Abstract
The algorithmic procedures for cell formation discussed so far are heuristics. As discussed, these procedures are affected by the nature of input data and the initial matrix and do not necessarily provide a good partition, even if one is possible. Thus, there is a need to develop mathematical models which can provide optimal solutions. The models provide a basis for comparison with the heuristics. The structure of the model thus developed also assists the researcher in suggesting efficient solution schemes. Moreover, the heuristics can be used as a starting point to drive an optimal algorithm towards searching for better, or even optimal solutions while saving on a great deal of computer time (Wei and Gaither, 1990).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adil, G.K., Rajamani, D. and Strong, D. (1993a) AAA-an assignment allocation algorithm for cell formation. Univ. Manitoba, Canada. Working paper.
Adil, G.K., Rajamani, D. and Strong, D. (1993b) An algorithm for cell formation considering alternate process plans, in Proceedings of IASTED International Conference, Pittsburgh, PA, PP. 285–8.
Adil, G.K., Rajamani, D. and Strong, D. (1993c) Cell formation considering alternate routings. Univ. Manitoba, Canada. Working paper.
Adil, G.K., Rajamani, D. and Strong, D. (1994) A two stage approach for cell formation considering material handling. Univ. Manitoba, Canada. Working paper.
Boctor, F.F. (1991) A linear formulation of the machine part cell formation. International Journal of Production Research, 29(2), 343–56.
Burbidge, J.L., (1975) The Introduction of Group Technology, Wiley, London.
Burbidge, J.L. (1993) Comments on clustering methods for finding GT groups and families. Journal of Manufacturing Systems, 12(5), 428–9.
Carrie, A.S. (1973) Numerical taxonomy applied to group technology and plant layout. International Journal of Production Research, 11(4), 399–416.
Chan, H.M. and Milner, D.A. (1982) Direct clustering algorithm for group formation in cellular manufacture. Journal of Manufacturing Systems, 1(1), 65–75.
Chandrasekaran, M.P. and Rajagopalan, R. (1986a) MODROC: an extension of rank order clustering algorithm for group technology. International Journal of Production Research, 24(5), 1221–33.
Chandrasekaran, M.P. and Rajagopalan, R. (1986b) An ideal seed non-hierarchical clustering algorithm for cellular manufacturing. International Journal of Production Research, 24(2), 451–64.
Chandrasekaran, M.P. and Rajagopalan, R. (1989) Groupability: an analysis of the properties of binary data matrices for group technology. International Journal of Production Research, 27(7), 1035–52.
Ham, I., Hitomi, K. and Yoshida, T. (1985) Group Technology: Applications to Production Management, Kluwer-Nijhoff Publishing, Boston.
Kasilingam, R.G. (1989) Mathematical programming approach to cell formation problems in flexible manufacturing systems. Univ. Windsor, Canada. Doctoral dissertation.
Kern, G.M. and Wei, J.C. (1991) The cost of eliminating exceptional elements in group technology cell formation. International Journal of Production Research, 29(8), 1535–47.
Kumar, K.R., Kusiak, A. and Vannelli, A. (1986) Grouping of parts and components in flexible manufacturing systems. European Journal of Operational Research, 24, 387–97.
Kusiak, A. (1987) The generalized group technology concept. International Journal of Production Research, 25(4), 561–9.
Kusiak, A. and Cho, M. (1992) Similarity coefficient algorithms for solving the group technology problem. International Journal of Production Research, 30(11), 2633–46.
Kusiak, A. and Chow, W.S. (1988) Decomposition of manufacturing systems. IEEE Journal of Robotics and Automation, 4(5), 457–71.
Kusiak, A., Vannelli, A. and Kumar, K.R. (1986) Clustering analysis: models and algorithms. Control and Cybernetics, 15(2), 139–54.
Lee, J.L., Vogt, W.G. and Mickle, M.H. (1982) Calculation of shortest paths by optimal decomposition. IEEE Transactions on Systems, Man and Cybernetics, 12, 410–15.
Logendran, R. (1992) A model for duplicating bottleneck machines in the presence of budgetary limitations in cellular manufacturing. International Journal of Production Research, 30(3), 683–94.
Miltenburg, J. and Zhang, W. (1991) A comparative evaluation of nine well known algorithms for solving cell formation problem in group technology. Journal of Operations Management, 10(1), 44–72.
Rajagopalan, R. and Batra, J.L. (1975) Design of cellular production systems: a graph theoretic approach. International Journal of Production Research, 13(6), 567–79.
Ribeiro, J.F.F. and Pradin, B. (1993) A methodology for cellular manufacturing design. International Journal of Production Research, 31(1), 235–50.
Seiffodini, H. and Wolfe, P.M. (1986) Application of the similarity coefficient method in group technology. IIE Transactions, 18, 271–7.
Shafer, S.M., Kern, G.M. and Wei, J.C. (1992) A mathematical programming approach for dealing with exceptional elements in cellular manufacturing. International Journal of Production Research, 30(5), 1029–36.
Song, S. and Hitomi, K. (1992) GT cell formation for minimizing the intercell part flow. International Journal of Production Research, 30(12), 2737–53.
Srinivasan, G. and Narendran T.T. (1991) GRAFICS-a nonhierarchical clustering algorithm for group technology. International Journal of Production Research, 29(3), 463–78.
Srinivasan, G., Narendran, T.T and Mahadevan, B. (1990) An assignment model for the part families problem in group technology. International Journal of Production Research, 28(1), 145–52.
Sule, D.R. (1991) Machine capacity planning in group technology. International Journal of Production Research, 29(9), 1909–22.
Vannelli, A. and Kumar, K.R. (1986) A method for finding minimal bottleneck cells for grouping part-machine families. International Journal of Production Research, 24(2), 387–400.
Vohra, T., Chen, D.S., Chang, J.C. and Chen, H.C. (1990) A network approach to cell formation in cellular manufacturing. International Journal of Production Research, 28(11), 2075–84.
Wei, J.C. and Gaither, N. (1990) An optimal model for cell formation decisions. Decision Sciences, 21(2), 416–33.
Wu, N. and Salvendy, G. (1993) A modified network approach for the design of cellular manufacturing systems. International Journal of Production Research, 31(6), 1409–21.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Chapman & Hall
About this chapter
Cite this chapter
Singh, N., Rajamani, D. (1996). Mathematical programming and graph theoretic methods for cell formation. In: Cellular Manufacturing Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1187-4_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1187-4_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8504-5
Online ISBN: 978-1-4613-1187-4
eBook Packages: Springer Book Archive