The objective of this study is to develop a mathematical framework for determining the minimum number of parts required in a product to satisfy a list of functional requirements (FRs) given a set of connections between FRs. The problem is modeled as a graph coloring technique in which a graph G with n nodes (representing the FRs) and m edges (representing the connections between the FRs) is studied to determine the graph’s chromatic number χ(G), which is the minimum number of colors required to properly color the graph. The chromatic number of the graph represents the minimum number of parts needed to satisfy the list of FRs. In addition, the study calculates the computational efficiency of the proposed algorithm. Several examples are provided to show the application of the proposed algorithm.

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