Clustering effectiveness of permutation generation heuristics for machine-part matrix clustering

Abstract

Abstract The first step in the design of a cellular manufacturing system (CMS) is the clustering of the binary machine-part matrix. This provides a visual basis for matching the machine groups to the part families they produce. Essentially, this requires that the orders of the machines and parts in the initial matrix be permuted independently a finite number of times. If machine-part clusters exist, they will appear as blocks of 1's along the diagonal of the matrix. Our study focuses on identifying a generic measure for the compactness of a good block diagonal form (BDF) in the final matrix produced by any heuristic. A difficult matrix in the literature known to have cluster overlap in both dimensions was solved using various graph theoretic heuristics for permutation generation. The compactness of the BDF in each of the final matrixes was evaluated using a new measure of BDF compactness developed by the authors. Comparisons were made with other measures of clustering effectiveness. The paper concludes with a discussion on how these measures could help to identify near-optimal BDFs to simplify machine grouping for detailed cell formation analyses.