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Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application

Fuqua School of Business, Duke University, Durham, North Carolina 27708
The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
gurhan.kok{at}duke.edu
fisher{at}wharton.upenn.edu

Assortment planning at a retailer entails both selecting the set of products to be carried and setting inventory levels for each product. We study an assortment planning model in which consumers might accept substitutes when their favorite product is unavailable. We develop an algorithmic process to help retailers compute the best assortment for each store. First, we present a procedure for estimating the parameters of substitution behavior and demand for products in each store, including the products that have not been previously carried in that store. Second, we propose an iterative optimization heuristic for solving the assortment planning problem. In a computational study, we find that its solutions, on average, are within 0.5% of the optimal solution. Third, we establish new structural properties (based on the heuristic solution) that relate the products included in the assortment and their inventory levels to product characteristics such as gross margin, case-pack sizes, and demand variability. We applied our method at Albert Heijn, a supermarket chain in The Netherlands. Comparing the recommendations of our system with the existing assortments suggests a more than 50% increase in profits.

Subject classifications: inventory; multi-item; stochastic; applications; heuristics; marketing; retailing; estimation.
History: Received October 2004; revision received August 2006; accepted September 2006.