An Approach to the Optimal Positioning of a New Product

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Abstract
This study examines the problem faced by a firm which wishes to position a new choice object in an existing product class. It is assumed that both the consumer and the firm are involved in a two-stage decision process. The consumer first decides on his budget for the product class. He then evaluates, within the product class, that subset of competing objects which have prices approximately equal to his budget constraint. This evaluation is performed through a weighted multi-attribute utility model. The product classes considered here are ones for which the consumer has a finite ideal level on each attribute. The consumer is hypothesized to choose, without error, that object which is closest to his ideal. Different individuals are assumed to be heterogeneous in both attribute weights and ideal levels. The firm is assumed to first identify, in the attribute space which contains ideal points and competing objects, promising product positions which would attract a large number of consumers. It then evaluates these positions in terms of costs and resulting profits. The problem of identifying the promising positions, given information on a sample of individuals, is formulated as a Mixed Integer Nonlinear Program. Due to the inability of such a program to solve even small sample problems, the spatial properties of the problem are examined. An exact solution algorithm which is computationally feasible for small samples is developed. It is based on an examination of intersections of indifference hyperellipsoids. For larger sample problems an efficient heuristic which is an extension of the random point search used in nonlinear programming is provided. It involves random line search procedures for our noncontinuous-type problem. The positioning approach and the heuristic are illustrated in a simulated positioning problem in the small car market.

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