Conjoint Optimization: An Exact Branch-and-Bound Algorithm for the Share-of-Choice Problem

Conjoint analysis is a statistical technique used to elicit partworth utilities for product attributes from consumers to aid in the evaluation of market potential for new products. The objective of the share-of-choice problem (a common approach to new product design) is to find the design that maximizes the number of respondents for whom the new product's utility exceeds a specific hurdle (reservation utility). We present an exact branch-and-bound algorithm to solve the share-of-choice problem. Our empirical results, based on several large commercial data sets and simulated data from a controlled experiment, suggest that the approach is useful for finding provably optimal solutions to realistically sized problems, including cases where partworths contain estimation error.