Cluster first-sequence last heuristics for generating block diagonal forms for a machine-part matrix

Abstract

Abstract Before detailed cell design analyses, rearranging the binary (or 0-1) machine-part matrix into a compact block diagonal form (BDF) is useful for controlling combinatorial explosion during subsequent decision-making involving machine duplication, subcontracting, intercell layout design, etc. Several authors have shown that a compact BDF corresponds to the implicit clusters in both dimensions being expressed as row and column permutations. A traditional approach for solving this problem has been to obtain the two permutations independently by solving the permutation problem in each dimension as a (unidimensional) travelling salesman problem (TSP). This paper describes cluster first-sequence last heuristics which combine the properties of the minimal spanning tree (MST) (clusters only) and TSP (sequence only) for improved permutation generation. The BDFs obtained with these heuristics were compared with those obtained using the TSP, linear placement problem (LPP), single linkage cluster analysis (SL...