Technical Note—Leveraging the Degree of Dynamic Substitution in Assortment and Inventory Planning

Optimizing Assortment and Inventory Under Stockout-Based Substitution In the realm of retail, a common challenge arises when retailers must decide the set of substitutable products to offer and how much inventory to stock at the beginning of a selling season when customers choose and substitute among the products that are available to them. This problem is challenging, as the demand for each product is shaped by the inventories of all products and the substitution behavior. In this paper, Zhang, Ma, and Topaloglu focus on the stockout-based substitution and develop a novel rounding scheme based on a fluid relaxation. The authors provide a rigorous theoretical analysis of the method, improving earlier results. In particular, for the multinomial logit model, they achieve an optimality gap that does not depend on the number of products. This result has practical implications for online retailers with vast product varieties, ensuring reliable performance, even when both the demand and the number of products are large.