Skip to main content
SpringerLink
Log in
Book cover

Cellular Manufacturing Systems pp 97–127Cite as

Mathematical programming and graph theoretic methods for cell formation

  • Chapter

  • 156 Accesses

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.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Adil, G.K., Rajamani, D. and Strong, D. (1993c) Cell formation considering alternate routings. Univ. Manitoba, Canada. Working paper.

    Google Scholar 

  • Adil, G.K., Rajamani, D. and Strong, D. (1994) A two stage approach for cell formation considering material handling. Univ. Manitoba, Canada. Working paper.

    Google Scholar 

  • Boctor, F.F. (1991) A linear formulation of the machine part cell formation. International Journal of Production Research, 29(2), 343–56.

    Article  Google Scholar 

  • Burbidge, J.L., (1975) The Introduction of Group Technology, Wiley, London.

    Google Scholar 

  • Burbidge, J.L. (1993) Comments on clustering methods for finding GT groups and families. Journal of Manufacturing Systems, 12(5), 428–9.

    Article  Google Scholar 

  • Carrie, A.S. (1973) Numerical taxonomy applied to group technology and plant layout. International Journal of Production Research, 11(4), 399–416.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ham, I., Hitomi, K. and Yoshida, T. (1985) Group Technology: Applications to Production Management, Kluwer-Nijhoff Publishing, Boston.

    Google Scholar 

  • Kasilingam, R.G. (1989) Mathematical programming approach to cell formation problems in flexible manufacturing systems. Univ. Windsor, Canada. Doctoral dissertation.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Kusiak, A. (1987) The generalized group technology concept. International Journal of Production Research, 25(4), 561–9.

    Article  Google Scholar 

  • Kusiak, A. and Cho, M. (1992) Similarity coefficient algorithms for solving the group technology problem. International Journal of Production Research, 30(11), 2633–46.

    Article  Google Scholar 

  • Kusiak, A. and Chow, W.S. (1988) Decomposition of manufacturing systems. IEEE Journal of Robotics and Automation, 4(5), 457–71.

    Article  Google Scholar 

  • Kusiak, A., Vannelli, A. and Kumar, K.R. (1986) Clustering analysis: models and algorithms. Control and Cybernetics, 15(2), 139–54.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ribeiro, J.F.F. and Pradin, B. (1993) A methodology for cellular manufacturing design. International Journal of Production Research, 31(1), 235–50.

    Article  Google Scholar 

  • Seiffodini, H. and Wolfe, P.M. (1986) Application of the similarity coefficient method in group technology. IIE Transactions, 18, 271–7.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Song, S. and Hitomi, K. (1992) GT cell formation for minimizing the intercell part flow. International Journal of Production Research, 30(12), 2737–53.

    Article  Google Scholar 

  • Srinivasan, G. and Narendran T.T. (1991) GRAFICS-a nonhierarchical clustering algorithm for group technology. International Journal of Production Research, 29(3), 463–78.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sule, D.R. (1991) Machine capacity planning in group technology. International Journal of Production Research, 29(9), 1909–22.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wei, J.C. and Gaither, N. (1990) An optimal model for cell formation decisions. Decision Sciences, 21(2), 416–33.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Manufacturing Engineering, Wayne State University, Detroit, USA

    Nanua Singh

  2. Department of Mechanical and Industrial Engineering, University of Manitoba, Winnipeg, Canada

    Divakar Rajamani

Authors
  1. Nanua Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Divakar Rajamani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints 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

Publish with us

Policies and ethics

Search

Navigation