Efficient Frontier and Applications in Product Offering and Pricing.

This article focuses on the joint assortment and pricing optimization problem under constrained multinomial logit (MNL) choice models, addressing challenges posed by product-differentiated price sensitivities and operational constraints such as cardinality limits and price bounds. It develops a unified methodology leveraging the concept of the efficient frontier and dimensionality reduction to transform the complex mixed combinatorial optimization into a tractable single-variable problem with respect to total choice probability. The approach characterizes optimal prices via a common adjusted markup and confines assortment decisions to efficient sets of polynomial size, enabling efficient solutions in static, randomized, and dynamic contexts. Notably, the randomized assortment strategy can outperform deterministic ones by mixing two candidate assortments, and the dynamic optimal policy exhibits a time-threshold structure with monotonic marginal resource values. The methodology’s robustness is further demonstrated through extensions to general operational constraints and consumer choice models, offering practical insights for revenue management in diverse business scenarios.