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.

This paper addresses two concerns with the state of the art in network revenue management with dependent demands. The first concern is that the basic attraction model (BAM), of which the multinomial logit (MNL) model is a special case, tends to overestimate demand recapture in practice. The second concern is that the choice based deterministic linear program, currently in use to derive heuristics for the stochastic network revenue management problem, has an exponential number of variables. We introduce a generalized attraction model (GAM) that allows for partial demand dependencies ranging from the BAM to the independent demand model (IDM). We also provide an axiomatic justification for the GAM and a method to estimate its parameters. As a choice model, the GAM is of practical interest because of its flexibility to adjust productspecific recapture. Our second contribution is a new formulation called the Sales Based Linear Program (SBLP) that works for the GAM. This formulation avoids the exponential number of variables in the earlier choice-based network RM approaches, and is essentially the same size as the well known LP formulation for the IDM. The SBLP should be of interest to revenue managers because it makes choice-based network RM problems tractable to solve. In addition, the SBLP formulation yields new insights into the assortment problem that arises when capacities are infinite. Together these two contributions move forward the state of the art for network revenue management under customer choice and competition.

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