Global Product Design Platforming: A Comparison of Two Methods to Find Equilibrium Solutions

We examine optimal-profit product design platforming problems for products sold across multiple markets. Firms have an incentive to platform to take advantage of cost reductions that are possible with increased production quantity, such as learning-by-doing. However, platforming may decrease sales compared to if the designs were customized for each market. The problem can be represented as a Nash equilibrium between multiple competing firms, each with a nonconvex mixed-integer nonlinear programing (MINLP) problem for maximizing their individual profits. We derive the Karush-Kuhn-Tucker (KKT) conditions for the problem and compare results from two algorithmic approaches: (1) an iterative MINLP approach that uses the BARON algorithm to solve each firm’s design and platforming problem and iterates until convergence to an equilibrium, and (2) an approach that solves the KKT conditions directly holding platforming decisions fixed, and compares profits for these platforming decisions to find an equilibrium. Results are presented for a case study of plug-in hybrid electric vehicles (PHEVs) where firms choose whether or not to platform the battery pack across the U.S. and China, and set the optimal battery capacity. We vary the learning rate and the difference in consumer willingness to pay for all-electric range between China and the U.S. Both algorithms agree on the same equilibrium solution in 98.4% of the cases. Results show that the optimum for each firm is to platform when learning rates are low, or the difference between optimal battery capacity in each market is relatively small.