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A Branch-and-Price Approach to the Share-of-Choice Product Line Design Problem

Department of Finance and Quantitative Analysis, Georgia Southern University, Statesboro, Georgia 30460
Department of Quantitative Analysis and Operations Management, University of Cincinnati, Cincinnati, Ohio 45221
Department of Marketing, University of Cincinnati, Cincinnati, Ohio 45221
xfwang{at}georgiasouthern.edu
jeff.camm{at}uc.edu
david.curry{at}uc.edu

We develop a branch-and-price algorithm for constructing an optimal product line using partworth estimates from choice-based conjoint analysis. The algorithm determines the specific attribute levels for each multiattribute product in a set of products to maximize the resulting product line's share of choice, i.e., the number of respondents for whom at least one new product's utility exceeds the respondent's reservation utility. Computational results using large commercial and simulated data sets demonstrate that the algorithm can identify provably optimal, robust solutions to realistically sized problems.

Key Words: branch and price; column generation; combinatorial optimization; conjoint analysis; integer programming; marketing; optimization; product line design; share of choice
History: Received: November 3, 2008; accepted: May 24, 2009.