We consider a Markov decision process model of a network revenue management problem. Working within this formal framework, we study policies that combine aspects of mathematical programming approaches and pure Markov decision process methods. The policies employ heuristics early in the booking horizon, and switch to a more-detailed decision rule closer to the time of departure. We present a family of formulations that yield such policies, and discuss versions of the formulation that have appeared in the literature. Subsequently, we describe sampling-based stochastic optimization methods for solving a particular case of the formulation. Numerical results for two-leg problems suggest that the resulting hybrid policies do perform strongly. By viewing the Markov decision process as a large stochastic program, we derive some structural properties of two-leg problems. We also show that these properties cannot, in general, be extended to larger networks.
Working paper 03-015, Department of IE/MS, Northwestern University