Journal of Manufacturing Systems Volume 12/No. 5 Clustering Effectiveness of Permutation Generation Heuristics for Machine-Part Matrix Clustering Charu Chandra, Shahrukh A. Irani, and Sant R. Arora, University of Minnesota, Minneapolis Abstract The first step in the design of a cellular manufactur- ing 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 l'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 effective- ness. 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. Keywords: Group Technology, Cellular Manufac- turing Systems, Block Diagonalization of Machine- Part Matrix, Cluster Analysis, Clustering Effectiveness Introduction A special application of group technology (GT) is the design of a cellular manufacturing system (CMS) where parts having similar (or identical) machine requirements and operation sequences are grouped into families and the complete set of machines in their routings are grouped into machine groups or cells. Any cell formation method must address the critical issues of (1) part family formation, (2) machine grouping, (3) machine sharing between cells, (4) intracell layout, and (5) intercell layout to meet the organizational and operational goals of a company. 1-7 The machine-part matrix clustering technique for cell formation seeks to identify machine groups and part families by rearranging the random initial 0-1 matrix into a block diagonal form (BDF). Each block of l's in the BDF represents a machine group that can perform all the operations for a particular part family. This paper evaluates a measure for characterizing a good BDF, addressing issues (1) and (2) listed above. Issues (3), (4), and (5) have a broader implication on CMS design and are not addressed as part of this research effort; they require a detailed knowledge of equipment categories for machine duplication analyses, the size and shape of individ- ual cells, intercell layout and material flows, and so on, as in Burbidge's production flow analysis procedure.a Here a broad definition of the problem of obtaining the best BDF is presented. Then a solution strategy is outlined to identify the best BDF, and a literature survey gives some of the graph theoretic clustering heuristics. Next is an analysis of the BDF for each of the machine-part matrixes obtained using these heuristics, and a final section provides conclusions and implications of this research for the cell design problem. Problem Definition A machine group and its part family together constitute a block along the diagonal of the final matrix. A block is visually identified as an area defined by a certain number of rows and columns in the matrix within which a large proportion of entries consists of l's. Rows (or columns) of identical or similar strings of l's and O's are placed consecu- tively in the final matrix. A quantitative expression for this "ease of visual identification" should 388