A probabilistic choice model for the product line design problem.

Designing optimal product lines is essential for any firm to stay competitive. Whereas a large number of optimization algorithms have been applied for solving the problem, most of them adopt the first choice rule to simulate the consumer's choice process. Researchers avoid using probabilistic choice models, such as the logit, since they tend to produce duplicate products in the line, due to the IIA problem. Furthermore preference heterogeneity among consumers is a factor usually neglected, although its representation form has a substantial impact in the design of the product line. We propose a probabilistic choice model that can be used with algorithms that solve the optimal product line design problem, using the share of choices criterion. Our model deals with the IIA problem, by incorporating the similarity among products through the use of a corrective method. In addition, preference heterogeneity among consumers is effectively represented, while the model's predictive accuracy is optimized through the use of Stochastic Logarithmic Search and Genetic Algorithms.