Exact First-Choice Product Line Optimization

Operations Research, Forthcoming

50 Pages Posted: 21 Aug 2017 Last revised: 29 Jun 2021

See all articles by Dimitris Bertsimas

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Velibor Mišić

University of California, Los Angeles (UCLA) - Anderson School of Management

Date Written: August 16, 2017


A fundamental problem faced by firms is that of product line design: given a set of candidate products that may be offered to a collection of customers, what subset of those products should be offered so as to maximize the profit that is realized when customers make purchases according to their preferences? In this paper, we consider the product line design problem when customers choose according to a first-choice rule and present a new mixed-integer optimization formulation of the problem. We theoretically analyze the strength of our formulation and show that it is stronger than alternative formulations that have been proposed in the literature, thus contributing to a unified understanding of the different formulations for this problem. We also present a novel solution approach for solving our formulation at scale, based on Benders decomposition, which exploits the surprising fact that Benders cuts for both the relaxation and the integer problem can be generated in a computationally efficient manner. We demonstrate the value of our formulation and Benders decomposition approach through two sets of experiments. In the first, we use synthetic instances to show that our formulation is computationally tractable and can be solved an order of magnitude faster for small to medium scale instances than the alternate, previously proposed formulations. In the second, we consider a previously studied product line design instance based on a real conjoint data set, involving over 3000 candidate products and over 300 respondents. We show that this problem, which required a week of computation time to solve in prior work, is solved by our approach to full optimality in approximately ten minutes.

Keywords: product line design, first-choice models, mixed-integer optimization, Benders decomposition

JEL Classification: C61, C63, M31

Suggested Citation

Bertsimas, Dimitris and Misic, Velibor, Exact First-Choice Product Line Optimization (August 16, 2017). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3020502 or http://dx.doi.org/10.2139/ssrn.3020502

Dimitris Bertsimas

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

Cambridge, MA 02142
United States
617-253-4223 (Phone)
617-258-7579 (Fax)

Velibor Misic (Contact Author)

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

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