A polynomial-time algorithm for optimal clustering in a special class of {0,1}-matrices

The process of forming group technology based families for cellular manufacturing applications often entails the identification of clusters in {0,1}-matrices. Most of the methods developed to date for cluster formation in this context employ heuristics that typically generate sub-optimal solutions (in terms of the number of exceptional elements). In this paper, we will describe a polynomial-time algorithm, based on a graph-theoretic approach, for optimal cluster formation in a class of {0,1}-matrices called vertex-tree graphic matrices. A comparison of the performance of this algorithm with popular heuristics is also provided. The algorithm can be used as a benchmarking tool for cluster formation heuristics.