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Journal of Applied Mathematics
Volume 2013, Article ID 285759, 9 pages
Research Article

A Mathematical Programming Model for Cell Formation Problem with Machine Replication

1Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, Selangor, Malaysia
2Department of Industrial Engineering, Lenjan Branch, Islamic Azad University, Esfahan, Iran

Received 12 December 2012; Accepted 8 February 2013

Academic Editor: Ricardo Perera

Copyright © 2013 Reza Raminfar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cell formation (CF) is a crucial aspect in the design of cellular manufacturing (CM) systems. This paper develops a comprehensive mathematical programming model for the cell formation problem, where product demands, cell size limits, sequence of operations, multiple units of identical machines, machine capacity, or machine cost are all considered. In this model, the intercell moves are restricted to be unidirectional from one cell to the downstream cells, without backtracking. The proposed model is investigated through several numerical examples. To evaluate the solution quality of the proposed model, it is compared with some well-known cell formation methods from the literature, by using group capability index (GCI) as a performance measure. The results and comparisons indicate that the proposed model produces solution with a higher performance.