Implications of Competitor Representation on Optimal Design

We investigate the effect of competitor product representation on optimal design results in profit-maximization studies. Specifically, we study the implications of replacing a large set of product alternatives available in the marketplace with a reduced set of selected competitors or with composite alternatives, as is common in the literature. We derive first-order optimality conditions and show that optimal design (but not price) is independent of competitors under the logit and nested logit models (where preference coefficients are homogeneous), but optimal design results may depend on competitor representation in latent class and mixed logit models (where preference coefficients are heterogeneous). In a case study of automotive powertrain design using mixed logit demand, we find some change in the optimal acceleration performance value when competitors are modeled using a small set of alternatives rather than the larger set. The magnitude of this change depends on the specific form and parameters of the cost and demand functions assumed, ranging from 0% to 3% in our case study. We find that the magnitude of the change in optimal design variables induced by competitor representation in our case study increases with the heterogeneity of preference coefficients across consumers and changes with the curvature of the cost function.