Heuristics for pricing and positioning a product-line using conjoint and cost data

TLDR: In this article, the authors formalize the problem as a mathematical program where the objective of the firm is either profit or total welfare, and they develop a new greedy heuristic for the profit problem, and its application to simulated problems shows that it too runs quickly, and with better performance than various alternatives and previously published heuristics.

Abstract: Designing and pricing a product-line is the very essence of every business. In recent years quantitative methods to assist managers in this task have been gaining in popularity. Conjoint analysis is already widely used to measure preferences for different product profiles, and build market simulation models. In the last few years several papers have been published that suggest how to optimally choose a product-line based on such data. We formalize this problem as a mathematical program where the objective of the firm is either profit or total welfare. Unlike alternative published approaches, we introduce fixed and variable costs for each product profile. The number of products to be introduced is endogenously determined on the basis of their desirability, fixed and variable costs, and in the case of profits, their cannibalization effect on other products. While the problem is difficult NP-complete, we show that the maximum welfare problem is equivalent to the uncapacitated plant location problem, which can be solved very efficiently using the greedy interchange heuristic. Based on past published experience with this problem, and on simulations we perform, we show that optimal or near optimal solutions are obtained in seconds for large problems. We develop a new greedy heuristic for the profit problem, and its application to simulated problems shows that it too runs quickly, and with better performance than various alternatives and previously published heuristics. We also show how the methodology can be applied, taking existing products of both the firm and the competition into account.