Resumen de A Randomized Concave Programming Method for Choice Network Revenue Management
The randomized linear programming (RLP) proposed in [23] is a very simple and fast simulation-based method that has been found to be surprisingly effective and robust for generating upper bounds and bid-price controls for network revenue management (see [26] for simulations comparing the alternatives). RM incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular (see [24]). Many network RM extensions of such models ([8], [15], [12], [28], [17]) have subsequently been proposed. The extensions to the choice model of customer behavior however are considerably more difficult to solve. The formulations have an exponential number of columns and the solution strategy is to use column generation. But finding an entering column is computationally easy only in a limited number of cases. Given the difficulties in solving these methods, it is natural to explore the RLP methodology for the choice model. In this paper we first give a segment-based deterministic concave-program (SDCP) upper bound to the dynamic program, that coincides with the CDLP upper-bound of [8] and [15] for non-overlapping segments. We then tighten the bound by a simulation-based randomized concave programming (RCP) method, similar to the RLP for the independent-class model. The advantage is that (i) we get a tighter bound for the non-overlapping segment model, and (ii) we are able to solve larger classes of choice models (with overlapping segments). If the number of elements in a consideration set for a segment is not very large, both (SDCP) and (RCP) can be applied to any choice model whatsoever, expanding the models well beyond tractable-but-restrictive ones such as multinomial-logit.
