Assortment Optimization under Consider-then-Rank Choice Models

Abstract

Consider-then-choose models, borne out by empirical literature in marketing and psychology, explain that customers choose among alternatives in two phases, by first screening products to decide which alternatives to consider, before then ranking them. In this paper, we develop a dynamic programming framework to study the computational aspects of assortment optimization models posited on consider-then-choose premises. Although ranking-based choice models generally lead to computationally intractable assortment optimization problems, we are able to show that for many practical and empirically vetted assumptions on how customers consider and choose, the resulting dynamic program is efficient. Our approach unifies and subsumes several specialized settings analyzed in previous literature. Empirically, we demonstrate the versatility and predictive power of our modeling approach on a combination of synthetic and real industry datasets, where prediction errors are significantly reduced against common parametric choice models. In synthetic experiments, our algorithms lead to practical computation schemes that outperform a state-of-the-art integer programming solver in terms of running time, in several parameter regimes of interest.