SMACOF Hierarchical Clustering to Manage Complex Design Problems with the Design Structure Matrix

Defense system engineering is complex in nature that requires systematic approaches. The design structure matrix (DSM) is a powerful tool for supporting architecture analysis and management of systems. This paper facilitates quantitative analysis by revealing the hidden problem structure. A combined approach using Scaling by MAjorizing a Complicated Function (SMACOF) and hierarchical clustering is proposed to manipulate the design DSM. This algorithm calculates the relevance among the system elements and shows how large problems can be organized into smaller, highly connected topologic modules that combine in a hierarchical manner into larger, less cohesive units. The algorithm also uses Cost and the Jaccard index to guide comparison of results. A simple example is used to illustrate the solution procedure. Also, two real industrial application examples—an aircraft design problem and a satellite multidisciplinary team organization problem—are chosen to demonstrate how the proposed DSM approach manages complexity in the design process.