Numerically Stable Design Optimization With Price Competition

Researchers in decision-based design (DBD) have suggested that business objectives, e.g., profits, should replace engineering requirements or performance metrics as the objective for engineering design. This requires modeling market performance, including consumer preferences and competition between firms. Game-theoretic “design-then-pricing” models—i.e., product design anticipating future price competition–provide an important framework for integrating consumer preferences and competition when design decisions must be made before prices are decided by a firm or by its competitors. This article concerns computational optimization in a design-then-pricing model. We argue that some approaches may be fundamentally difficult for existing solvers and propose a method that exhibits both improved efficiency and reliability relative to existing methods. Numerical results for a vehicle design example validate our theoretical arguments and examine the impact of anticipating pricing competition on design decisions. We find that anticipating pricing competition, while potentially important for accurately forecasting profits, does not necessarily have a significant effect on optimal design decisions. Most existing examples suggest otherwise, anticipating competition in prices is important to choosing optimal designs. Our example differs in the importance of design constraints, that reduce the influence the market model has on optimal designs.