Numerically Stable Design Optimization With Price Competition

Researchers in Decision-Based Design have asserted that business objectives, e.g. profits, should replace engineering requirements or performance metrics as the objective for engineering design. Using profits as the objective for engineering design, however, requires modeling consumer preferences and competition between firms. Game theoretic “design-then-pricing” models—i.e. product design with 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 proposes a method for solving design-then-pricing problems that exhibits improved efficiency and reliability, relative to existing methods. Numerical results for a vehicle design example using three solvers—matlab, KNITRO, and SNOPT—to validate this claim. We also highlight the importance of checking the Second-Order Sufficient Conditions in design-then-pricing problems that use Mixed Logit models of demand.