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

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 multi-attribute 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 datasets demonstrate that the algorithm can identify provably optimal solutions to realistically sized problems