Assortment Planning and Inventory Decisions under Stockout-Based Substitution

Posted: 21 Sep 2008 Last revised: 8 Oct 2011

See all articles by Dorothee Honhon

Dorothee Honhon

University of Texas at Dallas

Vishal Gaur

Cornell University - Samuel Curtis Johnson Graduate School of Management

Sridhar Seshadri

University of Illinois at Urbana Champaign; Indian School of Business

Date Written: March 26, 2009

Abstract

We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total customer demand is random and comprises of a fixed proportion of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering amongst products. A customer purchases the highest ranked product according to his type (if any) that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help characterize multiple local maxima. We use the properties of the optima to construct a method for efficiently solving the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the average demand and the degree of substitutability amongst products are high.

Keywords: Assortment planning, Inventory management, Product variety, Consumer Choice, Substitution

JEL Classification: M11

Suggested Citation

Honhon, Dorothee and Gaur, Vishal and Seshadri, Sridhar, Assortment Planning and Inventory Decisions under Stockout-Based Substitution (March 26, 2009). Johnson School Research Paper Series No. 08-09; McCombs Research Paper Series No. IROM-07-09. Available at SSRN: https://ssrn.com/abstract=1271270

Dorothee Honhon

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Vishal Gaur (Contact Author)

Cornell University - Samuel Curtis Johnson Graduate School of Management ( email )

Ithaca, NY 14853
United States

HOME PAGE: http://www.johnson.cornell.edu/faculty/profiles/Gaur/

Sridhar Seshadri

University of Illinois at Urbana Champaign ( email )

1206 South Sixth Street
Champaign, IL 61820
United States

Indian School of Business ( email )

Hyderabad, Gachibowli 500 019
India

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