Choice network revenue management based on new compact formulations

The choice network revenue management model incorporates customer purchase probabilities as a function of the offered products, and is the appropriate model for airline and hotel network revenue management, dynamic sales of bundles, and dynamic assortment optimization. The optimization problem is a stochastic dynamic program and is intractable; a linear programming approximation called choice deterministic linear program (CDLP ) is usually used to generate controls. Tighter approximations such as affine and piecewise-linear relaxations have been proposed, but their complexity for the simplest choice model, the multinomial logit (MNL) model with a single segment, was unknown. We first show that the affine relaxation (and hence the piecewise-relaxation) is NP-hard even for a single-segment MNL choice model. By analyzing the affine relaxation we derive a new linear programming approximation that admits a compact representation, implying tractability. We prove that its value falls between the CDLP value and the affine relaxation value, often coming close to the latter in our numerical experiments. This is the first tractable relaxation for the choice network revenue management problem that is provably tighter than CDLP . This formulation in turn leads to new policies that, in our numerical experiments, show promise of significant increases in revenue, 2% on average over CDLP . Our analysis also yields a more complicated tractable relaxation, as well as a hierarchial family of relaxations that approach the affine relaxation. We give extensions to the case with multiple customer segments with overlapping consideration sets where choice by each segment is according to the MNL model. ∗Indian School of Business, Hyderabad, 500032, India, email: sumit [email protected] †Imperial College Business School, South Kensington Campus, London SW7 2AZ, U.K. email: [email protected]