August 2000 Soaring with Synchronized Systems Coordinated scheduling, yield management and pricing decisions can make airline revenue take off By Timothy L. Jacobs, Richard M. Ratliff and Barry C. Smith Scheduling, pricing and yield management greatly influence an airline's revenue by controlling various aspects of market supply and demand. Decisions involving these activities, however, are often made in isolated departments within an airline, resulting in myopic planning and missed revenue. Research indicates that coordinating the three processes produces a more efficient alignment of the airline's resources, boosts demand for its scheduled flights and provides significant additional revenue opportunities. Scheduling, pricing and yield management (also known as revenue management) are among the most difficult and complex business areas to manage at an airline. Their coordination is further complicated by the fact that the time horizons associated with each area vary dramatically. Airline schedules are published well in advance of the departure date. The core schedule is typically established a full year before its departure date. The scheduling process consists of several discrete events that include frequency analysis, schedule generation and the distribution of the airline's resources to fly the schedule such that overall profit is maximized. A number of models and decision-support tools for evaluating the profitability of an airline schedule have attempted to incorporate the impact of passenger flow into the scheduling process. The most notable of these has been the use of leg-based traffic and revenue estimates in the fleet assignment process [1, 5]. Prices for itineraries typically vary by major seasons (e.g. winter versus summer). However, prices in key markets are continuously monitored and fine-tuned to account for competitive pressures and special sales up until about a month before departure. Pricing decisions involve a series of markets and competitor assessments followed by price adjustments. Although the schedule and prices are typically fixed for periods of time, the demand for itineraries within the schedule can vary widely from day to day. Yield management controls are used to manage the flow of passengers across the schedule based on fare, class availability and overbooking levels. The overall objective of the yield management process is to maximize the total network revenue from day to day given the schedule and prices in effect. A few authors have explored the benefits associated with a limited coupling of the pricing and yield management processes [2]. Because of the different time horizons and specialized needs associated with the scheduling, pricing and yield management processes, separate departments have evolved at most airlines to perform and manage each of these functions. Subsequent departmental differences in personnel, expertise and decision-support systems make it difficult to consistently coordinate scheduling, pricing and yield management decisions. As a result, most airlines use a sequential approach to plan and manage flights. It is easy to imagine scenarios in which a lack of interaction between scheduling, pricing and yield management result in inferior decisions. For example, consider the individual reactions of an airline's scheduling and pricing departments for a market that has historically shown high traffic levels. In isolation, the pricing department is likely to raise fares while the scheduling department increases the available capacity. As a result, market demand drops, the added capacity is not utilized and profitability suffers. Taken independently, these decisions seem appropriate when, in reality, the combined decisions are detrimental. Typical problems encountered in practice include: Raising fares in markets where additional capacity is later added due to independently observed strong traffic. Underestimating incremental traffic resulting from additional capacity (because spill models neglect demand stimulation from fare adjustments and YM availability controls that increase load factors). Fares and/or YM controls not immediately updated following a capacity change. This results in a significant increase in flights with supply and demand imbalances (relatively empty or highly overbooked) before the airline can respond. To illustrate the effect coordinating these planning and control processes can have on the total expected revenue, we'll present an example using a 10-city network with 48 flights serving more than 500 separate markets. Results indicate that coordination of the scheduling, pricing and yield management processes improved the net revenue earned (even after considering any associated cost increases). The "Optimal" Load Factor An airline's revenue is maximized when supply and demand for services are properly balanced for each O&D market (defined as a customer's origin, destination and fare class). The primary factors that influence market demand are flight times, types of service, origin point presence (frequency of service in a city) and fare levels. Supply is a result of scheduling decisions and yield management controls that govern how the available aircraft capacity is utilized. This utilization is often described as "load factor," which represents the percentage of aircraft seats that are filled with passengers. The optimal load factor and fare mix represents the point at which the service supply and market demand are balanced throughout the network [7]. The optimal load factor is less than 100 percent because full aircraft throughout the network implies substantial spill and imperfect YM controls or a completely deterministic market with constant passenger demand each day. Throughout this paper, revenue contribution (percent increase in revenue less variable cost) is used to denote improvement when scheduling decisions are a factor. The primary scheduling decision considered in this study is what size of aircraft to use on each leg in the schedule. This is often referred to as the fleet assignment problem. Pricing and yield management decisions can be compared using revenue only, but the variable costs associated with flying must be considered when comparing alternative fleet assignment options. Therefore, revenue contribution is used as the net improvement measure. To illustrate the concept of an optimal load factor, consider the case of a single flight leg with one fare class. For this example, we assume that the passenger demand follows a normal distribution with a mean of 125 and coefficient of variation of 0.3. (The coefficient of variation [CV] is a measure of a distribution's dispersion and is defined as the ratio of the standard deviation to the mean.) In addition, we assume the market is slightly elastic and has a constant price elasticity of -1.11. The capacity of the leg is assumed to be 150 seats. The relationship between revenue contribution and load factor (LF) is found by varying the price level and computing market demand as a function of price elasticity. For each case, the expected traffic and resulting total revenue is estimated using a simple spill model. Table 1 presents the results of this illustration. Table 1: Results for single leg ­ single class example. Figure 1 presents a graphical display of the normalized results for the one leg example. Results shown in Table 1 and Figure 1 used price variations of -10 percent, -6 percent, -3 percent, 3 percent, 6 percent, 10 percent, 13 percent and 15 percent, in addition to the base case. Each of these points is labeled in Figure 1. Results for this example indicate that the revenue contribution is maximized when the load factor is approximately 78 percent. The revenue varies considerably (by over 4 percent in this example) depending on the price, resultant demand and the ability to accommodate the demand given its variation. Figure 1: Single leg — single class example results showing optimal LF (e=-1.11, CV=0.3). The results presented in Table 1 and displayed in Figure 1 illustrate the sensitivity of the expected revenue to changes in the average fare and demand. Average fare and demand are related via the market price elasticity. Therefore, as the average fare decreases, the demand increases. This results in increased expected traffic over the leg but at a lower price per passenger. As the price is increased, the demand decreases, and the expected traffic over the leg declines. Depending on the starting point, fare increases may or may not result in revenue increases. At low load factors, demand stimulation through price reduction is generally desirable. At higher load factors, an inability to carry additional demand tends to favor price increases. To demonstrate this point, consider points 1 and 2 shown in Table 1. The change in price between points 1 and 2 is $3 with a corresponding increase in demand of 3.3 passengers. This price drop results in dilution amounting to $307.50 ($3 x 102.5 passengers). Although the demand increased by 3.3 passengers, the expected traffic increases by only 3 passengers due to a slight increase in spill. The traffic increase results in $508.50 ($169.5 x 3 passengers) of revenue stimulation. For this example, the net effect of dilution and stimulation is a favorable $201 ($508.50 — $307.50). In this example, 0.3 of the additional passenger demand are spilled. At higher load factors, this displacement becomes more pronounced. For example, comparing points 8 and 9, we see that an increase in demand of 6.6 results in a total increase in traffic of only 3.3 passengers. This nonlinear relationship between the displacement (or spill) and the total demand is the reason the revenue function has a distinct maximum and asymmetrical shape. The optimal load factor is influenced by the uncertainty associated with the demands for each fare class. The impact uncertainty has on the results is modeled by varying the coefficient of variation for the demand flowing across the leg. A low coefficient of variation translates to a nearly deterministic demand typical of fare-minded discount and leisure passengers, while a high coefficient of variation represents a highly uncertain demand typical of business travelers. Intuitively, if the average fare stays the same, we expect the total revenue contribution to increase as the coefficient of variation decreases (due to the fact that there is much less uncertainty associated with the demand). Similarly, we expect the optimal load factor to increase. The limiting case is the purely deterministic situation in which coefficient of variation equals zero, and the demand is known with certainty. In this limiting case, maximum revenue would correspond to a simple greedy allocation of seats to highest paying passengers until the plane was full. Figure 2 illustrates the impact demand uncertainties have on the optimal load factor and revenue contribution, using a constant demand elasticity of -1.5. The results presented use coefficients of variation ranging from 0.2 (relatively certain) to 0.6 (highly uncertain). Also, as in the example presented in Figure 1, various price/demand scenarios are evaluated to construct each curve. Figure 2: Impact of uncertainty (e=-1.5). In all cases shown in Figure 2, we see that the optimal load factor and maximum revenue contribution increases as the coefficient of variation decreases. A decrease in the coefficient of variation represents a decrease in the uncertainty associated with the market demand. Therefore, the expected traffic and load factor increases. The asymmetric form of the revenue contribution versus load factor relationships shown in Figure 2 is similar to that shown in Figure 1. However, the results shown in Figure 2 illustrate that both the load factors and the asymmetry of the relationship increases as the uncertainty decreases. The results also illustrate that the range of load factors for the nine cases considered increases as the coefficient of variation decreases. Demand elasticity also impacts the optimal load factor. Comparing the case in which the CV equals 0.3 in Figure 2 (where e=-1.5) with the example shown in Figure 1 (where e= -1.11), the reader notices that the optimal load factor is higher for the high elasticity case. Also, the revenue (and benefit) gap widens between the best and worst demand points in the high elasticity case. For inelastic markets, this behavior becomes more pronounced. By definition, a fare increase in an inelastic market always results in a proportionally smaller drop in the demand and expected traffic. Therefore, the revenue contribution always represents a gain. However, most airlines face practical (or legal) restrictions that limit their ability to raise fares above a certain amount. As such, Sabre's price optimization models to date have included user constraints in inelastic situations. Several observations can be drawn from the simple example shown in Figure 2. Results show that the optimal load factor depends primarily on demand uncertainty and elasticity. Demand uncertainties directly impact the expected traffic that influences the total revenue contribution. Elasticity defines the relationship between fare and demand. The relationship shown in Figure 1 is not symmetric due to the underlying nonlinearity of spilled demand. This illustrates that the revenue risk increases with aggressive demand stimulation from lower fares, especially in situations where the underlying demand is highly uncertain (such as with a new market or service). The optimal pricing strategy seems to depend heavily on an airline's forecasting ability and the underlying responsiveness of its customers to fare changes. Illustrative Network Example To further illustrate the concept of optimal load factors, consider a separate example using the 48-leg network shown in Figure 3. The network consists of 10 cities and 534 origin-destination (O&D) fare classes. Table 2 presents detailed information about the example. Figure 3: Network for illustrative example. Table 2: Network example data. To determine the impact of simultaneous YM, scheduling and pricing on a network example, the nine original pricing/demand scenarios presented in Table 1 were considered. A unique pricing structure and associated market demand distinguish each scenario. The following procedure was used for each scenario to illustrate the impact of coordinating YM, scheduling and pricing activities: Perform only YM optimization to maximize the expected revenue due to the allocation of aircraft seats to O&D fare classes (using base case fares and fleet assignment). Identify scheduled capacity adjustment opportunities (denoted as FAM for "fleet assignment model") using a network-based capacity assignment model that explicitly incorporates the O&D passenger flows (Sabre's O&D FAMTM) to maximize total expected network revenue [8]. Identify specific pricing opportunities for both cases listed above based on traffic generation, dilution due to fare changes and displacement due to changes in spill. Figure 4 presents the results of the procedure outlined above and clearly shows the impact of coordinating YM, scheduling and pricing activities. The relationship labeled (0), which represents the case in which no YM is performed and serves as a base case for this illustration, essentially represents a "first-come first-served" scenario. The relationship labeled (1) represents the case when only YM is performed to maximize the total revenue. The relationship labeled (2) shows the impact of simultaneously considering YM and pricing optimization to maximize total revenue. Relationship (3) shows the impact of combined YM and scheduling. Relationship (4) shows the results of simultaneously considering YM, scheduling and pricing. Figure 4: Results for 10 city — 48 leg network. The results presented in Figure 4 provide some interesting insights into the interactions between YM, scheduling and pricing. Revenue opportunities associated with coordinating YM and scheduling appear to be greater than those opportunities associated with pricing alone. There are three possible reasons for this result. First, model recommended price changes were limited to a maximum change of +/- 15 percent. This action avoided over-extrapolating from the original fare level, which would be a very real danger in an actual implementation. Second, coordinating YM and scheduling decisions involves altering the capacity and corresponding traffic flow throughout the network. Because changes in the capacity distribution throughout the network allow for a much larger redistribution of the passenger flow throughout the schedule, YM and scheduling coordination have a larger impact. This result may explain why airline industry efforts to model these two business processes are so well advanced. Third, the results may be specific to the demand assumptions and prevailing fare levels of the markets used in this example. In practice, the results may differ. However, although the increases associated with coordinating pricing are smaller in this example, they still show promise for improving an airline's performance. The results of this network example also show that the revenue contribution has a maximum. As price levels for each discount itinerary decrease, the total expected revenue increases to a maximum (then declines). As pricing levels for each discount fare class decrease, the associated demand increases. Thus, the total expected traffic increases. Solutions left of the optimal represent cases in which the average available resources are underutilized. In these situations, pricing levels are too high, and the resulting market demand is low. Solutions to the right of the optimal represent pricing levels in which the demand for discount itineraries is high, but their associated prices are too low. Because the coordination of scheduling with YM and pricing involves the use of discrete aircraft capacities, the contribution versus load factor relationship is no longer a smooth curve. Therefore, changing the capacity distribution throughout the network can significantly impact the total revenue contribution. This results in the somewhat erratic form of the relationships labeled (3) and (4) in Figure 4. Another way to view these results is that coordinating YM, scheduling and pricing controls into the optimization model introduces additional degrees of freedom to the control process. Additional degrees of freedom produce more opportunities to better balance service, supply and demand. As a result, the solution efficiency with respect to resource utilization increases. This perspective is illustrated in Figure 4 by an increase in the optimal load factor as coordination among the planning activities increases. This characteristic is similar to the effect of reducing the coefficient of variation (CV) in the single leg example. For the network case, added degrees of freedom allow the model to more effectively control the uncertainty in the O&D itinerary demand by intelligently altering the capacity and pricing structures as needed to maximize the expected revenue due to YM. The coordinated YM, scheduling and pricing model does this by reallocating low value capacity to high value markets not already served and by adjusting the pricing strategies to better match the YM process. Conclusions The results presented in this paper illustrate that the simultaneous consideration of YM, scheduling and pricing increases the quality of the overall solution, as evidenced by a substantial increase in total revenue contribution. These revenue opportunities are a direct result of increasing the degrees of freedom the model has to react to service, supply and demand imbalances. Unfortunately, solving the problems simultaneously is a different paradigm than practiced at today's airlines, and it necessitates powerful computer-driven optimization models. Currently, airlines do not have the tools to approach planning in an integrated framework. Today this process has been decomposed into three distinct and separate activities: fleet assignment, pricing and yield management. This approach leads to sub-optimal overall performance and organizational tensions between the groups charged with capacity planning, pricing and yield management. However, even without extensive model-based analysis capabilities, airlines can use the optimal load factor concept to improve their performance by merely identifying flight legs with exceptionally high or low load factors. Once identified, a manually coordinated YM, scheduling and pricing approach can be used to adjust pricing controls and capacity assignment so that the total expected revenue is maximized (or at least improved). The approach presented in this paper shows that benefits are maximized only when capacity planning, pricing and yield management processes are coordinated. Otherwise, revenue opportunities are missed. To accomplish this, a system-wide, O&D-based view of the problem is recommended. Research and development currently being done at Sabre focuses on the integration of the scheduling, pricing and yield management processes to improve the overall performance and effectiveness of an airline's schedule. Challenges to Integrating Scheduling, Pricing and Yield Management By Tim Jacobs, Richard Ratliff and Barry Smith While most, if not all, airlines recognize the potential benefits of greater integration of planning and marketing, achieving a high level of integration is not a simple matter. In many ways, barriers to effective integration are a result of the separate evolution of scheduling, pricing and yield management departments within the airline. These barriers include legacy decision-support systems not designed to share information with other processes, independent and isolated data sources, and differences in planning horizons and the type of data used by each group. At many airlines throughout the world, existing systems used within the scheduling, pricing and yield management departments are unable to communicate directly with one another. This limits the amount of information that can be effectively exchanged between departments and can isolate decisions made by each group. This problem is exacerbated by data requirements and planning horizons of each group. While the scheduling process uses historical and aggregated market data to finalize an airline's schedule approximately six months prior to departure, pricing and yield management decisions take effect from three months prior and continue through the day of departure, and they are based on current bookings and expected additional demand. We view airline planning and marketing as a continuous process that requires an exchange of data and feedback between scheduling, pricing and yield management. Three major steps constitute this process: enterprise planning, product planning, and tactics and operations. The table below summarizes these steps in terms of relatively simple tenets. First, the objective is the same across the planning horizon. Second, the scope of decisions is limited as departure approaches. Third, decisions made in one step often become constraints in the next. Models operating in one step must anticipate the effects of the downline processes. For example, the models run in the Product Planning step (for example fleet assignment) must anticipate the actions of pricing and yield management in order to estimate the revenues associated with a potential schedule. Coordinating these activities leads to a better balance between overall system demand and supply. To overcome the current challenges, airlines need to: 1) enhance their existing systems to better communicate with other business processes, 2) provide feedback mechanisms to improve the decision-making process and 3) make sure the models used for decision support are consistent throughout the planning horizon. Although these are big steps, many airlines are now moving in this direction by developing large "data warehouses," moving toward more robust O&D-based planning systems, and modifying their business process to allow for profitable schedule modifications near the day of departure. Even with today's efforts, it will be many years before airlines have a fully integrated business process. References J. Abara, 1989, "Applying Integer Linear Programming to the Fleet Assignment Problem," Interfaces, Vol. 19, pp. 20-28. G. Gallego and G. van Ryzin, 1997, "A Multi-Product Dynamic Pricing Problem and Its Application to Network Yield Management," Operations Research. Vol. 45, pp. 24-41. S. S. Kretsch, 1995, "Airline Fare Management and Policy," in the "Handbook of Airline Economics," D. Jenkins (ed.), The Aviation Weekly Group of the McGraw-Hill Companies, New York, N.Y., pp. 477-487. J. I. McGill and G. van Ryzin, 1999, "Revenue Management: Research Overview and Prospects," Transportation Science. Vol. 33, No. 2, pp. 233-256. R. A. Rushmeier and S. A. Kontogiorgus, 1997, "Advances in the Optimization of Airline Fleet Assignment," Transportation Science. Vol. 31, No. 2, pp. 159-169. B. C. Smith, J. F. Leimkuhler and R. M. Darrow, 1992, "Yield Management at American Airlines," Interfaces, Vol. 22, pp. 8-31. B. C. Smith, R. M. Ratliff and T. L. Jacobs, 1997, "Optimal Load Factors: Coordinated Schedule, Pricing and Yield Management Decisions," AGIFORS Symposium. B. C. Smith, E. Johnson and T. L. Jacobs, 1997, "O&D FAM: Incorporating Network Effects into the Fleet Assignment Process," Internal Report, Sabre Inc. B. Vinod, 1995, "Origin and Destination Yield Management," in the "Handbook of Airline Economics," D. Jenkins (ed.), The Aviation Weekly Group of the McGraw-Hill Companies, New York, N.Y., pp. 459-468. P. S. You, 1999, "Dynamic Pricing in Airline Seat Management for Flights with Multiple Legs," Transportation Science. Vol. 33, pp. 192-206. Tim Jacobs is a manager in the Operations Research and Decision Support Group at American Airlines. Prior to joining AA, Jacobs was a manager in Sabre's Flight Scheduling Development and Research Groups where he led the development and implementation of Sabre's patented O&D Fleet Assignment Model (O&D FAMTM). Richard Ratliff is vice president of technology and product integration at Sabre and is responsible for coordinating the OR model and data interactions among Sabre's airline applications. His primary expertise is in the area of yield management forecasting and optimization modeling. Barry Smith is senior vice president for Research at Sabre. Smith is an internationally recognized expert in yield management and reservation system design. He developed many of the yield management techniques used throughout the airline industry and pioneered the application of yield management techniques in other industries. Smith is the president of the Airline Group of the International Federation of Operational Research Societies (AGIFORS). 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