Structural properties of Markov modulated revenue management problems

The admission decision is one of the fundamental categories of demand‐management decisions. In the dynamic model of the single‐resource capacity control problem, the distribution of demand does not explicitly depend on external conditions. However, in reality, demand may depend on the current external environment which represents the prevailing economic, financial, social or other factors that affect customer behavior. We formulate a Markov Decision Process (MDP) to maximize expected revenues over a finite horizon that explicitly models the current environment. We derive some structural results of the optimal admission policy, including the existence of an environment‐dependent thresholds and a comparison of threshold levels in different environments. We also present some computational results which illustrate these structural properties. Finally, we extend some of the results to a related dynamic pricing formulation.