Analytical methods for perfect partition by set theory

Abstract

A recent interesting paper was published by Yin et al. (2014). They developed a structural architecture to investigate the previous literature with three types of research problems: what, why, and how. They utilised simple but rigorous set theory to define CM concepts, such as part family, machine cell, cellular manufacturing system, bottleneck machines. Then, they deduced sufficient and necessary conditions for perfectly partitioned cellular manufacturing systems. An algorithm was proposed to get perfectly partitioned manufacturing cells. The objective of this paper is to overcome the two problems in Yin et al.'s (2014) research. Firstly, we modify their algorithm to get perfectly partitioned manufacturing cells. Then we extend the analysis from machine groups to a cellular manufacturing system and compare the results with the ones of Yin et al. (2014). Based on the analysis of our new model, we propose a new algorithm to generate perfectly partitioned manufacturing cells.