Integrating Passenger Behavior into Revenue Management Models

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Sponsors:

National Science Foundation award SES-1130745

Researchers:

Mark Ferguson
Jeff Newman

Partner Institutions:

American Airlines

Shortly after the U.S. airline industry was deregulated in 1978, People Express Airlines started service in 1981. Through offering low fares on routes operated by legacy carriers, People Express was able to gain substantial market share. American Airlines responded to this new competitor by developing a revenue management (RM) system that was implemented in 1985. By forecasting demand for different products, the RM system was able to determine how many lower-priced and higher-priced tickets that American Airlines should sell. Unable to compete against American’s new system which was now able to offer a limited number of fares that were prices lower than the fares offered by People Express, in 1987 People Express ceased operations.

It is important to note that these first-generation RM systems were built in the mid 1980’s, under market conditions that are very different than those that exist today. The increased market penetration of low cost carriers combined with the increased use of the internet as a booking channel has helped spawn a new era of RM, commonly referred to as “choice-based RM.” Choice-based RM methods, which first appeared in the literature in 2004, use data that track individuals’ purchase decisions, as well as the menus of choices they viewed prior to purchases. That is, in contrast to traditional booking data, on-line shopping data provides a detailed snapshot of the products available for sale at the time an individual was searching for fares, as well as information on whether the search resulted in a purchase (or booking). This data enables firms to replace RM demand models based on time-series and other averaging methods with discrete choice models that better capture customer behavior by explaining how individuals make trade-offs among price, schedule, refundability, and other product attributes.

Choice-based RM systems require two sets of input parameters: customer preference weights (obtained from the discrete choice model) and a customer arrival rate (which represents market size, or the total number of potential customers). One of the key challenges practitioners have faced when trying to implement choice-based RM systems is that is has been difficult to estimate these two sets of input parameters. The difficulty arises because the customer arrival rate represents the total number of potential customers; however, airlines only have information about their own customers. The expectation-maximization (EM) method is an iterative statistical technique that can be used to solve for these input parameters; however, because the method is iterative and must converge upon a solution, the EM method is very slow and often takes hours or days to estimate these input parameters.

Drs. Mark Ferguson and Laurie Garrow in conjunction with research engineer Dr. Jeffrey Newman and American Airlines colleague Dr. Timothy Jacobs have developed estimation methods that find these input parameters much more quickly. They show that the choice-based estimation problem can be decomposed into two steps. The first step solves for the customer preference weights using observed booking data. The second step solves for the customer arrival rate using information about variations in observed sales over time. The two-step method is very fast, because the first step involves optimizing a globally concave function and the second step can be reduced to a one-dimensional nonlinear function.

Their two-step method drastically reduces computational times from hours to minutes. Dr. Newman explains: “I designed a simulation experiment based on data from an actual firm. The experiment was based on 365 booking days and 10 starting values. Our model consistently found the correct solution in under five minutes, in 100 replications. If I were to run the same experiment using the EM method, it would take at least eight months.”

In developing a method to estimate parameters for the "choice-based RM problem", Drs. Ferguson, Garrow, and Newman realized they could recast the problem as an extreme case of the "choice-based sampling problem" from the discrete choice modeling literature.  Choice-based sampling estimators were derived based on the assumption that each alternative in the estimation sample was observed to have been chosen at least once.  However, this assumption can be relaxed and alternative-specific constants can be estimated for certain types of discrete choice models when one or more alternatives is completely censored, or never observed to have been chosen in the estimation dataset.

Drs. Ferguson, Garrow, and Newman received a grant from the National Science Foundation to extend their work. The initial research was supported from proceeds from an annual revenue management and price optimization conference that is jointly hosted by Georgia Tech and Revenue Analytics.

 

Publications resulting from this research:

  1. Newman, J.P., Ferguson, M.E., Garrow, L.A., and Jacobs, T. (2014). Estimation of choice-based models using sales data from a single firm. Manufacturing and Service Operations Management 16(2): 184-197.
  2. Newman, J.P., Ferguson, M.E., Garrow, L.A. (2013). Estimating GEV models with censored data. Transportation Research Part B 58: 170-184.
  3. Newman, J.P., Ferguson, M.E. and Garrow, L.A. (2013). Estimating nested logit models with censored data. Transportation Research Record 2343: 62-67
  4. Ferguson, M.E., Garrow, L.A., and Newman, J.P. (2012). Application of discrete choice models to choice-based revenue management problems: A cautionary note. Journal of Revenue and Pricing Management  11: 536-54.
  5. Newman, J.,Ferguson, M., and Garrow, L. (2012). Estimating discrete choice models with incomplete data. Transportation  Record 2302: 130-137.