Assortment Optimization and Pricing Under the Threshold-Based Choice Models

Abstract

In this paper, we study revenue maximization assortment and pricing problems under the threshold-based choice model, in which, a product is placed into a consumer's consideration set if its utility to the consumer exceeds the utility of a specified threshold. We consider two cases: when the random shock is logistically distributed or Gumbelly distributed. For both these two cases, the revenue-maximizing assortment problem is NP-hard. Although in the two cases, the best revenue-ordered assortment and the same-price policy can not achieve the optimal profit for the assortment problem and the pricing problem, respectively, we show that, they can guarantee a good bound on the optimal revenue. Finally, we show that when the random shock is logistically distributed, our policies can be asymptotically optimal if the search cost of consumers is sufficiently small. When the random shock is Gumbelly distributed, the best revenue-ordered assortment can asymptotically admit a 0.77 approximation of the optimal revenue for the assortment problem; the same-price policy can be asymptotically optimal for the pricing problem. These suggest that our policies share some robustness to achieve a good performance guarantee for the optimal revenue.