In the last few years, there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior. This extension involves both modeling and computational challenges.One way to describe choice behavior is to assume that each customer belongs to a segment, which is characterized by a consideration set, i.e., a subset of the products provided by the firm that a customer views as options. Customers choose a particular product according to a multinomial-logit criterion, a model widely used in the marketing literature.In this paper, we consider the choice-based, deterministic, linear programming model (CDLP) of Gallego et al. [6], and the follow-up dynamic programming (DP) decomposition heuristic of van Ryzin and Liu [16], and focus on the more general version of these models, where customers belong to overlapping segments. To solve the CDLP for real-size networks, we need to develop a column generation algorithm. We prove that the associated column generation subproblem is indeed NP-Complete, and propose a simple, greedy heuristic to overcome the complexity of an exact algorithm. Our computational results show that the heuristic is quite effective, and that the overall approach has good practical potential and leads to high quality solutions.

We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stockouts or availability controls), and the seller knows its aggregate market share. The model combines a multinomial logit (MNL) choice model with a nonhomogeneous Poisson model of arrivals over multiple periods. Our key idea is to view the problem in terms of primary (or first-choice) demand; that is, the demand that would have been observed if all products had been available in all periods. We then apply the expectation-maximization (EM) method to this model, and we treat the observed demand as an incomplete observation of primary demand. This leads to an efficient, iterative procedure for estimating the parameters of the model. All limit points of the procedure are provably stationary points of the incomplete data log-likelihood function. Every iteration of the algorithm consists of simple, closed-form calculations. We illustrate the effectiveness of the procedure on simulated data and two industry data sets.Subject classifications: demand estimation; demand untruncation; choice behavior; multinomial logit model; EM method. Area of review: Revenue Management.

D iscrete choice models are appealing for airline revenue management (RM) because they offer a means to profitably exploit preferences for attributes such as time of day, routing, brand, and price. They are also good at modeling demand for unrestricted fare class structures, which are widespread throughout the industry. However, there is little empirical research on the practicality and effectiveness of choice-based RM models. Toward this end, we report the results of a study of choice-based RM conducted with a major U.S. airline. Our study had two main objectives: (1) to assess the extent to which choice models can be estimated well using readily available airline data, and (2) to gauge the potential impact that choice-based RM could have on a sample of test markets. We developed a maximum likelihood estimation algorithm that uses a variation of the expectationmaximization method to account for unobservable data. The procedure was applied to data for a test market from New York City to a destination in Florida. The outputs are promising in terms of the quality of the computed estimates, although a large number of departure instances may be necessary to achieve highly accurate results. These choice model estimates were then used in a simulation study to assess the revenue performance of the EMSR-b (expected marginal seat revenue, version b) capacity control policies and the current controls used by the airline relative to controls optimized to account for choice behavior. Our simulation results show 1%-5% average revenue improvements using choice-based RM. Although such simulated results must be taken with caution, overall our study suggests that choice-based revenue management is both feasible to execute and economically significant in real-world airline environments.

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