Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology

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Abstract
Block diagonalization of binary matrices is a primary step in the design of cellular production systems. ‘Grouping efficiency’ which is a weighted average of two measures that consider the voids in the diagonal blocks and exceptional elements in the off-diagonal blocks was the only criterion available to measure the goodness of block diagonal forms. The present work critically analyses this function and brings out its shortcomings, the most severe of them being its low discriminating power. A simple and elegant function has been derived in its place. The new function called grouping efficacy obviates all the defects of the earlier function while retaining the requisite properties. The mathematical properties of the function have been analysed and the function values compared with those of grouping efficiency in the case of well-structured and ill-structured data sets.

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