Are we there yet? Investigating the role of design process architecture in convergence time

In distributed design individual designers have local control over design variables and seek to minimize their own individual objectives. The amount of time required to reach equilibrium solutions in decentralized design can vary based on the design process architecture chosen. There are two primary design process architectures, sequential and parallel, and a number of possible combinations of these architectures. In this paper a game theoretic approach is developed to determine the time required for a parallel and sequential architecture to converge to a solution for a two designer case. The equations derived solve for the time required to converge to a solution in closed form without any objective function evaluations. This result is validated by analyzing a distributed design case study. In this study the equations accurately predict the convergence time for a sequential and parallel architecture. A second validation is performed by analyzing a large number of randomly generated two designer systems. The approach in this case successfully predicts convergence within 3 iterations for nearly 98% of the systems analyzed. The remaining 2% highlight one of the approach's weaknesses; it is susceptible to numerically ill conditioned problems. Understanding the rate at which distributed design problems converge is of key importance when determining design architectures. This work begins the investigation with a two designer case and lays the groundwork to expand to larger design systems with multiple design variables.