Data-driven assortment optimization

Assortment optimization refers to the problem of selecting a set of products to offer to a group of customers so as to maximize the revenue that is realized when customers make purchases according to their preferences. Assortment optimization is essential to a wide variety of application domains that includes retail, online advertising and social security; however, it is challenging in practice because one typically has limited data on customer choices on which to base the decision. In this paper, we present a two-step approach to making effective assortment decisions from transaction data. In the first step, we use the data to estimate a generic ranking-based model of choice that is able to represent any choice model based on random utility maximization. In the second step, using the estimated model, we find the optimal assortment by solving a mixed-integer optimization (MIO) problem that is scalable and that is flexible, in that it can easily accommodate constraints. We show through computational experiments with synthetic data that (1) our MIO model is practically tractable and can be solved to full optimality for large numbers of products in operationally feasible times; (2) our MIO model is able to accommodate realistic constraints with little impact to solution time; (3) our estimation procedure is computationally efficient and produces accurate out-of-sample predictions of the true choice probabilities; and (4) by combining our estimation and optimization procedures, we are able to find assortments that achieve near-optimal revenues that outperform alternative parametric and non-parametric approaches.