Improving Revenue Management Decision Making for Airlines by Evaluating Analyst-Adjusted...

INTRODUCTION

Revenue management (RM) is the process of selling the right type of capacity to the right customer, at the right price, at the right time (Smith, Leimkuhler, & Darrow, 1992). The process involves rationally pricing and controlling reservations of perishable assets across market segments to maximize revenue (Cross, 1997; Baker & Murthy, 2005). A number of service firms reported significant increases in profitability due to RM. American Airlines reported approximately a 4-5% increase ($1.4 billion over 3 years) in revenue (Smith et al., 1992; Cook, 1998). Oliveira (2002) discussed improved consequences on the Brazilian Rio de Janiero-Sâo Paulo route due to RM. Hertz car rental reported a 5% increase in average revenue per rental (Carroll & Grimes, 1995). Chevy's Mexican Restaurants experienced a similar increase in revenue (Kimes & Thompson, 2004). Due to such laudable results in the airline, car rental, hotel, and restaurant industries, the concept and practice of RM-the focus of this article-is increasingly gaining the attention of other service industries such as performing arts, media and broadcasting services, professional services, and even hospital services (Wirtz, Kimes, Theng, & Patterson, 2003).

RM research in the airline and hotel industries focuses primarily on different allocation methods for developing future rate and availability controls for a relatively fixed inventory mix (Baker & Collier, 1999; Kimes & Thompson, 2004). Required inputs include passenger demand forecasts for different predetermined fares (rates) for different lengths of usage (origin-destination, flight legs, or length of stay; Kimes & Thompson, 2004) and overbooking levels. RM research also explored new areas such as auction-based models (Baker & Murthy, 2002, 2005) and order-driven production systems (Barut & Sridharan, 2005). In the demand forecasting area, RM research investigated new ways of unconstraining demand data (Weatherford & PoIt, 2002; Zeni & Kenneth, 2004). By means of actual booking data from a major U.S. airline, Weatherford and Poll (2002) showed that upgrading the unconstraining process can lead to revenue gains of 2-12%. Baker, Murthy, and Vaidyanathan (2002) studied the forecast allocation problem accounting for dependence between demand and availability of various hotel service packages. New ways of optimizing the RM seat allocation problem included research in areas such as origin and destination-based RM (Colville, 1996) and new heuristic decision rules such as leg-based bid price (Weatherford & Belobaba, 2002). RM research also looked at advanced models that account for customer diversion from one product to another (Belobaba & Weatherford, 1996) and aspects of competitively aware pricing (Gorin & Belobaba, 2004; Ratliff & Vinod, 2005). Additionally, prior research has emphasized the importance of integrating RM with customer relationship management (CRM) (lieberman, 2002; Noone, Kimes, & Renaghan, 2003), e-commerce (Boyd & Bilegan, 2003), and project management issues in implementing new RM models and systems (Swift, 2002; Skugge, 2002; Clarke, 2004).

While RM research strives to include ever-more sophisticated modeling into RM systems, those ultimately responsible for translating model recommendations into real world business decisions are, in many cases, unable to interact effectively with these complex systems (Belobaba, 2002). Belobaba expresses concern that the growing gap between RM system complexity and actual decision making may shape a future in which the adoption of new RM tools is slowed, the impact of these tools falls short of its promise, and the credibility of RM professionals is questioned. He stresses that incremental gains from addressing the shortcomings of existing RM systems are almost certainly greater than those of new technologies. For example, in the airline industry, improving forecasts, and thus their adjustment decisions, can be critical because the gains from improving the forecasts in existing leg-based RM systems can rival those of implementing complex RM optimization models (Belobaba, 2002). This article develops a method for assessing the value of forecast adjustment decisions made by RM analysts (RMAs) for airlines. Based on such a development, the article then discusses how the RM daily decision-making process can improve through human interventions to computer models. Thus, our study addresses an interdisciplinary problem at the intersection of human decision making and RM.

The RM System (RMS) in the Airline Industry

Airlines use two fundamental approaches to carry out the RM process: either manipulation of the release of inventory at fixed price points or manipulation of price at different times (Bitran & Caldentey, 2003). The former approach assumes that prices or fares are fixed and the managers and RMAs are in charge of making decisions regarding opening (selling) or closing different fare classes as demand evolves (Weatherford & Bodily, 1992). The second approach dynamically adjusts price as the demand evolves (Gallego & van Ryzin, 1994; Feng & Gallego, 2000). Our work relates to the former approach.

The key to successful seat control in an airline is to limit sales to low-revenue passengers to protect space for more profitable passengers who normally buy close to departure. To do this, airlines must forecast high numbers (sometimes in the millions) of high-revenue passengers for all flights. The process of proper seat allocation is widely known as the seat-mix problem in the airline industry (Belobaba, 1987). The seat-mix problem is complex because demand changes dynamically as bookings are made sometimes over a year before a flight departs. In addition, customary airline fare changes and control policy (viz. advance purchase restrictions, discounts, etc.) complicate the process of estimating passenger demand. Airlines use a computerized reservation system (CRS) that attempts to prevent discount passengers from taking too many seats from the higher fare passengers. An RMS attempts to maximize the expected revenue of a flight by properly allocating the number of seats available at each fare in the CRS. In doing so, an RMS ideally attempts to minimize the number of high-fare passengers turned away. The daily operation of generating a good solution for the seat-mix problem is widely known as RM or yield management practice in the airline industry.

This article is organized as follows: In the next section, we discuss the research problem. This section also highlights the objectives and contributions of this article. The third section presents a generalized framework of the passenger demand forecasting process adopted by many airlines. The following section proposes a practical RMA-friendly method to resolve the problems related to forecast performance analysis. The fifth section reports results and analysis from a major airline's dataset. The last section provides conclusions, managerial insights, and future research directions.

RESEARCH PROBLEM AND OBJECTIVE

RM is heavily dependent on accurate passenger demand forecasting and its subsequent monitoring (McGiIl & van Ryzin, 1999; SABRE, 1999). Cutting forecast errors can significantly increase expected flight revenues when demand exceeds capacities (Weatherford & Belobaba, 2002). To avoid the complex cycles of forecasting and optimization, van Ryzin and McGiIl (2000) proposed a new RM approach that directly updates booking policy parameters for the next departure based on simple observations of booking records. However, more research is needed to provide theoretical guarantees on the long-run performance of approaches that do not target forecasting improvements.

Machine-based RM processes almost universally allow regular (human) RM interventions in business-critical markets before a flight departs, because complete analyst knowledge cannot be captured in the historical data used by the forecasting system. In addition, most RMS, although tuned to provide the best overall forecast, have flaws that appear in particular markets and time periods. Forecasts often cannot accurately predict seasonal transitions, either because they react too rapidly (treating the season change as a step function) or too gradually. RMAs often adjust the system forecasts to improve revenue, but due to the enormous number of flights, must be selective in how they intervene. One RMA may handle up to 200 flights per day, from about 350 days prior to departure and for dozens of fare products. Because of this, they concentrate on critical flights and/or critical time periods prior to departure. They may not intervene on some flights at all, or they may make broad-brush adjustments that work well on most important flights and time periods but do not provide uniform improvement in less critical ones.

Previous RM research paid little attention to RMA adjustments. One such study (Zeni, 2003) attempted to isolate the impact of analyst adjustments on revenue from all US Air flights in a single day. However, conducting the experiment on the live flights carried a revenue risk to the airline, thereby imposing many restrictions on the experimental procedures. In addition, the study did not focus specifically on forecast adjustments.

What Makes a Good Forecast?

How does an airline choose which forecast will work best for it? Conceptually, the best forecast is the one that produces the highest revenue. However, there are many operational problems with this definition. Designing an experiment that measures revenue impact is costly and likely prone to errors and biases. Finding a valid control group usually defeats any effort to define a real-world experiment testing the impact of two different forecasts. No two markets are ever quite the same, nor are two time periods ever quite the same in a market. Simulation methods to determine the revenue impact of different forecasts are sensitive to the assumptions and simplifications of the simulator. Thus, in practice, the evaluation of different forecasts is generally made on forecast accuracy. This is because the more the forecast diverges from the true demand, the more seats are sold to the wrong customer or are not sold at all.

Research Problem

RM prefers forecasts of true passenger demand as input to a seat control optimizer as opposed to observed demand. True demand is the observed demand plus any demand denied due to the closure of a fare product. RM aims to utilize any revenue opportunity that may exist in accounting for denied demands from one flight to the next. This causes a major difficulty in the decision-making process of RMAs and managers, who have no way of knowing how well they forecast the true demand of a product closed for sale. The true demand of a flight product is estimated using the historical bookings of the same product. The process of estimation is complex and may depend on many factors that can vary highly across fare products. The main problem is in assessing the accuracy of the forecast adjustments. RMAs must overcome the problem of comparing two different things-forecasts of true demand with observed demand. When adjusting forecasts, RMAs usually guess true demand without any systematic feedback.

Having this feedback is critical when decisions are made repeatedly for the same problem. Whalen and Samaddar (2001 ) state that an iterative decision-making process involves Simon's (1959) three phases of problem solving: intelligence, design, and choice. The intelligence phase, specific to the decision-making process of an RMA, involves his or her knowledge of the micro-market, overall demand trends, and knowledge of consumer behavior relating to the flight at hand. The design phase involves creating all possible adjustments in potential demand. This phase also provides subsequent guidance regarding seat release or blocking to maximize revenue. Finally, in the choice phase, the decision maker (RMA) picks one adjustment based on the criterion of revenue maximization. The learning process starts and repeats through a feedback mechanism that helps the RMA assess how well the previous decision fared.

Research Objective

In theory, analysts can exploit news of events not captured in the historical data used by the demand forecasts to adjust and improve their accuracies and thus increase revenue. In practice, RMAs rarely consider their jobs to be improving forecast accuracy. Often, they make adjustments because it is a convenient way to change seat allocation, whether this improves the forecast or not. In this research, we attempt to explore whether analyst forecast adjustments actually improve the forecast and to investigate whether the improvements are well targeted. Broadly, can we measure whether the combination of man and machine is better than machine alone?

We propose a heuristic-based approach to resolve the issue of how to generate a reasonable comparison of observed demand and forecasts for true demand. The method enables feedback for how well a previous forecast and its adjustment worked into the intelligence phase of the next RM decision. Thus, the proposed method contributes significantly to the daily RM decision-making process in airlines and other similar service industries that deal with managing perishable assets. To the best of our knowledge, this is the first study to do so.

DEMAND FORECASTING AND FORECAST ACCURACY

Demand forecasting predicts the number of passengers expected to fly on each combination of itinerary and fare category (Colville, 1996). A major airline can have thousands of unique fare categories or products because, on a very fundamental level, values to variables (such as city-pairs, number of stops, advance purchase requirements, Saturday restrictions, time of day [red-eye flights, etc.], sale fares, competitor pricing, and other market conditions) give rise to thousands of unique fare products. At the most detailed level, one distinct fare product is known in the airline industry as fare basis code (FBC). However, in handling the seat-mix problem, to avoid computational complexity and time consuming reservation decision making, airlines do not deal with the thousands of unique FBCs. Instead, airlines cluster these FBCs into a more manageable number of classes, called buckets, in each cabin based on the fare product's economic value. From the airline's point of view, due to differences in attributes of itinerary such as origin and destination, time of the day, and so on, passengers in the same fare class on the same flight are not equally valuable. RM generates forecasts and seat availability numbers at bucket levels.

A Generalized Framework of Forecasting

Usually, forecasts for a flight are made on the basis of unconstrained demand (an estimate of true demand) during a set of time interval periods for a group of similar flights in the same market. If a flight product is open for sale, the observed booking for the product during the period is equal to unconstrained hnnkina

Let us say, for example, the forecast date/tf is Oct 16, 2006, Monday, for a flight departing in 14 days on Oct 30,2006. The RMS forecasts for two incremental intervals: 14-7 and 7-0. IfRMAs choose the value of N = 8, historical bookings from eight most recent flights (Oct 23, Oct 16, Oct 9, Oct 2, Sep 25, Sep 18, Sep 11, and Sep 4, all in 2006) will be used for 14-7 incremental forecast. The incremental forecast for the interval 7-0 is generated from historical bookings from eight most recent flights: Oct 16, Oct 9, Oct 2, Sep 25, Sep 18, Sep 11, Sep 4, Aug 28 in 2006. The system computes final forecasts by adding the incremental forecasts of intervals 14-7 and 7-0 with bookings on hand up to Oct 16,2006 all the way from DL = 350.

PROPOSED APPROACH OF FORECAST ADJUSTMENT ASSESSMENT

Accuracy Measurement Levels

Monitoring forecast accuracies based on buckets could sometimes involve low demand numbers, because some of the high revenue buckets may not observe any bookings at all in many flights. Percentage forecast error for these buckets will be high even if there is only one seat difference between the actual value and the forecasted value. Therefore, it is better to evaluate forecast accuracy in terms of critical booking threshold (CBT), which represents the sum of the bookings in a bucket and all higher-valued buckets above. The calculation for the thresholds starts with calculating the cumulative percent of bookings for each bucket. Let us assume that that there are 16 (a realistic assumption based on two of the authors' experience in two top airlines in the U.S.) buckets in coach class, Yl through Y16, with Yl being the highest-revenue-yielding bucket and Y16 the lowest. Table 1 illustrates an example of CBT.

The total or cumulative bookings for a cabin are accumulated at the bucket level from Yl to Y16. Using these bookings for a cabin, the cumulative percent of bookings in each bucket is calculated.

Next, we select the buckets with the top percentiles in terms of revenue to be measured. We define the booking top percentile thresholds as 10%, 25%, 50%, 75%, 90%, and 100% of cabin bookings. The percentile levels may vary from market to market depending on RMA experience. The bucket selected is the first bucket that is greater than or equal to the percentile to be measured (fifth column in Table 1). This also means that when a bucket spans two thresholds, it will be selected for both.

Forecast Accuracy Measures

We measure mean absolute error (MAE) and bias for all forecasts at the CBT levels. Bias shows whether, on the average, forecasts were under or over the actual unconstrained demand. MAE shows how much, on average, the forecasts were off the truth. We computed bias and MAE at CBT levels.

The Method and Data

There are different approaches to computing forecast accuracy. In one approach, only open buckets are used in the calculation of MAE and bias. The approach uses thresholds in which there are no buckets closed for the calculation of MAE and bias. Top closed bucket (TCB) is the bucket in which the seats available in that bucket are less than or equal to zero and the seats available in each bucket above are greater than zero. The method excludes thresholds at or below TCB from the calculations. All buckets that are part of or below a threshold that has closed buckets will be rejected. If the TCB is at or above the 10% threshold, that observation is excluded for MAE and bias calculations. Because most of the observations from critical flights with high revenue yields are thrown away, this approach does not add any significant value in terms of analysis.

Our approach uses all observations, open or closed. The estimate of total remaining rejected demand is added to the bookings on hand to estimate total unconstrained demand at departure. The unconstrained actual is then compared with the forecasts, adjusted or unadjusted, to compute error statistics. All results reported in this study involve forecasts at DL = 56 to DL = 7 in 7-day intervals. The proposed algorithm for unconstraining the observed actual demand and computing error statistics is given below:

Steps:

i. Collect rejected demand for all intervals to departure beyond forecast dates.

ii. Sum all those rejected demands from step i.

iii. Add summed rejected demands to observed actual at midnight before departure to obtain the unconstrained actual.

iv. Compare this unconstrained actual with forecast to compute error statistics.

We collected data from all flights (103 flight departures) during April 20-26, 2001 departures in a business market of one major U.S. airline. We used eight time-series forecast data. We used seven data points for 15 flight departures that had missing information at DL = 7. We analyzed results at top 25, 50, and 75 percentile CBT levels.

RESULTS AND ANALYSIS

Intragroup Analysis

The top 25% group is the most important group due to its high-revenue-generating demands. Accurate forecasts in this group are critical to generating more revenue for airlines. The top 50% group includes the most important (top 25%) group along with the next quartile. Accurate forecasts are also important in this group to generate more revenue for airlines. The top 75% includes the top 50% group and the next quartile. Forecasts for the quartile (>50% and <75%) are not as important from the perspective of RM practice, because airlines typically want to protect seats for high-revenue passengers. However, underreporting the demands in this group may result in spoilage when too many seats are protected for higher groups.

Top 25% CBT group

Table 2 and Figure l(a) report forecast adjustment accuracy and the cumulative improvement by the RMAs. Unadjusted forecast (also called raw, system or machine forecast) is forecast computed by airline computer models. The mean actual column in Table 2 is the mean value of the estimates of unconstrained actual across all the flight departures in the sample for the top 25% CBT group. For example, at DL = 56 (Table 2), the expected average bookings in the top 25% CBT group in a sample of 103 departures is 53. We computed forecast accuracies (bias and MAE) by subtracting actual from forecast. Thus, a negative bias value of a forecasting system means that the system was underforecasting on the average. Raw bias is the bias without analyst adjustment, while adjusted bias is the bias with analyst adjustment. By inspecting the raw bias and the adjusted bias, we infer that while the system underforecasted, the analyst adjustment caused the forecasts to go up. In other words, the analyst expected to get more business passengers in the market as opposed to the system forecasts. For example, at DL = 56, the raw bias is -22.27 and the adjusted bias is 26.3. Two statistics-raw MAE and RMA adjusted MAE (26.3 versus 25.26)-justified the value of adjustments, which improved forecasts. The window of opportunity to improve forecasts and revenue is mostly between DL = 56 and DL = 28 before advanced purchase restrictions into passenger ticket come into play. By then, the airline has already accounted for most of its low-fared passengers. Analysts definitely improved the forecasts in the window of opportunity, whereas system forecasts generally did well for windows closer to departure (cumulative improvement statistic CI in Table 2). For example, for DL = 56, RMA adjustment is approximately one passenger better than the system forecast on the average for 103 departures. The analysts adjusted forecasts for many flights (% of system forecasts changed or statistic PC in Table 2). This may indicate that either RMAs have little confidence in the system forecast, or too often they want to change the protection levels by adjusting the forecasts. From DL = 56 to DL = 21, RMAs improved machine forecast more than 50% of the time they adjusted (% of improved adjusted forecast statistic FI in Table 2). The performance of analysts close to departure (DL = 7) is inferior to system performance. The analysts should learn from their mistakes and apply their knowledge for future forecast adjustments. Sometimes the average improvement in forecast by the analysts is more than one high-revenue passenger (for example, 1.05 at DL = 56). The improvement is extremely valuable from an RM point of view. Frequency of improvement in the adjusted flight forecasts is also high in the window of opportunity. Interestingly, adjustment accuracy declined when RMAs had more information about the flights at DL < 21. In the very close-in period, forecast accuracy is strongly impacted by cancel-down and passenger-churn (one passenger booking while another cancels). This tends to distort measurement. Through the application of our assessment method, RMAs can now recognize that they should adjust forecasts in the opportunity window of 56 to 28 for future flights.

Top 50% CBT group

Table 3 and Figure l(b) report the results of RMA forecast adjustment accuracy and the cumulative improvement. We infer that while the machine underforecasted, the analyst adjustments made the forecasts go up. Analysts were definitely improving the forecasts in the window of opportunity (improved MAE statistic from DL = 56 to DL = 28). The analysts clearly adjusted forecasts for several flights (PC statistic in Table 3), indicating their low confidence in the system forecasts. However, the performance of analysts close to departure (DL = 7) went down significantly. Sometimes, however, the average improvement in forecast by the analysts is more than 10 high-revenue passengers (for example, 10.08 at DL = 56). The improvement is also valuable from an RM point of view. The frequency of improvement in the adjusted flight forecasts is also high in the window of opportunity. Interestingly, the adjustment efficiency went down again at DL < 28 when analysts had more information about the flights.

Top 75% CBT group

Table 4 and Figure l(c) report the results forecast adjustment accuracy and the cumulative improvement. While the system underforecasted, the analyst adjustment generally caused the forecasts to go up. Analysts definitely improved the forecasts in all windows of opportunity. The analysts clearly adjusted forecasts for many flights, generally indicating their low confidence in the system forecasts in this market. However, performance of analysts close to departure (DL = 7) went down quite a bit. Sometimes the average improvement in forecast by the analysts was more than 10 high-revenue passengers (for example, CI = 12.08 at DL = 56). The frequency of improvement in the adjusted flight forecasts is also high in the window of opportunity. The adjustment accuracy went down again when the RMAs had more information about the flights at DL < 28.

Intergroup analysis

Figure 2 compares adjusted biases of all groups. The variance in adjustment bias is more from the high-revenue group than the less lucrative groups of 50% CBT and 75% CBT, in that order. This is possibly due to more caution applied for the most lucrative group. Overall, the best performance for any group happens sometime in the middle of the timeframe (i.e., between 35 and 28 DLs). Performance is worst early and close to departure. Analysts over-forecast early and underforecast late. One reason for this pattern may be due to RMAs' decreasing optimism about consumer demand as time nears departure in this market. However, this pattern, consistent across all three groups, emphasizes the importance of feeding back the information to the next round of decision making for the same flights at a future date in order to take the necessary steps to correct the pattern.

The dispersion among the performances for the three groups is wider close to flight departure. Consequently, more corrective actions may be necessary for future adjustments by the RMAs for higher CBT groups than lower CBT groups.

CONCLUSION

Creating accurate demand forecasts is critical to the success of airline RMS. Forecast errors translate directly into turning away high-value passengers because lowvalue passengers booked earlier, as well as turning away passengers and flying with empty seats. If RMAs can reliably improve system-generated forecasts on critical flights at critical times, airlines can generate significantly more revenue. Measuring forecast accuracy is complex because true demand is not observable when fare products are closed for sale. For various reasons, including RMA expertise in understanding specific markets, flaws in the system forecast, and information affecting demand that is not captured in history, we can hope that RMAs provide added accuracy, and therefore, value. This research shows that improvements are real, especially in the critical period when the majority of low-value passengers are booking.

Improving Decision Making in RM

Our study proposed a simple method by which RMAs can determine in which markets they are performing better than the system forecasts and in which markets they are not. Such findings, or feedback, are critical to improving decision making. By learning from their mistakes, RMAs can realize even more revenue from available opportunities.

Theories of decision making (Simon, 1959) recommend that the decisionmaking process be iterative and cyclical, involving three phases of problem solving-intelligence, design and choice-as shown in Figure 3(a). Without our method of assessment, RMA decision making for forecast adjustments is based solely on the micro-market intelligence. However, in the absence of a feedback loop [Figure 3(a)] from the adjustment choices made in the prior cycle, the information regarding how well those choices performed is lost. Thus, the inventory adjustment decisions in the next cycle do not benefit or learn from any new intelligence gathered from the current cycle. We propose an intelligence-gathering loop [Figure 3(b)] for the next cycle. The learning from such feedback need not be limited to one fare class, one flight segment, or one market. Consequently, with the addition of more feedback loops, cumulative learning is now possible [Figure 3(c)]. This accumulation of feedback and learning may result in better intelligence, design, and choice for RM decisions.

Managerial Implications

One of the most difficult problems in RM is the creation of measures that show whether RMAs are performing well, and RMAs' lack of control over the many factors that impact overall revenue in their markets. From an executive management perspective, the RM department's primary goal is to increase revenue. A competitor adding flights in a market or a fare can drastically decrease revenue in even the best-managed markets. More often than not, revenue fluctuations hide the impact of RMA adjustments. The most significant implication of a forecast accuracy measure is that it is an important step toward creating a significantly better measure of RMA performance. The best opportunity for RMAs to improve a forecast is precisely when the market is undergoing major changes, such as when a competitor adds flights. During those times the system will perform badly because the history it depends on for forecasting does not represent the new state of the world.

Because our proposed method can be used to evaluate adjustments made by RMAs, it provides a step toward building future approaches to evaluate analysts' contributions to revenue gains or losses. Such a use has implications beyond RM and the RMA decision-making process-it can help measure an individual RMA's performance and thus shape human resource planning and incentives by the airlines. As Zeni (2003, p. 38) points out: "Ideally, airlines would like to measure the value of their analysts' contribution. This information could be used to refine business practices, provide feedback to the analysts and measure individual performance." On a subject related more to the human resource decisions made by airline management, Zeni (2003 p. 38) states: "Ultimately, if the value of each additional analyst were known, an airline could optimize its staffing levels by increasing the analyst headcount until the compensation of an analyst exceeded his or her marginal revenue contribution." Our work can make such evaluation possible for RM.

Future Research

An airline can try a few different approaches to correct the incompatibility between the forecast and the actual in measuring accuracy. One approach would be to eliminate observation where the actual is constrained. We did not adopt this approach because the method does not account for the deleted observations in computing forecast accuracy. Thus, by eliminating the high outcomes on demand, this method creates a bias in the accuracy measurement. Our method keeps all forecasts to compute accuracy measures. We unconstrained the actual by the amount of rejected demand-the number of customers who were turned away. The justification for using this method is that if an airline has settled on the best method of estimating rejected demand, it makes sense to use it in both the forecast and the accuracy measurement. In another approach, one can constrain the forecasts to the number of seats available for booking. In this approach, consistently high forecasts may appear more accurate. For example, if the actual booking is constrained at 10, then forecasts of 10, 12, and 22 will all be constrained at 10, and thus the accuracy of each of these three forecasts will be perfect. This bias can manifest in several different ways. This is easily apparent in a case in which two different forecasts are being compared-one that is controlling the flights and a potential new one. The new forecast is measured as more accurate even if it is consistently high. One of the major aims of future research is to determine whether these biases from different methods are significant in an experiment with live airline data given the amount of variability in a real situation and what differences might appear in using the different methods. The value of forecast adjustment can also be extended to a more rigorous analysis of translated revenue dollars for airlines. [Received: March 2006. Accepted: February 2007.]