Assortment Optimization in the Presence of Context Effects

Abstract

Problem definition. We study choice modeling and assortment optimization under context effects, where an item’s perceived attractiveness depends on the other items displayed alongside it. Methodology. We study the Contextual Multinomial Logit (CMNL) model, in which each item’s utility adjusts linearly with the presence of other items, yielding a pairwise (second-order) approximation to general context-dependent choice while preserving a structure that is simple to estimate and optimize. CMNL encompasses classical phenomena such as attraction, compromise, and similarity effects. Results. Theoretically, we establish strong hardness and inapproximability results for CMNL-based assortment optimization, yet identify practically motivated regimes that admit polynomial or pseudo-polynomial algorithms. On the estimation side, we prove the log-likelihood function is concave and provide necessary and sufficient identifiability conditions, enabling scalable and well-posed fitting. Empirically, on large SKU-level transaction data, CMNL improves predictive accuracy over standard benchmarks and converts these gains into a measurable revenue lift. We also provide an exact MILP formulation and practical heuristics for general instances. Managerial implications. CMNL provides a parsimonious, estimation-friendly framework that captures salient context effects and enables tractable and high-quality assortment decisions at scale, delivering not only superior predictive fit but also measurable revenue gains.