Robust Product Line Design

AbstractThe majority of approaches to product line design that have been proposed by marketing scientists assume that the underlying choice model that describes how the customer population will respond to a new product line is known precisely. In reality, however, marketers do not precisely know how the customer population will respond and can only obtain an estimate of the choice model from limited conjoint data. In this paper, we propose a new type of optimization approach for product line design under uncertainty. Our approach is based on the paradigm of robust optimization where, rather than optimizing the expected revenue with respect to a single model, one optimizes the worst-case expected revenue with respect to an uncertainty set of models. This framework allows us to account for parameter uncertainty, when we may be confident about the type of model structure but not about the values of the parameters, and structural uncertainty, when we may not even be confident about the right model structure to use to describe the customer population. Through computational experiments with a real conjoint data set, we demonstrate the benefits of our approach in addressing parameter and structural uncertainty. With regard to parameter uncertainty, we show that product lines designed without accounting for parameter uncertainty are fragile and can experience worst-case revenue losses as high as 23%, and that the robust product line can significantly outperform the nominal product line in the worst case, with relative improvements of up to 14%. With regard to structural uncertainty, we similarly show that product lines that are designed for a single model structure can be highly suboptimal under other structures (worst-case losses of up to 37%), while a product line that optimizes against the worst of a set of structurally distinct models can outperform single model product lines by as much as 55% in the worst case and can guarantee good aggregate performance over structurally distinct models.