Dynamic Programming Decomposition for Choice-Based Revenue Management with Flexible Products

Abstract

We reconsider the stochastic dynamic program of revenue management with flexible products and customer choice behavior as proposed in the seminal paper by Gallego et al. [Gallego G, Iyengar G, Phillips R, Dubey A (2004) Managing flexible products on a network. Working paper, Columbia University, New York]. In the scientific literature on revenue management, as well as in practice, the prevailing strategy to operationalize dynamic programs is to decompose the network by resources and solve the resulting one-dimensional problems. However, up to now, these dynamic programming decomposition approaches have not been applicable to problems with flexible products, because the underlying state space is based on commitments rather than resources.

In this paper, we contribute to the existing research by presenting an approach to operationalize revenue management with flexible products and customer choice in a dynamic programming environment. In particular, we propose a generic and formal procedure that transforms the original dynamic program with flexible products into an equivalent dynamic program with a resource-based state space. This reformulation renders the application of dynamic programming decomposition approaches possible. The procedure is based on Fourier-Motzkin elimination and is applicable to arbitrary network revenue management settings with regard to the considered network structure and the number and specifications of flexible products.

Numerical experiments show a superior revenue performance of the new approach with average revenues close to the expected upper bound from the choice-based deterministic linear program (CDLP). Moreover, our reformulation improves revenues by up to 8% compared with an extended variant of a standard choice-based approach without flexible products that immediately assigns flexible products after sale.

Keywords: Revenue Management, Flexible Products, Dynamic Programming Decomposition, Fourier-Motzkin Elimination

JEL Classification: C6, L8, M10, M30