Near-Optimal Algorithms for the Assortment Planning Problem Under Dynamic Substitution and Stochastic Demand

Operations Research, Forthcoming

MIT Sloan Research Paper No. 5139-15

32 Pages Posted: 26 Mar 2015 Last revised: 14 Aug 2015

See all articles by Vineet Goyal

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Danny Segev

Tel Aviv University - School of Mathematical Sciences

Date Written: March 24, 2015

Abstract

Assortment planning of substitutable products is a major operational issue that arises in many industries, such as retailing, airlines and consumer electronics. We consider a single-period joint assortment and inventory planning problem under dynamic substitution with stochastic demands, and provide complexity and algorithmic results as well as insightful structural characterizations of near-optimal solutions for important variants of the problem. First, we show that the assortment planning problem is NP-hard even for a very simple consumer choice model, where each customer is willing to buy only two products. In fact, we show that the problem is hard to approximate within a factor better than 1-1/e. Secondly, we show that for several interesting and practical choice models, one can devise a polynomial-time approximation scheme (PTAS), i.e., the problem can be solved efficiently to within any level of accuracy. To the best of our knowledge, this is the first efficient algorithm with provably near-optimal performance guarantees for assortment planning problems under dynamic substitution. Quite surprisingly, the algorithm we propose stocks only a constant number of different product types; this constant depends only on the desired accuracy level. This provides an important managerial insight that assortments with a relatively small number of product types can obtain almost all of the potential revenue. Furthermore, we show that our algorithm can be easily adapted for more general choice models, and present numerical experiments to show that it performs significantly better than other known approaches.

Keywords: assortment planning, dynamic substitution, polynomial time approximation schemes

Suggested Citation

Goyal, Vineet and Levi, Retsef and Segev, Danny, Near-Optimal Algorithms for the Assortment Planning Problem Under Dynamic Substitution and Stochastic Demand (March 24, 2015). Operations Research, Forthcoming, MIT Sloan Research Paper No. 5139-15, Available at SSRN: https://ssrn.com/abstract=2584790

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Danny Segev (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

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