On Assortment Optimization with Endogenized Market Size

Abstract

In this paper, we consider the joint effects of product substitution and endogenized market size. Under the substitution effects, a product's demand may be cannibalized by other substitutable products; while the market size, measured by the number of customers who are interested in one of the products from the same category, may be largely in uenced by the product offer set. We show that the "loss-leader" phenomenon may arise because of the endogenized market size: a product is sold at a price below its marginal cost, in order to stimulate other sales of more profitable products. We further establish the NP-hardness for the assortment problem under the joint effects and develop a fully polynomial-time approximation scheme.