Products and services can be thought of as bundles of attributes that are each made up of many levels. Consumers consider tradeoffs between various attributes and levels before making a purchase decision for a product. A popular marketing research technique called conjoint analysis is used to study these tradeoffs. The data on consumer preferences is generally decomposed using a regression procedure into utility values that the consumer associates with each level of every attribute. In the design of a new product, it is critical to determine a judicious combination of attribute levels that is likely to perform well in a market containing competitor products. Using these utility measures, a firm can design products that would best meet consumer expectations and the seller's objectives.; A popular way to measure the success of a new product is to calculate the amount of market share it is expected to capture in a competitive market. Researchers have proposed the share-of-choice problem whose objective is to maximize the number of respondents from a conjoint study who prefer a new product to their status-quo products. The share-of-choice problem is NP-hard. The linear-programming based branch-and-bound algorithm is inefficient in solving real world instances of the share-of-choice problem. Several heuristic procedures to solve the share-of-choice problem have appeared in the literature. In this research, an exact algorithm is proposed to solve real world instances of the share-of-choice problem to optimality. An experiment is designed to test the run-time performance of the exact algorithm using a set of simulated problems that mimic real world problem characteristics. We also suggest potential extensions of the exact algorithm to solve modified versions of the share-of-choice problem, and also to solve the related product line design problem.
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