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Finding the optimal product prices and product assortment are two fundamentalproblems in revenue management. Usually, a seller needs to jointly determinethe prices and assortment while managing a network of resources with limitedcapacity. However, there is not yet a tractable method to efficiently solvesuch a problem. Existing papers studying static joint optimization of price andassortment cannot incorporate resource constraints. Then we study the revenuemanagement problem with resource constraints and price bounds, where the pricesand the product assortments need to be jointly determined over time. We showedthat under the Markov chain (MC) choice model (which subsumes the multinomiallogit (MNL) model), we could reformulate the choice-based joint optimizationproblem as a tractable convex conic optimization problem. We also proved thatan optimal solution with a constant price vector exists even with constraintson resources. In addition, a solution with both constant assortment and pricevector can be optimal when there is no resource constraint.

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