A General Attraction Model and an Efficient Formulation for the Network Revenue Management Problem

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 model (MNL) is a special case, may overestimate recapture in certain cases. The second concern is that the choice based deterministic linear program (CBLP), currently in use to derive heuristics for the stochastic network revenue management (SNRM) problem, has an exponential number of variables. We introduce a generalized attraction model (GAM) that has both the BAM and the independent demand model (IDM) as special cases. We also provide an axiomatic justification for the GAM and an E-M to estimate its parameters. As a choice model, the GAM should be of interest to those seeking a model that is not as optimistic as the BAM nor as pessimistic as the IDM in estimating recaptured demand. Our second contribution is a new formulation called the Sales Based Linear Program (SBLP) for the GAM. This formulation avoids the exponential number of variables in the CBLP and is essentially the same size as the formulation for the IDM. The SBLP should be of interest to revenue managers (even if their preferred choice model is the BAM) as it dramatically reduces the number of variables. Together these two contributions move forward the state of the art for network revenue management and allow for a wide range of effects including: partial demand dependencies, multiple time periods, inventory sharing across cabins, and competitive effects. In addition, the formulation yields new insights into the assortment problem that arises when capacities are infinite.