CAPACITY ARC FLOW = 96 FIGURE 2. FLLGHT I. A TO B TO C, ARRIVING AT B 10:00 AM. FLIGHT 2. C TO B TO D, ARRIVING AT B 11:00 AM. TO B PI, 4 TO A PI D 1 TO A PI, 3 A AlRC~\FT CAPA C1TY ARC One segment of a tlight cnects terminals A and B in Figure I. A flow of 96 units the arc cnecting A to B indicates 96 passengers, various itineraries, traveling segment A to B of that flight. Two fare classes are possible in this example, Y and M. The flow Y = 60 e "back arc" cnecting B to A indicates 60 passengers a PI traveling at fare class Y from.a. to B. M = 36 indicates 36 passengers traveling the same PI at fare class M. In Figure 2, two tlights are represented schematically: Flight I cnects A to B to C, in that order, and Flight 2 cnects C to B to D. Flight I arrives at B e hour prior to Flight 2's arrival at B, so that passengers the first segment of Flight I can transfer to Flight 2 at B for ctinued travel to D. INTERFACES June 1982 77

The PI's, in this PI # -,- Back arcs in # I ; C to B for PI PI and D to A for PI cnects A to B 2 3 4 5 6 A to B to C C to B B to D C to D 7 A to B ( I) then B to D 2) ::::: Dfor for the PI which terminal B over the span between Flow the dashed arc B to B rprlr",:pntc at B from to time C. Flow each forward arc is limited the --J,,-'C"J and flow each back arc limited the demand for the PI and class that back arc represents. These limits translate into upper bounds the arcsc An increment revenue is associated with each unit of flow each back are, to the of the ticket at the fare class that arc represents. This network formulati itself can be shown to represent the of circumstances as, for if no sequence of transfer arcs and segment arcs can create a directed or otherwise. More it suffices if each PI/fare-class arc lies at most directed The latter cditi satisfied if not network formulati by itself was The existence of a number of Pllfare-class arc a number of such cstrained. The existence of more than e may cause the sum of PI flows to exceed the intended to be used the PI's. The additial cstraints this PI/fare-class arc compent, in the system we finds that flow each lrc which maximizes revenue the carrier's network. without the aircraft cstraints and the upper bounds the demands at their associated fare classes. 78 INTERFACES June 1982

If If the satisfied, the cstraints that e, Gill and and The system built for Frtier Airlines was to accommodate a network of 600 and PI's with up to five fare classes per PI. The number of side cstraints ranges from about 1 but our finds that 40 to 60 of these Executi time a 16 bit pre- and built into it for easy interacti with the system and revenue the system makes it reservati allocati decisis. informati for better hpfn~''''"1 Programming New York. Glover, Fred and pfementuti Netherlands. l'v1cmillan, C. and Taylor. Novemr,er. Optimizali, fw"u~"m Press, Network Problems,", Sijthoff and Support System for Intcnlllliai Cference to Management," Airline June

FRONTIER AIRLINES Frller Airlines. Inc 62'50 Smllh Road Oenve(, Colorado 60207 Telephe (303) 398-5151 Apr i 1 15, 1982 Or. R. [. O. Wool sey Department of Mineral Ecomics Colorado School of Mine. Golden, CO 80701 Dear Or. Wool.ey: I am IIriting to infn you that the deci.i.upport system described in the paper, "The Passenger Mix Problem in the Scheduled Airlines," by Glover and others was in fact cstructed and has been implemented at Frtier Airlines. We are using that system p"esently, and it has improved our capability of pri c i ng our produc t and deve 1 opi ng our di scount j nven tory. It has al so given us the ability to give v~ll'able cormtents to our scheduling department as well as to provide input;to ")lr planning functi., ;!)iyr1~: ". '/,.' / I ~ltl- cyg ~ark S. Schnei der Director - Pricing & Capacity Ctrol MSS:ctb 80 INTERFACES June 1982