Optimizing assortment and pricing of multiple retail categories with cross-selling

This paper investigates the joint optimization of assortment and pricing decisions for complementary retail categories. Each category comprises substitutable items (e.g., different coffee brands) and the categories are related by cross‐selling considerations that are empirically observed in marketing studies to be asymmetric in nature. That is, a subset of customers who purchase a product from a primary category (e.g., coffee) can opt to also buy from one or several complementary categories (e.g., sugar and/or coffee creamer). We propose a mixed‐integer nonlinear program that maximizes the retailer’s profit by jointly optimizing assortment and pricing decisions for multiple categories under a classical deterministic maximum‐surplus consumer choice model. A linear mixed‐integer reformulation is developed which effectively enables an exact solution to relatively large problem instances using commercial optimization solvers. This is encouraging, because simpler product line optimization problems in the literature have posed significant computational challenges over the last decades and have been mostly tackled via heuristics. Moreover, our computational study indicates that overlooking cross‐selling between retail categories can result in substantial profit losses, suboptimal (narrower) assortments, and inadequate prices.