A Branch-and-Cut Algorithm for the Latent Class Logit Assortment Problem

Abstract We study the product assortment problem of a retail operation that faces a stream of customers heterogeneous with respect to preferences. Upon arrival, each customer checks the offer set displayed by the firm, and either chooses one of those products according to a multinomial-logit (MNL) criterion or quits without purchasing. The firm's goal is to maximize the expected revenue extracted from each customer. The general version of the logit assortment problem is known to be NP-Hard. In this paper, we analyze uncapacitated and capacitated (i.e., with a limited number of products to display) versions of it, and propose a branch-and-cut algorithm that is computationally feasible and leads to high-quality solutions.