Assortment and Price Optimization under MNL Model with Price Range Effect

In this paper, we study the assortment and price optimization problems under Multinomial Logit (MNL) model with price range effect, where the utility of a product is affected by the relative position of its price with respect to the highest and the lowest prices in the offer set. This model is motivated by the so-called Range Theory popularized in the behavioral economics and psychology literature. It addresses the limitation of a single-point interpretation of reference price, which ignores the impact of all other distributional information. We investigate the pure assortment problem, the pure pricing problem, and the joint assortment and pricing problem under the MNL model with price range effect. For each model, we first identify the structure of the optimal policy, and then we propose tractable algorithms that either output the optimal solution in polynomial time or admit an Fully Polynomial-Time Approximation Scheme (FPTAS)