A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system

In the past several years, many studies have been carried out on cellular manufacturing based on a two-dimensional machine–part incidence matrix. Since workers have important role in doing jobs on machines, assignment of workers to cells becomes a crucial factor for fully utilization of cellular manufacturing systems. In this paper, an attempt is made to solve cell formation problem and minimize the number of voids and exceptional elements in a three dimensional (cubic) machine–part–worker incidence matrix. The proposed mathematical model captures the capability of workers in doing different jobs. To demonstrate the effectiveness of the proposed model, the solution of some test problems is compared with the literature method.