Numerically Stable Design Optimization With Price Competition

Abstract

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.

Compliance by Design: Influence of Acceleration Trade-offs on CO2 Emissions and Costs of Fuel Economy and Greenhouse Gas Regulations

“…The engineering design literature, on the other hand, develops detailed models of the trade-offs among product attributes based on physics. − In this literature, it is common to determine a particular firm’s choices of engineering design variables and prices that maximize the firm’s profits. − With a few notable exceptions, − however, this body of research generally ignores the strategic nature of competing firms’ price and design decisions. The studies that do account for competitor design and pricing decisions are focused on relatively simple examples with ten or fewer products in the market and identical design trade-offs and costs for all firms.…”

Should Optimal Designers Worry About Consideration?

“…Thus it is reasonable to consider a case where firms learn more about preferences when they offer the portfolio designed and exercise price flexibility to maximize profits. Suppose that the MNL, RCL, NML, and CTC models inform the design of the product portfolio but that prices can be changed even the product is offered (as in, e.g., [65]). How much more profits could the firm recover by using the true choice behavior in order to set optimal prices, for fixed designs?…”