Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions

Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited capacity. However, there is not yet a tractable method to efficiently solve such a problem. Existing papers studying static joint optimization of price and assortment cannot incorporate resource constraints. Then we study the revenue management problem with resource constraints and price bounds, where the prices and the product assortments need to be jointly determined over time. We showed that under the Markov chain (MC) choice model (which subsumes the multinomial logit (MNL) model), we could reformulate the choice-based joint optimization problem as a tractable convex conic optimization problem. We also proved that an optimal solution with a constant price vector exists even with constraints on resources. In addition, a solution with both constant assortment and price vector can be optimal when there is no resource constraint.