Developing a mathematical model for cell formation in cellular manufacturing systems

Cellular manufacturing is an application of group technology (GT) concepts. The aim of a cellular manufacturing system (CMS) is to identify similar manufacturing processes and features where machines are grouped into machine cells based on their contributions to the production process. It has been realised that CMSs benefit from the advantages of both product-based manufacturing systems and job shop manufacturing systems. The cell formation problem (CFP) is one of the key issues in the design of CMS which deals with the identification of machine cells and part families. Many authors adopt either a sequential or a simultaneous procedure to group the parts and machines. The sequential procedure used in some of these studies determines the part families first, followed by machine assignments. On the other hand, the simultaneous procedure determines the part families and machine groups concurrently. This paper proposes a mathematical model to identify machine cells and part families simultaneously, so that the number of voids and exceptional elements are minimised. To evaluate performance of the proposed model, a number of test problems adopted from the literature are solved and the solutions are compared with those of previous well-known methods using the grouping efficacy measure.