Most recent research in network revenue management incorporates choice behavior that models the customers buying logic. These models are consequently more complex to solve, but they return a more robust policy that usually generates better expected revenue than an independent-demand model. Choice network revenue management has an exact dynamic programming formulation that rapidly becomes intractable. Approximations have been developed, and many of them are based on the multinomial logit demand model. However, this parametric model has the property known as the independence of irrelevant alternatives and is often replaced in practice by a nonparametric model. We propose a new approximation called the product closing program that is specifically designed for a ranking-based choice model representing a nonparametric demand. Numerical experiments show that our approach quickly returns expected revenues that are slightly better than those of other approximations, especially for large instances. Our approximation can also supply a good initial solution for other approaches.
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