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

Abstract

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.integer programming, combinatorial optimization, product design, marketing, conjoint analysis, optimization

An Interdisciplinary Review of Research in Conjoint Analysis: Recent Developments and Directions for Future Research

“…A number of optimization algorithms have been applied to solve such difficult problems including dynamic programming, beam search, genetic algorithms, and Lagrangian relaxation with branch and bound [12,23]. More recently, alternative heuristics have been devised employing conjoint and choice models.…”

Product Attribute Design Using an Agent-Based Simulation of an Artificial Market

“…Conjoint analysis [14,15] and fuzzy multi-attribute decision techniques [16][17][18] have been introduced to describe consumers' preferences. Optimisation techniques, such as genetic algorithms [15], Lagrangian relaxation with a branch and bound algorithm [19], and particle swarm optimisation [20,21], which are all associated with preference measures, have been applied to determine the combination of product attributes that maximises a company's expected profit or the consumers' total utility.…”

Designing and Pricing Services Based on Customer-Perceived Value: An Airline Company Feasibility Study

“…Albers and Brockhoff (1977) showed how the problem can be formulated as a mixed integer nonlinear programming problem. Other more recent studies include Camm et al (2006), who made use of an exact branchand-bound algorithm and showed that this approach is very appropriate for large-scale problems as well as cases with partworths containing estimation errors, and Gruca and Klemz (2003), who presented an innovative method that utilizes genetic algorithms to come up with an optimal positioning strategy. Draganska and Jain (2006) showed that yogurt's consumers value line attributes more than flavor attributes through a discrete-choice model formed by both a demand-side and a supply-side model.…”

“…Draganska and Jain (2006) showed that yogurt's consumers value line attributes more than flavor attributes through a discrete-choice model formed by both a demand-side and a supply-side model. Other studies contain sophisticated operations research models that take into consideration consumer preferences as well as several tests to check the reliability of results obtained from different models (for example, see Netzer et al 2008;Camm et al 2006;Green et al 1991Green et al , 1993.…”