Global Product Design Platforming: A Comparison of Two Equilibrium Solution Methods

Abstract

Global product platforms can reduce production costs through economies of scale and learning but may decrease revenues by restricting the ability to customize for each market. We model the global platforming problem as a Nash equilibrium among oligopolistic competing firms, each maximizing its profit across markets with respect to its pricing, design, and platforming decisions. We develop and compare two methods to identify Nash equilibria: (1) a sequential iterative optimization (SIO) algorithm, in which each firm solves a mixed-integer nonlinear programming problem globally, with firms iterating until convergence; and (2) a mathematical program with equilibrium constraints (MPEC) that solves the Karush Kuhn Tucker conditions for all firms simultaneously. The algorithms’ performance and results are compared in a case study of plug-in hybrid electric vehicles where firms choose optimal battery capacity and whether to platform or differentiate battery capacity across the US and Chinese markets. We examine a variety of scenarios for (1) learning rate and (2) consumer willingness to pay (WTP) for range in each market. For the case of two firms, both approaches find the Nash equilibrium in all scenarios. On average, the SIO approach solves 200 times faster than the MPEC approach, and the MPEC approach is more sensitive to the starting point. Results show that the optimum for each firm is to platform when learning rates are high or the difference between consumer willingness to pay for range in each market is relatively small. Otherwise, the PHEVs are differentiated with low-range for China and high-range for the US.