A study of convergence in decentralized design processes

The decomposition and coordination of decisions in the design of complex engineering systems is a great challenge. Companies who design these systems routinely allocate design responsibility of the various subsystems and components to different people, teams or even suppliers. The mechanisms behind this network of decentralized design decisions create difficult management and coordination issues. However, developing efficient design processes is paramount, especially with market pressures and customer expectations. Standard techniques to modeling and solving decentralized design problems typically fail to understand the underlying dynamics of the decentralized processes and therefore result in suboptimal solutions. This paper aims to model and understand the mechanisms and dynamics behind a decentralized set of decisions within a complex design process. By using concepts from the fields of mathematics and economics, including Game Theory and the Cobweb model, we model a simple decentralized design problem and provide efficient solutions. This new approach uses matrix series and linear algebra as tools to determine conditions for convergence of such decentralized design problems. The goal of this paper is to establish the first steps towards understanding the mechanisms of decentralized decision processes. This includes two major steps: studying the convergence characteristics and finding the final equilibrium solution of a decentralized problem. Illustrations of the developments are provided in the form of two decentralized design problems with different underlying behavior.