Technical Note—Assortment Optimization with Small Consideration Sets

Abstract

In the paper “Assortment Optimization with Consideration Sets,” we study a customer choice model that captures purchasing behavior when there is a limit on the number of times that a customer will consider purchasing. Under this model, we assume each customer is characterized by a ranked preference list of products and, upon arrival, will purchase the highest ranking offered product. Because we restrict ourselves to settings in which customers consider a limited number of products, we assume that these rankings contain at most k products. We call this model the k-product nonparametric choice model. We focus on the assortment-optimization problem under this choice model. In this problem, the retailer wants to find the revenue-maximizing set of products to offer when the buying process of each customer is governed by the k-product nonparametric choice model. We develop a linear programming–based randomized rounding algorithm that gives the best known approximation guarantee.