First Order and Fixed-Point Approaches to Assortment Planning with Cross-Item Effects

Abstract

Assortment planning in retail involves the strategic selection of products to offer customers and their inventory levels, with the goal of maximizing profit. While cannibalization or more generally substitution effects are widely studied in the assortment planning literature, complementarity effects remain relatively unexplored. Cannibalization occurs when a product is bought instead of a similar one, and complementarity occurs when two products are bought together because they will be used together. Examples of complementary items are milk and cereals in FMCG or a dark t-shirt and a pair of light jeans in fast fashion. This paper introduces a novel demand model that captures cannibalization and complementarity effects. We also introduce a first order approach and a fixed point method to compute solutions for the assortment planning problem under the aforementioned demand model.Through experiments on synthetic and real-world retail datasets, we demonstrate the effectiveness of our proposed approaches in improving assortment planning outcomes, particularly in scenarios with complex interdependencies between items. Our findings underscore the importance of considering both cannibalization and complementarity effects in assortment planning and provide practical insights for retailers.

Keywords: assortment planning, cross-item effects