Assortment Optimization Under History-Dependent Effects

Abstract

This paper examines how to plan multi-period assortments when customer utility depends on historical assortments. We formulate this problem as a nonlinear integer programming model and show it is NP-hard in the presence of a negative history-dependent effect (such as a satiation effect). We build solution methodologies for obtaining global optimal solutions under a general setting that the history-dependent effects could be a mixture of positive and negative. We propose using a lifting-based framework to reformulate the problem as a mixed-integer exponential cone program that state-of-the-art solvers can solve. We also design a sequential revenue-ordered policy and show that it solves our problem to optimality in polynomial time when historical assortments positively affect customer utility (such as an addiction effect). Additionally, we identify an optimal cyclic policy for an asymptotic regime, and we also relate its length to the customer's memory length. Finally, we present a case study using a catering service dataset, showing that our model demonstrates good fitness and can effectively balance variety and revenue.