Robust assortment optimization under sequential product unavailability

Assortment planning is a central piece in the revenue management strategy of every retail company. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential ranking-based choice model and a cardinality constraint. Our choice model captures the increasing customer frustration of finding multiple products unavailable as a factor affecting purchasing decisions. To model the highly uncertain order in which a customer explores the products to buy, we present a bi-level optimization approach to maximize the expected revenue assuming that the customer visits a sequence of unavailable products that minimizes the likelihood of staying in the store. We show that the resulting problem is NP-hard and develop exact and greedy solution approaches that can solve different instances efficiently in terms of both solution time and optimality gap. We develop a model extension that includes multiple customer categories and also show a special case of the problem that can be solved in polynomial time. We perform a computational study to demonstrate the performance of our methods and illustrate the sensitivity of the optimal assortment to variations in the input parameters.