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MULTINOMIAL AND NESTED LOGIT MODELS OF AIRLINE PASSENGERS’ NO-SHOW AND STANDBY BEHAVIOR Laurie A. Garrow, Ph.D.* Georgia Institute of Technology School of Civil and Environmental Engineering 790 Atlantic Drive, N.W. Atlanta, GA 30322-0355 Ph: (404) 385-6634 Fax: (404) 894-2278 Email: [email protected] Frank S. Koppelman, Ph.D. Department of Civil and Environmental Engineering Robert R. McCormick School of Engineering and Applied Science Northwestern University 2145 Sheridan Road Evanston, IL 60208-3109 Ph: (847) 491-8794 Fax: (847) 491-4011 Email: [email protected] Paper accepted to Journal of Revenue and Pricing Management AGIFORS YIELD MANAGEMENT CONFERENCE – ISSUE 3.3 First submitted: May 16, 2004 Last updated: July 21, 2004 Laurie A. Garrow is an Assistant Professor of Civil and Environmental Engineering at the Georgia Institute of Technology. Prior to joining the faculty, she worked in the Research and Development Revenue Management Group for a major U.S. carrier where she was involved in developing new no-show models. Her research interests include modeling travelers’ behavior using passenger information and developing efficient estimation methods for advanced discrete choice models. Frank S. Koppelman is a Professor of Civil and Environmental Engineering at Northwestern University. His research interests include the development and application of advanced logit models to the study of travel demand and the development of activity based travel demand models. He has published several papers related to air traveler preferences for carriers, schedule, and fare classes. Koppelman is a former Associate Editor of Transportation Research Part B, former Chairman of the Transportation Research Board Committee on Travel Demand Analysis and Forecasting, Emeritus Member of the Transportation Research Board, and a recipient of the International Association for Travel Behavior Research’s Lifetime Achievement Award.

*

Corresponding author.

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MULTINOMIAL AND NESTED LOGIT MODELS OF AIRLINE PASSENGERS’ NO-SHOW AND STANDBY BEHAVIOR

Abstract

This study models airline passengers’ no-show and standby behavior using passenger and outbound and inbound itinerary information. We describe factors that influence no-show and standby behavior in continental U.S. markets using multinomial and nested logit models. Our model accounts for early standby opportunities on other itineraries flown by the carrier of interest, i.e., it incorporates information about booking levels on the carrier’s itineraries departing on the same day. Empirical and validation analyses highlight the importance of distinguishing between outbound and inbound itineraries.

We conclude by describing a

framework carriers can use to implement our no-show model.

Keywords: No-show; demand forecasting; air traveler behavior; rescheduling behavior; nested logit

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INTRODUCTION The airline industry is very dynamic. Even though the number of airline passengers has returned to its pre-September 11th level, the structure of the industry has changed dramatically and airlines have become even more intense about their search for ways to control costs and increase revenues. Faced with competitive pressure from low-cost carriers, network carriers seek to develop more sophisticated revenue management algorithms that incorporate competitive information. Central to all these models are assumptions about how individuals choose carriers, flights, and fares. Ironically, few airlines use passenger data or directional itinerary information in forecasting models. For example, there are only two published studies we are aware of (based on decision tree methods) that use passenger data to forecast no-show rates (Kalka & Weber, 2000; Pastor, 2000). This study advances the state-of-the-art in airline forecasting models by using discrete choice models that incorporate passenger and directional itinerary information. Multinomial (MNL) and nested logit (NL) models are formulated and estimated to predict the probability that a booked passenger will show, no-show, or standby for a different itinerary with the carrier of interest. A standby is defined as a passenger who voluntarily takes a different itinerary with the carrier of interest. Early (late) standbys arrive at the airport and board flights that depart earlier (later) than their booked itineraries. Empirical results and a validation analysis demonstrate the importance of incorporating passenger and outbound and inbound information and provide rich behavioral and business interpretations.

For example, the study provides evidence that

passengers use conservative booking strategies on inbound itineraries and may be exploiting “irrationalities” in pricing structures.

One example of a pricing irrationality occurs when it is

cheaper to buy two low-yield round trips than one high-yield round trip. In this case, the

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passenger uses the outbound itineraries of both low-yield tickets and no-shows on the inbound itineraries; thereby obtaining a less expensive fare without consideration of some of the constraints associated with low-yield itineraries such as duration of stay.

This practice is

commonly referred to in the airline industry as back-to-back ticketing. Thus, while advanced algorithms are being developed to account for a low-cost competitive environment, our analysis suggests that airlines should also focus on understanding customer purchasing behavior and their propensity to manipulate irrationalities in the fare structure. The balance of this paper contains six sections. First, the conceptual model of airline passengers’ no-show and standby behavior is described.

Second, the methodology and

estimation data are described. Third, empirical results are presented. Fourth, a validation analysis is presented. Fifth, an implementation framework for our no-show model is described. Finally, major conclusions are summarized.

CONCEPTUAL MODEL This section describes the conceptual model used to analyze airline passengers’ day of departure show, no-show, early standby, and late standby choices; rescheduling decisions that occur prior to day of departure are captured in cancellation data and are excluded from analysis. Four categories are used to describe passengers’ initial booking reservations and inbound and outbound travel decisions. These include traveler characteristics (e.g., booking class, frequent flyer status, number of people traveling together, etc.), familiarity with the air transportation system (e.g., passengers who travel often and are a member of a frequent flyer program are likely to be more familiar with the air transportation system), availability of viable alternatives, and trip

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characteristics (e.g., uncertainty in the duration of a client meeting may lead a business traveler to early standby on the inbound itinerary if the meeting concludes earlier than anticipated). The categories overlap in the sense that traveler characteristics such as price insensitivity and frequent flyer status provide improved access to standby opportunities on the carrier of interest and competitors. Specifically, passengers with high-yield, unrestricted tickets can use those tickets for travel on most competitors. Similarly, elite members of a carrier’s frequent flyer program with boarding priority over general and non-members have more access to standby activities. In addition to providing access to standby opportunities, traveler characteristics can influence the original scheduling activity. Conceptually, price-sensitive travelers buying lowyield fares may search for and make multiple bookings on different carriers. While these fares usually must be paid for (or ticketed) within 24 or 48 hours after the initial reservation is made, the complexity of fare rules makes it difficult for automated data cleaning routines to identify and remove these bookings. Subsequently, these low-yield fares are reflected in no-show rates for outbound travel. This effect is not necessarily observed for inbound itineraries because some airlines (including the one that provided data for this study) use an additional data cleaning routine that cancels the return portion of an itinerary when the passenger no-shows on the outbound portion.

Several practitioners including Ratliff (1998) and Pastor (2000) have

qualitatively or quantitatively noted the importance of including ticketing information in predictive models. [Insert Figure 1 about here]

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In addition to incorporating a rich set of passenger variables, the conceptual framework is innovative in how it represents the availability of viable alternatives and competitive market information.

Availability is modeled by determining which alternatives to include in an

individual’s choice set and by including carrier and competitive schedule information as descriptive variables. When generating choice sets, we assume that the show and no-show alternatives always appear but that the early (late) standby alternative is included only if there is at least one itinerary of the same or higher level of service that arrives earlier (later) than the passenger’s original booked itinerary. In addition, we incorporate schedule information for the carrier of interest by including capacity information (or the number of seats sold in the market) for other itineraries flown by the carrier. These itineraries are scheduled to depart in defined periods before/after the booked itinerary and have a level of service equivalent to or higher than the level of service of the booked itinerary. Competitive information is captured via a variable that measures the carrier’s market presence as a function of the number of flight departures at the itinerary’s departure city relative to those of its top competitor. Departure city presence is modeled as:

 

 

Market Sharecarrier of interest  1 Market Sharetop competitor if Market Sharecarrier > Market Sharetop competitor

2

Market Sharetop competitor Market Sharecarrier of interest



if Market Sharecarrier  Market Sharetop competitor

(1)

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where  is 0.5. Parametric values for  were estimated over the range of 0.4 to 2.0 and 0.5 was found to give good results over a wide range of contexts. Statistically, we find market presence increases the probability a passenger will standby only when the carrier of interest has dominant market share in the departure city (i.e.,  2 is statistically not different from 0). In summary, the conceptual model used to study airline passengers’ no-show and standby behavior is able to explore a broad range of analysis questions because of the availability of disaggregate passenger data. It is interesting to note that some of these effects are significant only when considered in interaction with other variables. For example, schedule variables were statistically significant only when level of service effects were incorporated, the carrier’s departure city presence increases early and late standby rates only when the carrier has dominant market share relative to its top competitor, and capacity on itineraries of the same or higher level of service as the original booking influences early and late standby behavior. Research by Coldren, et al. (2003) related to passengers’ itinerary choices also highlights the importance of incorporating level of service variables relative to market conditions, i.e., they show that the probability of purchasing a connecting itinerary differs depending on whether the highest level of service offered in the market is a non-stop or a connection.

METHODOLOGY Airline passengers’ day of departure rescheduling behavior is modeled using multinomial logit (MNL) and nested logit (NL) models. This section provides a brief description of these models.

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For additional information on MNL and NL models see Ben-Akiva and Lerman (1985) or Train (2003). A description of data and estimation procedures is also included. Finally, we describe data limitations.

Multinomial Logit and Nested Logit Models MNL and NL models are random utility maximizing models that describe how individuals choose one alternative among a finite set of mutually exclusive and collectively exhaustive alternatives. The individual chooses the alternative that has the maximum utility. The utility function for a MNL model is defined as

U ni    xni   ni  Vni   ni where Uni

(2)

is the total utility of alternative i for individual n,

Vni

is the observed portion of the utility,



is the vector of parameters associated with attributes x. Utility is assumed to be a linear in parameters function of attributes x,

xni

is the vector of observed attributes that varies across individuals and alternatives and

 ni

is the unobserved portion of the utility function.

We estimate the utility function of Equation (2) as

Vˆni  ˆ  xni   ni where Vˆni

ˆ

is the estimated value of the observed utility and is the vector of parameter estimates of  .

(3)

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Under the assumption that the error terms is distributed independently and identically Gumbel, the probability individual n selects alternative i is represented by the MNL as follows ˆ

e  xni ˆ . Pni  P i | xni ,   ˆ xnj e





(4)

j

Because the MNL is known to have limitations, e.g., it imposes restrictive substitution patterns across alternatives; the more advanced nested logit (NL) model was also estimated. The NL model groups alternatives that share common unobserved attributes into nests. The utility for an alternative i in nest m can be decomposed into the utility associated with nest m that is common to all alternatives in nest m and the additional utility associated only with alternative i. Suppressing the index for individual n, utility of these nested alternatives is given by

U im  Vi / m  Vm   i   m

(5)

where Uim is the true utility that is composed of Vi/m, the systematic portion of utility associated with alternative i, given nest m, and Vm is the systematic portion of utility associated with nest m. The total error,  i / m   m , is distributed IID G(0,1) which has variance equal to

2 6

. The error

associated with the nested alternatives is distributed IID G(0, 1 / μm) which has variance equal to

 2  m2 6

where μm is restricted to the 01 range. The parameter, μm, often called the logsum or

inclusive value parameter, is a measure of the degree of correlation among alternatives in nest m. Higher values of μm imply less and lower values imply more correlation among alternatives in the nest. A value of μm=1 for all nests is equivalent to a MNL model (no correlation across alternatives). The probability that individual n selects alternative i is given as:

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Vi / m

Pi  Pi|m  Pm 

e

m

Vj /m

e



m

jm

eVm  m m M

Vm   m m

e

m 1

,

Vj / m    m  ln   e m   jm   

(6)

The first component of the product is the probability of selecting alternative i among all

j alternatives in nest m, conditional on the choice of m, and the second product is the probability of selecting nest m among all nests. The estimation problem is to solve for the vectors of parameter estimates, ˆ and ˆ ,

given a sample of observations using maximum likelihood estimators. An iterative modeling approach guided by judgment and statistics was used to find a preferred model specification; the final model was selected from among 250 estimated utility specifications. All models were estimated using the GAUSS programming language (Aptech). The estimation software was selected to ensure that the NL models are consistent with utility maximization theory. This is an important issue as some commercial software packages use a non-normalized NL model that is not consistent with utility maximization theory unless normalized by the user. See Koppelman and Wen (1998) for a discussion of these normalization differences.

Data Description

Our analysis is based on data from a major U.S. carrier that includes booking, ticketing, flight and itinerary schedule, frequent flier membership class, and check-in information.

Only

continental U.S. itineraries departing in March 2001 are used for model estimation. March was selected because historically it experiences an average or lower than average monthly load

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factor. This results in fewer censored data points, i.e., passengers who attempt to standby but are unable to do so due to non-availability of seats on other itineraries. A second dataset for March 2002 is used for a validation analysis and described in more detail later in this paper. The estimation data are distinguished by whether they represent outbound or inbound itineraries on round trips. One-way and multi-stop itineraries are excluded from the analysis. Likelihood ratio tests were conducted on MNL models to validate the need for separate segments. For example, a “restricted” model, that combined outbound and inbound data, was compared to two “unrestricted” models that used data from only one segment. The likelihood ratio test, formally expressed as  2[ LL(  restricted 

2  LL( unrestricted )] ~  Number of restrictions ,

(7)

segments

rejects the null hypothesis that the restricted model is the true model at a very high level of 2 significance ( ˆ 2  149   34,0.005  59 ).

Sampling Framework and Maximum Likelihood Estimators

Because the carriers’ actual data contains millions of monthly booking transactions with small fractions of no-show, early standby and late standby travelers, a choice-based sample was selected to contain approximately equal choice frequencies across the four choices. This sampling retains a high level of estimation efficiency with substantially reduced computational time/cost.

The outbound segment contains 2,761 observations representing passengers’

outbound itineraries for continental U.S. markets that departed in March 2001. Population choice probabilities for show, no-show, early standby and late standby are 92.7%, 6.3%, 0.89%

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and 0.13%, respectively. Similarly, the inbound segment contains 3,674 observations and has population choice probabilities of 86.9%, 10.0%, 2.99%, and 0.13%, respectively. The number of observations differs for each segment due to the underlying sampling process and data cleaning procedures. The use of a choice-based sample has implications on which estimators can be used to solve for the parameters of MNL and NL models. For MNL models using choice-based samples, it is common to use the exogenous sampling maximum likelihood (ESML) estimator (Manski & Lerman, 1977), which is an efficient estimator that is available in popular estimation software. When MNL models are specified with a full set of alternative specific constants, the ESML estimator produces consistent and efficient estimates of all parameters except for the alternative specific constants; however, since population rates are known, consistent estimators can be recovered for them by subtracting ln (sample/population rates) from the estimated constants. McFadden’s proof of this property is reported in Manski and Lerman (1977). In a separate analysis, we show McFadden’s proof can be extended to NL models (Garrow, 2004). Specifically, we show that consistent estimates for the constants of a two-level NL model can be recovered by subtracting  m ln  sample / population rates  from the estimated constants where

 m is the logsum coefficient associated with nest m, i  nest m , 0 <  m  1 . This is an important finding because the ability to recover consistent parameter estimates for NL models using ESML estimators provides practitioners and researchers with a practical method to obtain estimators which are both consistent and efficient for NL models using choice-based data; prior estimators reported in the literature are inefficient or difficult to implement (e.g., see Manski and Lerman, 1977; Cosslett, 1981; Imbens, 1992).

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Data Limitations

Before presenting empirical results, it should be emphasized that the data used for the study is derived from a single major U.S. carrier. As such, the results presented here will be more applicable to major U.S. carriers than to low-cost or international carriers. Nonetheless, the methodological contribution of using passenger data to predict no-show behavior provides insight into the broad range of managerial and analysis questions that can be answered. Indeed, only by using passenger-level data can we define standby choices, identify passengers’ outbound and inbound itineraries, and explore behavioral differences due to traveler characteristics such as frequent flyer status. To the extent that these factors influence no-show rates and vary across a carrier’s flights, the forecasting benefits of using passenger and directional itinerary information can be generalized to other carriers.

EMPIRICAL RESULTS

We categorize variables used to describe passengers’ rescheduling behavior as flight/itinerary and passenger variables. Flight/itinerary variables include dummy variables for the itinerary’s departure day of week, departure time period, and itinerary duration. Also included are carrier capacity and carrier presence measured at the itinerary’s departure city. Passenger variables include dummy variables for e-ticket purchases, booking class, frequent flyer status, and group size (or the number of people traveling together on the same booking record; for this analysis we examine people traveling in alone or in groups of up to 10 travelers). This section first describes how these variables influence airline passengers’ no-show, early standby, and late standby

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behavior and then explores differences between MNL and NL models. Table 1 summarizes MNL and NL models discussed in this section. See Garrow and Koppelman (2004) for a more detailed discussion of empirical results based on MNL models, including an analysis of changes in standby behavior due to the events of September 11, 2001. [Insert Table 1 about here] No-Show Results

No-show behavior is best explained by passenger attributes, including e-ticket indicators, booking class, frequent flyer status, and group size. As shown in Table 1, e-ticket is a very powerful predictor of no-show rates because it helps discriminate among speculative and confirmed bookings; bookings that are not e-tickets have either not been paid for or have been paid for and confirmed via another purchase medium like paper tickets. Passengers with etickets are much less likely to no-show than passengers without e-tickets, passengers traveling in first and business classes are less likely to no-show compared to other booking classes, frequent flyer members are less likely to no-show compared to non-members, and people traveling in groups are less likely to no-show compared to those traveling alone. The only flight/itinerary variable that was found to be significant was time of day, that is passengers traveling between 9:01 a.m. – 7 p.m. are less likely to no-show than passengers traveling during other time periods. The most important finding related to no-show behavior is observed by comparing outbound and inbound segments.

Population rates for March 2001 outbound and inbound

segments reveal that no-show rates are higher for inbound itineraries (10.0%) than outbound itineraries (6.2%). This finding is somewhat surprising given that if a passenger no-shows on the outbound itinerary, the carrier may automatically cancel the inbound itinerary (thereby deleting

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the inbound record from the dataset). The no-show rate increase for inbound passengers may reflect a greater amount of rescheduling activity for inbound itineraries as well as the effect of back-to-back ticketing. No-show rates will increase if more passengers with tickets purchased for travel on the carrier of interest use their tickets to fly on competitors1. No-show rates will also increase if passengers fail to rebook their return itinerary for a later departure date prior to the time their original booked itinerary departs. To summarize, no-show rates may be higher for inbound itineraries for several reasons. From a business perspective, it is important to determine whether increases in no-show rates are due to passengers’ exploiting irrationalities in major network carriers’ pricing structures, particularly as these carriers face increased competition from low-cost carriers. While advanced algorithms are being developed to account for this new competitive environment, this study provides evidence that attention should also be directed to one of the key inputs of these algorithms, namely pricing structures.

Early Standby Results

Both passenger and flight/itinerary variables are important in describing early standby behavior. In terms of passenger variables, frequent flyer members are more likely to early standby compared to non-members while passengers traveling in groups or in first and business classes are less likely to early standby compared to those traveling alone or in coach classes. Distinct from the discussion of no-show behavior, numerous flight/itinerary variables are significant predictors of early standby behavior. Increases in carrier capacity, both within a given market as

1

Passengers with paper tickets for high-yield coach, business, and first class fares can use these tickets to fly a competitor airline. Passengers with low-yield coach fares must have their tickets reissued for a high-yield fare class before being able to fly a competitor airline.

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reflected in the carrier capacity variable and at a hub, as reflected in the departure city presence variable, lead to increases in early standby rates. Day of week and itinerary duration are also important. In particular, passengers are more likely to early standby for both outbound and inbound itineraries that depart late in the work week (i.e., Wednesday through Friday). Passengers are less likely to early standby for longer itineraries. Intuitively, this makes sense because passengers on longer itineraries may have less flexibility in rescheduling travel and nontravel activities. The most important finding related to early standby behavior is reflected in departure time variables. Departure time parameters associated with the early standby alternative are all negative relative to the reference time period of 7:01 p.m.-midnight. Further, these differences are larger in magnitude for itineraries departing earlier in the day.

This reflects a strong

resistance of passengers to early standby the earlier in the day the itinerary departs. This is a particularly important finding given that the check-in data provided for this study and used in the airline’s current no-show model often marks these standby passengers as no-shows (as part of this study, we developed a process to distinguish no-show and standby passengers).

This

classification error leads to inflated no-show rates that are sensitive to load factors on the carrier’s earlier itineraries. More importantly, this sensitivity is greatest for flights departing later in the day. The relationship between early standbys and denied boardings in the carrier’s current noshow model is best clarified by an example. Figure 2 depicts a hypothetical flight that has 90 seats and 100 bookings. If we assume 90 of the bookings on this flight show, five no-show, and five successfully standby for an earlier flight, there will be no empty seats or denied boardings. Because early standbys are classified as no-shows in the carrier’s current data structure, 90% of

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future bookings on the hypothetical flight are expected to show and 10% are expected no-show. However, if the earlier flights are full and there are no seats available for early standby passengers, 95 passengers will “show” for the hypothetical flight resulting in five denied boardings. Thus, when a carrier’s load factors suddenly2 increase in a market, not only is the carrier more likely to see denied boardings, but these denied boardings are most likely to occur on flights departing later in the day. These denied boardings are particular costly to airlines because a later itinerary may not be available and the airline must pay for overnight accommodations and/or pay a competitor airline to accommodate the denied boarding passengers (usually at the high-yield coach price).

By distinguishing early standbys from no-show passengers, the

sensitivity of current no-show forecasts to load factors on the carriers’ earlier itineraries can be alleviated. Moreover, carriers may be able to further alleviate denied boardings by incorporating outbound and inbound information. As seen in population choice rates, early standbys occur more than three times as often on inbound itineraries (3.0%) than outbound ones (0.89%). In addition, early standby behavior is more likely to occur on inbound itineraries during the 4:01 – 7 p.m. departure time interval. [Insert Figure 2 about here] Late Standby Results

Late standbys occur very infrequently, i.e., 0.13% for both outbound and inbound segments. When interpreting late standby results it is important to remember that changes a passenger made to an existing reservation before the original flight departed are not captured in this analysis, but 2

It is the sudden increase that causes denied boardings; current time-series models capture gradual changes.

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rather are reflected in cancellation rates. As such, late standbys represent passengers who willingly or unwillingly missed their flight and arrived at the airport hoping to take a later flight. Both passenger and flight/itinerary variables help predict late standby behavior. Passengers purchasing first/business and high yield coach tickets, frequent flyer members, and passengers traveling in groups are less likely to late standby. Unlike early standbys, the only significant flight/itinerary variables relate to carrier capacity. In particular, increases in carrier capacity on an itinerary or at the departure city lead to increases in late standby rates.

Synthesis of MNL Results

Choice probabilities can be computed for a hypothetical passenger to gain insight into the relative impact of different variables using the MNL and NL models. Table 2 contains choice probability forecasts using the MNL model estimates for a hypothetical passenger who has a low-yield booking, is a general member of the carrier’s frequent flyer program, and is traveling alone. Also, assume the passenger is traveling on an itinerary that departs on Monday and has duration of 3½ hours. Although the carrier does not have dominant market share in the departure city, it does have other itineraries, one during each departure time period (i.e., six total itineraries that depart one, two, and three hours before and after the booked itinerary). Each competing itinerary has a capacity of 120 seats. Using this hypothetical passenger and market, Table 2 compares choice probabilities along three dimensions: e-ticket, departure time periods, and outbound/inbound itineraries. Passengers with e-tickets are more likely to show than other passengers. The difference between show percent with and without e-ticket, is in the range of 11 to 14% (for all time periods for both inbound and outbound itineraries). This difference is

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mostly reflected in a reduction in no-show percent. Passengers are most likely to no-show during the earliest and latest time periods (6-9 a.m. and 7:01 p.m. to midnight). Passengers are most likely to early standby later in the day, after 4:01 p.m. The effect of departure time on early standby percent is stronger for inbound itineraries, particularly for the 4:01-7 p.m. departures, e.g., the e-ticket inbound itinerary early standby rates are 0.77%, 1.60%, 3.33%, and 3.63%, respectively, and are 1.9, 3.0, 3.5 and 2.2 times greater than those for the e-ticket outbound itinerary, respectively, and the non-e-ticket inbound itinerary early standby rates are 0.65%, 1.39%, 2.90%, and 3.08% and are 1.9, 2.9, 3.4 and 2.1 times greater than those for the non-eticket outbound itinerary. [Insert Table 2 about here]

Extension to Nested Logit Models

NL models are estimated with the same utility specifications as their MNL counterparts. As seen in Table 1, there are only small differences between the coefficients for MNL and the corresponding NL models for the show, early standby and late standby nest. While it is possible that a statistically superior NL model may be found by using different utility functions, in practice the search for this function is usually not undertaken and is generally not successful. In addition, by using the same specification for NL and MNL models, a validation analysis can be performed that isolates the impact of using a MNL versus NL error structure. NL models were estimated for all two-level nesting structures for the March 2001 outbound and inbound segments. That is 13 nesting structures for each itinerary type. Three structures are significant for at least one segment and have a value in the zero to one range

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(bolded in Table 3). The nest including show, early standby and late standby is selected over the nests (i.e., those that include only show and early standby or only show and late standby) despite the fact that it is only significant for the inbound itineraries. The nest including show, early standby and late standby has acceptable values (within the zero to one range) for both segments and these values are significant for three of four segments, i.e., for the outbound 2001 and for two segments not reported here (outbound 2002 and inbound 2002). The NL logsum coefficients for this structure suggest a high degree of correlation in error terms between these three alternatives. This implies the factors not captured in the observed portion of the utility function (and revealed via error components) are similar for show, early standby, and late standby alternatives. Intuitively, this makes sense as these alternatives indicate a commitment to fly on the carrier of interest. [Insert Table 3 about here]

VALIDATION ANALYSIS

This section measures the prediction accuracy of the MNL and NL models presented in the study. There are two key objectives of the validation analysis. First, the analysis provides insight into the benefit of using outbound and inbound itinerary information, which is currently not used by the airline industry (current airline revenue management systems are based on nondirectional itineraries or flights). Second, the analysis explores the benefit of using the more complicated model nested logit structure. This section describes the validation methodology and presents validation results.

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Validation methodology

The validation methodology was designed to reflect carriers’ current revenue management forecasting practices. Specifically, while itinerary information can be used to forecast no-show rates, current revenue management systems base seat allocation decisions on flight or cabin noshow rates. Thus, it is desirable to measure forecasting accuracy at flight or cabin levels. For this analysis, we report validation results for the coach cabin.

The relationship between

itineraries and flight cabins influences the validation methodology in two key ways. First, as shown in Figure 3 (adapted from Coldren, et al. 2003), numerous itineraries can influence a flight cabin’s no-show rate. Figure 3 shows a simplified network representing a flight from Chicago to Denver. The flight participates in itineraries linking 36 non-directional city pairs and 72 directional outbound/inbound city pairs. The no-show models in this study forecast an itinerary no-show rate for each booking record. Itinerary no-show forecasts are assigned to a specific flight legs and subsequently aggregated to obtain a non-directional flight cabin no-show rate.

Second, our analysis contains a subset of the carrier’s itineraries, specifically those

originating and terminating in the continental U.S. However, continental U.S. flights carry passengers from international and other non-continental U.S. itineraries.

Thus, a direct

comparison of the carrier’s actual and study’s predicted flight cabin no-show rates is not possible (without estimating additional models for international itineraries, which was beyond the scope of this study). Since a direct comparison of flight cabin no-show rates is not feasible, we use a validation sample of observed data for March 2002 departures that represent approximately 500,000 continental U.S. travel itineraries (versus the millions of records of booked travelers). The validation data set is a choice-based sample that contains all no-show, early standby, and late standby records and a random sample of show records.

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[Insert Figure 3 about here]

Predictive accuracy is measured as the difference in the predicted vs. observed choice rates (or shares) for coach passengers averaged over all flights in the validation sample that had four or more coach bookings3. In addition to the models previously reported a non-directional model is estimated to provide a reference to quantify the benefits of using directional itinerary information. The non-directional model combines outbound and inbound observations. The non-directional MNL and NL models use the same underlying utility functions calibrated for the outbound and inbound models. Four forecasts are used to explore the benefit of using directional itinerary information and to assess whether MNL or NL models provide greater accuracy. Forecasts are defined along two dimensions: directional/non-directional and MNL/NL. Models estimated using March 2001 sample data are used to forecast March 2002 behavior.

This study quantifies forecasting

accuracy for the coach cabin using mean absolute error (MAE), which measures prediction accuracy independent of whether the prediction is above or below the observed value. MAE was chosen because it was used in prior studies of the carrier’s no-show forecasting accuracy. Formally, MAE for choice i is: MAEi 

3

actual ratechoice i  predicted ratechoice i Number of coach cabins in validation sample

.

(8)

Excluding coach cabins with less than four booking observations helps mitigate the effects of outliers and is consistent with the carrier’s current practice of measuring predictive accuracy by excluding flights that have load factors less than 30%. Including coach cabins with less than four bookings leads to higher error measures and was not found to change general conclusions.

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Validation Results

For the MAE values reported for non-directional and directional MNL and NL models (Table 4), the NL model consistently outperforms the MNL models.

Models that include directional

outbound and inbound information outperform models that do not include this information for the show, no-show and late standby percents but not the early standby percents. The benefit of including directional itinerary information is substantially larger than the benefit of using a more complicated NL structure for the show alternative and is larger for the no-show alternative. However, the benefit of the nesting structure is greater for the early and late standby alternatives. [Insert Table 4 about here]

CONCEPTUAL IMPLEMENTATION FRAMEWORK

While a formal assessment of the benefit of using disaggregate passenger data (versus aggregate data currently used by carriers) is beyond the scope of this study, there is an attractive characteristic of the disaggregate model that is of particular interest to carriers developing no-show models. Specifically, the predictive accuracy of the carrier’s current no-show model is insensitive to the amount of time remaining before the flight departs. However, the disaggregate model is expected to become more accurate as the date of departure approaches. This is because the measurement accuracy of flight/itinerary and passenger variables improves as the number of days before departure decreases. As shown in Figure 4, the implementation framework of the no-show models of this study predict no-show rates as a function of forecasted bookings and current bookings at departure, i.e., adjusted for cancellations expected to occur before departure.

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Forecasted bookings predict how many more passengers will book on a future flight while current bookings represented passengers who have made reservations for the flight. More information is available for actual bookings than forecasted bookings. Specifically, predictions about future bookings include information about booking class, group size, flight, and itinerary but do not include passenger information such as frequent flyer affiliation or e-ticket purchases. In addition, schedule information about competitors’ schedules is currently not used. From an implementation perspective, it is envisioned that separate models will predict no-show rates for bookings to date and predicted bookings; the latter will include less information. As the number of days before departure decreases, the predicted no-show rate is based on a larger percentage of current booking information.

Since current booking information is more accurate than

forecasted booking information, the disaggregate no-show model should become more accurate the closer the flight is to departing. This is particularly relevant to the airline industry, where the planning horizon (or number of days before an itinerary departs that a passenger can make a reservation) is slightly less than one year and most bookings are made within six to eight weeks of flight departures. Finally, the disaggregate no-show model is expected to be more accurate than the current model because it distinguishes between early standbys and no-shows and adjusts show rates according to load factors on the carrier’s competing itineraries. [Insert Figure 4 about here]

SUMMARY

This study advances the state-of-the-art in airline forecasting models by offering the first comprehensive analysis of airline passengers’ rescheduling behavior. It is one of the first to

25

empirically demonstrate the benefit of incorporating passenger and directional itinerary information in airline forecasting models.

Moreover, it confirms some of the working

assumptions held by industry practitioners including the benefit of incorporating passenger and flight/itinerary variables in no-show models and the importance of including ticketing information (e.g., see Ratliff, 1998, for a discussion). It also adds to the existing literature that considers the interaction of booking levels across multiple flights (e.g., see van Ryzin & Karaesmen, 1999).

Finally, the study presents a new framework for incorporating schedule

strength and competitive market information that considers level of service effects; this framework is similar in spirit to that proposed by Coldren, et al. (2003). Future research can extend our no-show and standby analysis to other segments including international markets and group bookings (defined as ten or more people traveling together). Additional information such as ticketing and price information can also be included. Finally, the methodology presented in the study can be extended to other airline models, including cancellation and demand forecasts.

ACKNOWLEDGEMENTS

The authors would like to thank the U.S. carrier who supported this study and Gregory Coldren, a doctoral student at Northwestern University, who provided assistance in obtaining and interpreting flight and itinerary variables.

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REFERENCES

Aptech Systems, Inc. Maple Valley, WA, USA. Ben-Akiva, M., & Lerman, S. (1985). Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, MA: MIT Press. Coldren, G., Koppelman, F., Kasturirangan, K., & Mukherjee. A. (2003). Air travel itinerary share prediction: Logit model development at a major U.S. airline. Journal of Air Transport Management, 9(6), 361-369. Cosslett, S. (1981). Maximum likelihood estimation for choice-based samples. Econometrica, 49, 1289-1316. Garrow, L. (2004). Comparison of choice models representing correlation and random taste variation: An application to airline passengers’ rescheduling behavior. Published doctoral dissertation. Northwestern University, Evanston, Illinois. Garrow, L., & Koppelman, F. (2004). Predicting air travelers’ no-show and standby behavior using passenger and directional itinerary information. Journal of Air Transport Management, in press. Imbens, G. (1992). An efficient method of moments estimator for discrete choice models with choice-based samples. Econometrica, 60(5), 1187-1214. Koppelman, F. & Wen, C.-H. (1998). Alternative nested logit models: Structure, properties, and estimation. Transportation Research Part B, 32B(15), 289-298. Kalka, K., & Weber, K. (2000). PNR-based no-show forecast. Presented at the AGIFORS Reservation and Yield Management Study Group, New York City. Manski, C., & Lerman, S. (1977). The estimation of choice probabilities from choice based samples. Econometrica, 45, 1977-1988. Pastor, J. (2000). What exactly is data mining. Presented at the AGIFORS Reservation and Yield Management Study Group, New York City. Ratliff (1998). Ideas on overbooking. Presented at the AGIFORS Reservation and Yield Management Study Group, Melbourne, Australia. Train, K. (2003). Discrete Choice Methods with Simulation. Cambridge, United Kingdom: University Press. van Ryzin, G. & Karaesmen, I. (1999). Overbooking with substitutable inventory classes. Presented at the AGIFORS Reservation and Yield Management Study Group, London, United Kingdom.

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LIST OF TABLES AND FIGURES

TABLE 1. MNL and NL model results calibrated on March 2001 flight departures TABLE 2. MNL choice probability forecasts for a hypothetical passenger and itinerary TABLE 3. Comparison of NL logsum coefficients TABLE 4. Error analysis of MNL and NL forecasts for coach cabin FIGURE 1. Conceptual model of airline passengers’ rescheduling behavior FIGURE 2. Relationship between early standbys and denied boardings FIGURE 3. Relationship between itinerary and flight cabin no-show rates FIGURE 4. Implementation framework for passenger no-show models

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Table 1 MNL and NL model results calibrated on March 2001 flight departures MNL Outbound MNL Inbound NL Outbound NL Inbound Constants (ref. = show) Alternative specific constant NS 1.33 (11.8) 1.52 (13.3) 1.18 (7.6) 1.20 (9.4) ASC ESB: Duration ≤ 180 mins -0.42 (2.0) 0.25 (1.8) -0.36 (2.0) 0.17 (1.7) ASC ESB: 180 < duration ≤ 300 mins -0.55 (2.5) 0.09 (0.5) -0.48 (2.4) 0.04 (0.3) ASC ESB: Duration > 300 mins -0.87 (3.5) -0.53 (2.9) -0.73 (3.1) -0.38 (3.0) Alternative specific constant LSB -0.37 (3.4) -0.23 (2.0) -0.32 (3.3) -0.20 (2.5) 0.26 (2.9) 0.35 (4.7) 0.22 (2.5) 0.26 (4.4) Day of Week: Wed – Fri ESB Dept. Time (ref. = after 7 pm and for NS 6-9 am) Depart 9:00 am – 7:00 pm NS -0.29 (3.3) -0.21 (2.4) -0.30 (3.4) -0.30 (3.2) Depart 6:00 am – 9:00 am ESB -1.46 (7.2) -1.58 (7.1) -1.23 (5.0) -1.17 (6.1) Depart 9:01 am – 4:00 pm ESB -1.16 (7.3) -0.85 (8.4) -0.98 (5.4) -0.66 (7.0) Depart 4:01 pm – 7:00 pm ESB -0.58 (3.6) -0.10 (1.0) -0.49 (3.2) -0.10 (1.3) Carrier Capacity (100’s seats) before scheduled departure for ESB / LSB Arrive 1-90 mins earlier 0.39 (7.0) 0.28 (6.4) 0.33 (5.4) 0.23 (6.7) Arrive 91-150 mins earlier 0.27 (4.6) 0.19 (4.5) 0.24 (4.5) 0.15 (4.7) Arrive 151-300 mins earlier 0.07 (2.0) 0.07 (2.4) 0.06 (2.0) 0.05 (2.6) Arrive 1-90 mins later 0.08 (1.6) 0.11 (2.4) 0.08 (1.9) 0.10 (3.2) Arrive 91-150 mins later 0.15 (3.0) 0.21 (4.1) 0.12 (2.9) 0.17 (4.5) Arrive 151-300 mins later 0.11 (3.6) 0* 0.10 (3.5) 0* Schedule Presence (Ratio of total flights for carrier vs. nearest competitor)^0.5*** Departure city presence ESB 0.14 (3.1) 0.14 (4.6) 0.13 (3.3) 0.12 (5.1) Departure city presence LSB 0.33 (8.8) 0.27 (7.6) 0.28 (6.2) 0.24 (6.4) -1.81 (20.2) -1.49 (19.8) -1.81 (20.8) -1.48 (19.7) E-ticket NS Booking Class (ref. = low yield) First and business NS -0.74 (3.9) -0.19 (1.3) -0.66 (3.2) -0.01 (0.1) First and business ESB -1.01 (4.2) -1.09 (6.6) -0.85 (3.7) -0.80 (6.9) First and business LSB -1.03 (6.4) -1.56 (6.0) -0.87 (4.1) -1.11 (5.8) High yield NS 0.08 (0.7) 0.26 (2.7) 0.10 (1.1) 0.21 (2.3) High yield ESB -0.25 (2.1) 0.11 (1.2) -0.21 (2.2) 0.07 (1.1) High yield LSB -0.46 (4.5) -0.07 (0.6) -0.39 (3.9) -0.05 (0.7) Frequent Flyer (ref. = not a member) General member NS -0.54 (4.6) -0.59 (5.3) -0.53 (5.3) -0.60 (5.7) General member ESB 0.33 (2.4) 0.37 (3.9) 0.28 (2.7) 0.26 (3.4) General member LSB -0.63 (5.6) -0.44 (3.8) -0.54 (4.7) -0.32 (3.7) Elite member NS -0.13 (1.0) -0.02 (0.2) -0.13 (1.1) -0.05 (0.4) Elite member ESB 0.57 (4.2) 0.31 (2.5) 0.48 (3.4) 0.22 (2.4) Elite member LSB -0.47 (3.7) -0.11 (0.9) -0.41 (3.4) -0.08 (0.9) Group Size (ref. = travel alone) Two-ten people traveling together NS -0.60 (5.2) -0.46 (5.0) -0.55 (4.9) -0.35 (4.2) Two-ten people traveling together ESB -0.71 (6.0) -0.63 (7.2) -0.59 (4.4) -0.44 (5.0) Two-ten people traveling together LSB -0.50 (4.6) -0.33 (2.9) -0.42 (4.1) -0.23 (2.5) 0.84 (1.4)** 0.71 (3.9)** NL logsum parameter (SEL nest) Model Fit Statistics LL Zero / LL Constants -3575 / -3539 -4798 / -4681 -3575 / -3539 -4798 / -4681 LL Model -3112 -4160 -3112 -4155 ρ2zero / ρ2constant 0.130 / 0.121 0.133 / 0.111 0.130 / 0.121 0.134 / 0.112 Number of cases / Number of variables 2,761 / 34 3,674 / 33 2,761 / 35 3,674 / 34 NOTES: Parameter (t-stat). *Constrained to be zero to avoid negative value. **T-stat reported against one. ***Carrier has dominant share. KEY: SH=show; NS=no-show; ESB=early standby; LSB=late standby.

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Table 2 MNL choice probability forecasts for a hypothetical passenger and itinerary E-ticket 6-9 am 9am-4 pm 4-7 pm 7pm-mid 6-9 am Outbound SH 96.17% 96.85% 96.44% 94.92% 82.05% NS 3.37% 2.54% 2.53% 3.32% 17.55% ESB 0.40% 0.54% 0.96% 1.68% 0.34% LSB 0.07% 0.07% 0.07% 0.07% 0.06% Inbound SH 93.81% 93.97% 92.32% 91.10% 79.31% NS 5.32% 4.32% 4.24% 5.16% 19.94% ESB 0.77% 1.60% 3.33% 3.63% 0.65% LSB 0.11% 0.11% 0.11% 0.11% 0.09% KEY: SH=show; NS=no-show; ESB=early standby; LSB=late standby.

No e-ticket 9am-4 pm

4-7 pm

7pm-mid

85.74% 13.72% 0.48% 0.07%

85.42% 13.67% 0.85% 0.07%

81.15% 17.35% 1.44% 0.06%

81.83% 16.68% 1.39% 0.10%

80.58% 16.42% 2.90% 0.09%

77.37% 19.45% 3.08% 0.09%

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Table 3 Comparison of NL logsum coefficients

NEST OUTBOUND INBOUND S (NEL) 1.23 (2.5) 1.24 (2.9) N (SEL) 0.84 (1.4) 0.71 (3.4) E (SNL) 0.92 (0.4) 0.85 (1.2) L (SNE) 0.81 (1.6) 0.99 (0.1) (SN) EL 1.05 (0.4) 1.02 (0.2) (SE) NL 0.69 (3.0) 0.76 (3.3) (SL) NE 0.72 (2.1) 0.75 (2.3) (NE) SL 1.05 (0.7) 1.15 (1.8) (NL) SE 1.09 (1.0) 1.03 (0.3) (EL) SN 1.23 (2.0) 1.03 (0.3) (SN) (EL) 1.05 (0.4); 1.23 (2.0) 1.02 (0.2); 1.03 (0.3) (SE) (NL) 0.70 (2.9); 1.06 (0.7) 0.76 (3.4); 1.01 (0.1) (SL) (NE) 0.73 (2.0); 1.03 (0.4) 0.77 (1.9); 1.13 (1.5) NOTE 1: Logsum parameter (t-stat against 1). NOTE 2: alternatives in a common nest are enclosed in parenthesis. Highlighted coefficients are significant at 0.05. Bolded rows represent structures for which one or both segments is significant and both parameters are in the acceptable 0 1 range. The preferred specifications include show, early and late standby in a common nest. KEY: S=show; N=no-show; E=early standby; L=late standby.

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Table 4 Error analysis of MNL and NL forecasts for coach cabin

Show MNL NL NL improvement No-show MNL NL NL improvement Early Standby MNL NL NL improvement Late Standby MNL NL NL improvement

2001 Pooled

2001 O/I

Benefit of using O/I information

8.48 8.46 +0.02

8.26 8.23 +0.03

+0.22 +0.23

7.38 7.12 +0.26

7.06 6.79 +0.27

+0.32 +0.33

2.29 2.24 +0.05

2.54 2.49 +0.05

-0.25 -0.25

0.32 0.21 +0.11

0.29 0.20 +0.09

+0.03 +0.01

KEY: O/I=forecast created using outbound and inbound information.

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Traveler characteristics

Automated data cleaning

Familiarity with air travel system Trip characteristics (duration, rigidity)

Booking

Ticketing

Outbound travel

Inbound travel

Availability of viable alternatives

Fig. 1. Conceptual model of airline passengers’ rescheduling behavior.

33

Early standbys occur when there are seats on earlier flights… No-show

5

Early standby

5

10% “No-show”

… but they turn into denied boardings when there are no longer seats on earlier flights. No-show

5

Denied boarding

5

Capacity = 90 Show

90

90% “Show”

Show

90

5% “No-show” Capacity = 90 95% “Show”

Fig 2. Relationship between early standbys and denied boardings.

34

BOS

SEA

LGA

PDX SFO

DEN

PHL

ORD

LAX

DCA SAN

FLL

Fig. 3. Relationship between itinerary and flight cabin no-show rates

35

Current bookings

Current bookings at departure

Cancellations

Forecasted bookings

Forecasted bookings at departure

Itinerary NS forecast (current bookings) Other data

Cabin NS forecast (wt. average of forecasts)

NS adjustment (ESB opportunities)

Itinerary NS forecast (forecasted bookings)

Fig. 4. Implementation framework for passenger no-show model