October 1998 Yield management has helped individual airlines soar to new profitability. Now global alliances between multiple carriers create the need for alliance revenue management. This new twist on a familiar problem adds considerable complexity. Yield management has helped individual airlines soar to new profitability. Now global alliances between multiple carriers create the need for alliance revenue management. This new twist on a familiar problem adds considerable complexity. By Andrew Boyd Perhaps the most hotly watched issue in the airline industry today is that of global alliances. Alliances quickly began to form in the mid-1980s in response to deregulation in the United States. While major carriers could not profitably offer service to low density markets, established regional carriers with smaller aircraft could. Code sharing provided a way for both types of carriers to expand their customer base by feeding into each other's flight networks. The symbiosis was further solidified by the simultaneous development of hub-and-spoke systems. The same principles lie behind the advent of the more recent global alliances, though the focus is more upon developing global networks and building hub-to-hub traffic. Although the driving factor behind alliances is clearly long-term profitability, their actual formation tends to be for strategic rather than operational reasons. High-level decision-makers focus on issues such as access to larger markets, establishing global brand loyalty, and so forth. However, actually realizing improved profitability requires proper operational control of alliance resources — whatever form this control may take. By code sharing flights, alliances are forced to ask the question, Who gets access to what seats on a flight? The answers have been anything but uniform, ranging from apportioning blocks of seats among the alliance partners to allowing alliance partners access to inventories on a first-come, first-served basis. The alliance revenue management problem is generally equated with maximizing the combined revenues of the alliance partners, and is the main topic of this article. Equally important, but often treated as a separate, secondary issue, is the problem of how revenues should be shared. A potentially alliance-breaking issue, revenue sharing is commonly handled through contractual arrangements allowing for a "fair" distribution of code-share revenues. Carriers continue to grapple with the problem, but its newness has not allowed for any extensive analysis. Remarkably, the impact of properly controlling seat inventories on carrier profitability can be found in over a decade of work on this problem under the name of yield or revenue management. Classical revenue management consists of forecasting demand and solving an optimization problem to establish control parameters by which accept/reject decisions are made for booking requests. Heralded by Don Garvett as by far the most significant factor driving airline profitability [3], revenue management is perhaps the most respected application of operations research in the airline industry today. Revenue improvements from implementing a revenue management system can range from 2-8 percent (or more) depending on the carrier. In the June 1998 issue of OR/MS Today, Thomas Cook of SABRE Technology Solutions noted that the yield management system at American Airlines generates almost $1 billion in annual incremental revenue [2] while overall operating earnings at American only approached this level for the first time in history in 1997. While the need for alliance revenue management is clearly appreciated, the practice is still in its infancy. Centralized Revenue Management Perhaps the most obvious resolution of the alliance revenue management problem is simply to treat the flight networks of alliance partners as comprising a single network. Forecasting, optimization and inventory control can then be performed on the combined network. By virtue of the fact that seat inventories can be allocated more efficiently on the combined network than on each individual flight network separately, expected total revenues from centralized revenue management will be correspondingly higher. While a natural proposal, there are a multitude of practical difficulties associated with this approach. Over the past decade, revenue management systems have evolved into highly complex on-line entities that often extract and write hundreds of gigabytes of data from multiple data sources while processing these data in a fixed nightly processing window. Newer generation systems will be more dynamic and even more complex. Coordinating the flow of information from different alliance members to and from a centralized source is a logistical nightmare, especially when confronted with changing alliances and evolving IT structures. An even more fundamental issue is the autonomy of the individual alliance partners. As carriers grow ever more sophisticated in their use of revenue management, they choose methodologies that provide a competitive advantage over other carriers and tune these methodologies to their specific requirements. In most instances, carriers have made substantial investments in their revenue management infrastructure. Asking the revenue management departments of two or more carriers to agree on the details of how a combined revenue management system should be operated and then implementing such a system is a painful and expensive proposition, if not altogether impossible. Decentralized Revenue Management Setting aside the many difficulties associated with centralized revenue management, an analysis of this approach provides some very practical and not entirely obvious ways of addressing the alliance revenue management problem. (A detailed analysis can be found in the Appendix of [1]). It is based on setting up a centralized version of an optimization model commonly used in the study (and in some instances the practice) of revenue management. In general terms, the centralized optimization problem for two carriers, A and B, seeks to answer the question, How should seat inventories on each flight leg in the combined network be allotted so as to maximize total revenue? Optimization theory provides two different ways to solve this problem. The first, of course, is through solving the problem directly to achieve the actual allotment of seats. This is the centralized approach. The second is to arrive at a set of marginal revenue equilibrium conditions between the two carriers. Although it is not obvious, these marginal revenue equilibrium conditions guarantee that the combined revenues are identical to those that would be achieved through solving the centralized problem directly. The conditions themselves are easily stated. If seat inventory on a flight leg is split between the two carriers A and B, the marginal revenue of an additional seat is identical for each carrier. If carrier A is apportioned all of the seat inventory on a flight leg, then the marginal revenue of an additional seat for carrier A is at least as large as the marginal revenue of an additional seat for carrier B. If carrier B is apportioned all of the seat inventory on a flight leg, then the marginal revenue of an additional seat for carrier B is at least as large as the marginal revenue of an additional seat for carrier A. Similar conditions can be established for alliances consisting of multiple carriers. These conditions are unlikely to hold without some exchange of seat inventories, which is why alliance revenue management has profitability implications in the first place. What is especially important to recognize is that if these conditions are not satisfied, there are natural economic forces working to achieve them. No form of centralized optimization is required if carriers are free to exchange seats based on an evaluation of their economic value. Consider, for example, a leg where condition (1.) is not satisfied; that is, suppose carrier A determines that the marginal revenue it could generate from an additional seat on leg (l) is $400 while carrier B determines that the marginal revenue it could generate from an additional seat on leg (l) is $100. Then both carriers have economic incentive to reapportion the seat from carrier A's inventory to carrier B's, with a resultant increase in the combined carrier revenues of $300. With additional seat inventory, carrier A's marginal revenue will tend to decrease from $400, and with a reduction in seat inventory, carrier B's will tend to increase from $100. This form of exchange also provides guidance in establishing how revenues should be shared. Of the $400 realized by carrier A, carrier B should receive at least $100 or it should keep the seat for sale from its own inventory. Exactly how the additional $300 should be shared is open to resolution by the carriers, but no matter how it is apportioned, both carriers come out ahead. The equivalence of solving a combined resource allocation problem and reaching a state of marginal revenue or price equilibrium is not new. The work leading to these kinds of results was sufficiently groundbreaking in the mid-20th century that Leonid Kantorovich and T. C. Koopmans were awarded the 1975 Nobel Prize in Economics "for their contributions to the theory of optimum allocation of resources." Professor Kantorovich, a renowned Soviet economist, was cited for demonstrating "the connection between the allocation of resources and the price system" and for showing "how the possibility of decentralizing decisions in a planned economy is dependent upon the existence of a rational price system" [4]. What is especially interesting is to see how these ideas naturally emerge from one of the most commonly cited models in the application of network revenue management. Calculating Marginal Seat Revenues For the equilibrium conditions to be applied in practice it's necessary to actually calculate marginal seat revenues. Because demand is stochastic, all marginal revenues are at best expected values; to provide a true measure of marginal seat revenue the full effect of the seat on network revenues must be accounted for. The inability of a carrier to confidently establish good marginal revenues could pose a serious impediment to seeking an equilibrium solution. Fortunately this issue has been largely addressed in the airline industry through research by the revenue management community on bid price control mechanisms. Bid prices are monetary values attached to flight legs that are intended to represent the displacement cost of giving up a seat, or the marginal revenue that an additional seat would be expected to generate. In their simplest form, bid price mechanisms accept a booking if the fare exceeds the sum of the bid prices of the legs in the booking. Bid price methods have proven remarkably effective as a means of inventory control, and as such have established their credibility as a measure of marginal seat revenue. The model analyzed in the Appendix formed the basis for one of the first bid price methods, and its performance remains quite good in comparison with most algorithms proposed for airline passenger revenue management. The Equilibrium Conditions in Practice The marginal revenue equilibrium conditions provide a specific, practical way for finding seat inventory allocations that maximize combined revenues: exchange seats until marginal seat revenues are balanced. Even if equilibrium is never actually achieved, the equilibrium conditions imply that the mere process of exchanging seats when marginal revenues are out of balance works in favor of combined revenue maximization. To appreciate the significance of this distinction, we consider two of the more common control environments used in practice. Blocked Seat Allotment. Blocked seat allotment is the practice of partitioning seats among carriers and then allowing each carrier individual control of the seats they have been assigned. Variations range from hard blocks, in which partitioning remains fixed once it is established, to soft blocks, which provide contingencies for periodically re-allotting seats as sales are realized. In either case, there are specific points in time where actual seat allotments are established, and it makes sense to facilitate the process of finding an optimal allotment by employing a specialized algorithm that seeks to arrive at the equilibrium conditions. In the absence of mathematical degeneracy, both the optimal seat allotments and marginal revenues are uniquely determined. However, the marginal revenues generated in the course of finding the equilibrium solution depend upon the method chosen for iterating through potential inventory allotments. Classical resource directive decomposition has the drawback that it requires a centralized coordinator to propose alternative network-wide allotments until equilibrium is reached, but an analysis of the formal decomposition procedure yields many insights. In resource directive decomposition, the central coordinator proposes seat allotments to individual carriers, who in turn provide their assessment of the marginal revenue of seats on each leg under this allotment back to the central coordinator, who uses these marginal revenues to propose another, better set of seat allotments. Of great practical significance is the fact that the central coordinator and the carriers only communicate through allotments and marginal revenues. Carriers are free to establish fares, demand forecasts and track itineraries of their own choosing, without the need for sharing or coordinating the flow of this information with other alliance carriers. For these reasons, resource directive decomposition represents a good alternative for intelligently establishing blocked seat allotments. Free Sale. A more dynamic alternative than establishing blocked allotments is free sale. With free sale, the carrier operating a flight provides direct or indirect access to inventory by providing information about seat availability to non-operating alliance carriers. This information is generally limited to what booking classes are available, and possibly limits on the number of seats. Non-operating carriers can then book seats subject to the limitations established by the operating carrier. The key difference between free sale and blocked allotments is that free sale never actually seeks to establish complete inventory allotments. Instead, the focus is on establishing only enough information for alliance partners to make here-and-now accept/reject decisions. In light of the marginal revenue equilibrium conditions, even without establishing complete inventory allotments, carriers work in favor of maximizing combined revenues if they enter into transactions based on marginal revenue assessments. These transactions are especially elegant when both carriers are using bid price mechanisms to control inventory, but are equally simple to implement when exchanges are based on booking class availability. This latter consideration is especially important given that the present regulatory environment in different parts of the world limits what information can be exchanged between carriers. Revenue Sharing Unlike revenue management for a single carrier, there are two objectives for alliance groups: maximizing combined revenues and maximizing the revenues of each individual alliance partner. Maximizing combined revenues is valuable only to the extent that it improves revenues for each alliance partner, and this can only be guaranteed if there is an appropriate mechanism in place for distributing any additional revenues generated by the alliance. In the case of free sale, the question of revenue sharing is in many ways more difficult than that of maximizing combined network revenues. Revenue sharing tends to be resolved in the course of alliance negotiations, often without a full understanding of the revenue impact of the decisions that are made. The most common means of distributing revenues is through some form of cost-based proration scheme; for example, prorating the revenue of each ticket based on the relative number of miles a passenger flies on each carrier. Efforts to share revenues based on cost rather than revenue can lead to a severely inequitable distribution of revenues, and may actually cause an alliance partner to lose revenue. Consider an example with two flight legs of the same length, the first being operated by carrier A and the second by carrier B. Suppose there is one seat left on each leg, and it is known that there are two passengers looking to purchase tickets: one who is willing to pay $400 for an itinerary consisting only of carrier A's leg, and another who is willing to pay $500 for an itinerary consisting of both carriers' legs. To maximize combined network revenues, the second passenger should be accepted. However, if mileage proration is used as the basis for revenue sharing, both carriers would receive $250 — a clearly suboptimal solution for carrier A, since it could recognize revenues of $400 by accepting the first passenger. Of course, it is in the best interest of both carriers to accept the second passenger if the marginal revenue equilibrium conditions are used as the basis for distribution, with carrier A receiving at least $400 and carrier B receiving the balance. As simple and equitable as this approach is, where arguments can arise is in the calculation of marginal revenues. Does each carrier have the right to establish its own marginal revenue or price for purposes of revenue sharing transactions? Mathematics provides no right or wrong answers to such questions, but it can provide a quantification of the revenue implications under alternative policies; and the alliance revenue management problem is sufficiently important and complex to warrant quantification. Conclusions The marginal revenue equilibrium conditions provide two important insights about alliances. First, combined alliance revenues can be maximized in a decentralized environment if carriers are free to exchange seat inventories based on disequilibria in marginal revenues. This alleviates many of the obstacles associated with implementing centralized revenue management. Second, marginal revenue disequilibria can provide the basis for an intelligent method of revenue sharing. The last decade has demonstrated that controlling seat inventories through the practice of revenue management is vital to a carrier's profitability. By providing new ways for inventory to be distributed, alliances present an opportunity for carriers to realize increased revenues while offering improved client service. But they also present an opportunity for carriers to realize decreased revenues. The net result depends upon fully understanding their revenue implications. How Much Centralization is Necessary? At the heart of many alliance revenue management issues is a very simple question: How much centralization is necessary? Centralization brings with it the need for increased coordination, communication and formalized agreement among carriers. Decentralization can potentially lead to less than optimal resource allocation. The question of common fares for identical flights is a good example. For all intents and purposes, carriers offering a code shared flight are identical from the consumer standpoint if, as is normally the case, frequent flier miles can be accrued on the carrier of choice. If the alliance partners offer different fares for a ticket with the same restrictions, the consumer should be expected to purchase the lowest fare ticket. One could argue that an agreement should be reached and infrastructure set up by which all alliance partners offer identical fares for essentially identical tickets. Alternatively, if the operating carrier is free to control the cost at which it will make its seat inventory available to alliance partners, market forces will work toward bringing the fares into equilibrium without the need for any centralized decision-making. It could be argued that this allows the operating carrier too great of a role in establishing the price of a seat, but in point of fact it is the operating carrier's inventory to begin with. Also, regulators are almost certain to view any efforts to establish prices through a formal agreement as anti-competitive. Another good example is that of demand forecasting. Demand forecasting is commonly regarded as one of the most important issues in revenue management. With demand strongly intertwined on code share flights, some sharing of data is almost certain to provide better forecasts. But should all carriers be required to agree on a single set of forecasts? Should they be required to share data on all flights, or just code share flight? The only certainty is that alliances pose many operational challenges. — Andrew Boyd References 1. Boyd, E.A., "Alliance Revenue Management," PROS Strategic Solutions Technical Report, PROS Strategic Solutions, Inc., 3223 Smith Street, Houston, Texas, 77006. 2. Cook, T.S., "Sabre Soars," OR/MS Today, June 1998, pp. 26-31. 3. Garvett, D.S., "What Drives Airline Profits? A First Look," presentation at the Sixth International Airline CEO Conference, April 28, 1998. 4. Press release of the Royal Swedish Academy of Sciences announcing the 1975 Nobel Prize in Economics, Oct. 14, 1975. 5. Williamson, E.L., "Airline Network Seat Control" Ph. D. thesis, MIT Flight Transportation Laboratory, Cambridge, Mass., 1992. E. Andrew Boyd is vice president of R&D at PROS Strategic Solutions, Inc., a revenue management firm serving more than 70 clients in the airline, cargo, energy and services industries worldwide. He received his Ph.D. from MIT, and was a professor at Texas A&M University prior to joining PROS. He can be reached via email at boyd@prosx.com. Table of Contents OR/MS Today Home Page OR/MS Today copyright © 1998 by the Institute for Operations Research and the Management Sciences. All rights reserved. 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