Integration Schemes and Decomposition Modes in Complex Problem Solving

Integrated product development requires that decomposition and integration schemes be congruent and in harmony with each other. This harmony marks a complex and large scale product development project with success. In domain of problem solving one needs to resort to a priori knowledge about problem structure indicating the problems underlying couplings/complexity. Here, we refer to the problem structure as the self map of the system. Usually for large scale problems the self needs to be decomposed for tractability purposes. The structure of the problem after decomposition is the real structure to be dealt with. In this paper we measure the complexity of systems before and after decomposition. We refer to complexity of the system/problem before decomposition as self complexity and that of system after decomposition as real complexity. It is shown that real complexity cannot be less than self complexity regardless of the decomposition type, and therefore decomposition does not reduce the overall complexity of problem. Also it is shown that by using real complexity measure of decomposed system, weak and strong emergence can be detected in the system. This would have important implications in problem classification and choosing the right design process that is in congruence with complexity of the problem