Assortment Optimization for Choosy Customers

We study two different choice models that capture the purchasing behavior of customers who only consider purchasing one of two substitutable products. We refer to these customers as choosy. The first choice model captures substitution behavior through probabilistic transitions between products. Under this choice model, a customer’s buying process can be captured in two steps: an arrival with the intention of purchasing a product and a single transition to a substitute product if the initial product is unavailable. We refer to this choice model as the Two Step choice model. The second choice model that we study assumes each customer is characterized by a ranking of the products. An arriving customer will purchase her highest ranked product that is offered. Since we model choosy customers, we assume that these rankings contain at most two products. We call this second model the Two Product Nonparametric choice model. This paper focuses on the assortment optimization problem under these two choice models. 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 either the Two Step or Two Product Nonparametric choice model. Under both choice models, we give hardness results for the assortment problem, and motivated by these hardness results, we develop novel approximation schemes. Through a series of computational experiments, we show that the approximation schemes are easy to implement, efficient to run, and perform significantly better than their theoretical guarantees.