Skip to main content
SpringerLink
Log in

Exact model for the cell formation problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The cell formation problem (CFP) consists in an optimal grouping of the given machines and parts into cells, so that machines in every cell process as much as possible parts from this cell (intra-cell operations) and as less as possible parts from other cells (inter-cell operations). The grouping efficacy is the objective function for the CFP which simultaneously maximizes the number of intra-cell operations and minimizes the number of inter-cell operations. Currently there are no exact approaches (known to the authors) suggested for solving the CFP with the grouping efficacy objective. The only exact model which solves the CFP in a restricted formulation is due to Elbenani and Ferland (Cell formation problem solved exactly with the dinkelbach algorithm. Montreal. Quebec. CIRRELT-2012-07, 1–14, 2012). The restriction consists in fixing the number of production cells. The main difficulty of the CFP is the fractional objective function—the grouping efficacy. In this paper we address this issue for the CFP in its common formulation with a variable number of cells. Our computational experiments are made for the most popular set of 35 benchmark instances. For the 14 of these instances using CPLEX software we prove that the best known solutions are exact global optimums.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Askin, R.G., Subramanian, S.P.: A cost-based heuristic for group technology configuration. Int. J. Prod. Res. 25(1), 101–113 (1987)

    Article  Google Scholar 

  2. Boctor, F.F.: A linear formulation of the machine-part cell formation problem. Int. J. Prod. Res. 29(2), 343–356 (1991)

    Article  Google Scholar 

  3. Boe, W., Cheng, C.H.: A close neighbor algorithm for designing cellular manufacturing systems. Int. J. Prod. Res. 29(10), 2097–2116 (1991)

    Article  MATH  Google Scholar 

  4. Carrie, S.: Numerical taxonomy applied to group technology and plant layout. Int. J. Prod. Res. 11, 399–416 (1973)

    Article  Google Scholar 

  5. Chan, H.M., Milner, D.A.: Direct clustering algorithm for group formation in cellular manufacture. J. Manuf. Syst. 1(1), 64–76 (1982)

    Google Scholar 

  6. Chandrasekharan, M.P., Rajagopalan, R.: MODROC: an extension of rank order clustering for group technology. Int. J. Prod. Res. 24(5), 1221–1233 (1986a)

    Article  Google Scholar 

  7. Chandrasekharan, M.P., Rajagopalan, R.: An ideal seed non-hierarchical clustering algorithm for cellular manufacturing. Int. J. Prod. Res. 24(2), 451–464 (1986b)

    Article  MATH  Google Scholar 

  8. Chandrasekharan, M.P., Rajagopalan, R.: ZODIAC: an algorithm for concurrent formation of part families and machine cells. Int. J. Prod. Res. 25(6), 835–850 (1987)

    Article  MATH  Google Scholar 

  9. Chandrasekharan, M.P., Rajagopalan, R.: Groupability: analysis of the properties of binary data matrices for group technology. Int. J. Prod. Res. 27(6), 1035–1052 (1989)

    Article  Google Scholar 

  10. Elbenani, B., Ferland, J.A.: Cell Formation Problem Solved Exactly with the Dinkelbach Algorithm. Montreal. Quebec. CIRRELT-2012-07, pp. 1–14 (2012)

  11. Ghosh, S., Mahanti, A., Nagi, R., Nau, D.S.: Manufacturing cell formation by state-space search. Ann. Oper. Res. 65(1), 35–54 (1996)

    Article  MATH  Google Scholar 

  12. Goncalves, J.F., Resende, M.G.C.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)

    Article  Google Scholar 

  13. James, T.L., Brown, E.C., Keeling, K.B.: A hybrid grouping genetic algorithm for the cell formation problem. Comput. Oper. Res. 34(7), 2059–2079 (2007)

    Article  MATH  Google Scholar 

  14. King, J.R.: Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm. Int. J. Prod. Res. 18(2), 213–232 (1980)

    Article  Google Scholar 

  15. King, J.R., Nakornchai, V.: Machine-component group formation in group technology: review and extension. Int. J. Prod. Res. 20(2), 117–133 (1982)

    Article  Google Scholar 

  16. Kumar, K.R., Kusiak, A., Vannelli, A.: Grouping of parts and components in flexible manufacturing systems. Eur. J. Oper. Res. 24, 387–397 (1986)

    Article  Google Scholar 

  17. Kumar, K.R., Chandrasekharan, M.P.: Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology. Int. J. Prod. Res. 28(2), 233–243 (1990)

    Article  Google Scholar 

  18. Kumar, K.R., Vannelli, A.: Strategic subcontracting for efficient disaggregated manufacturing. Int. J. Prod. Res. 25(12), 1715–1728 (1987)

    Google Scholar 

  19. Kusiak, A.: The generalized group technology concept. Int. J. Prod. Res. 25(4), 561–569 (1987)

    Article  Google Scholar 

  20. Kusiak, A., Chow, W.S.: Efficient solving of the group technology problem. J. Manuf. Syst. 6(2), 117–124 (1987)

    Article  Google Scholar 

  21. McCormick, W.T., Schweitzer, P.J., White, T.W.: Problem decomposition and data reorganization by a clustering technique. Oper. Res. 20(5), 993–1009 (1972)

    Article  MATH  Google Scholar 

  22. Mosier, C.T., Taube, L.: The facets of group technology and their impact on implementation. OMEGA 13(6), 381–391 (1985a)

    Article  Google Scholar 

  23. Mosier, C.T., Taube, L.: Weighted similarity measure heuristics for the group technology machine clustering problem. OMEGA 13(6), 577–583 (1985b)

    Article  Google Scholar 

  24. Paydar, M.M., Saidi-Mehrabad, M.: A hybrid genetic-variable neighborhood search algorithm for the cell formation problem based on grouping efficacy. Comput. Oper. Res. 40(4), 980–990 (2013)

    Article  MathSciNet  Google Scholar 

  25. Seifoddini, H.: A note on the similarity coefficient method and the problem of improper machine assignment in group technology applications. Int. J. Prod. Res. 27(7), 1161–1165 (1989)

    Article  Google Scholar 

  26. Seifoddini, H., Wolfe, P.M.: Application of the similarity coefficient method in group technology. IIE Trans. 18(3), 271–277 (1986)

    Article  Google Scholar 

  27. Srinivasan, G., Narendran, T.T., Mahadevan, B.: An assignment model for the part-families problem in group technology. Int. J. Prod. Res. 28(1), 145–152 (1990)

    Article  Google Scholar 

  28. Stanfel, L.: Machine clustering for economic production. Eng. Costs Prod. Econ. 9, 73–81 (1985)

    Article  Google Scholar 

  29. Waghodekar, P.H., Sahu, S.: Machine-component cell formation in group technology MACE. Int. J. Prod. Res. 22, 937–948 (1984)

    Google Scholar 

Download references

Acknowledgments

The authors are partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057.

Author information

Authors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, 136 Rodionova, Nizhniy Novgorod, 603093, Russian Federation

    Ilya Bychkov, Mikhail Batsyn & Panos M. Pardalos

  2. Center of Applied Optimization, University of Florida, 401 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Authors
  1. Ilya Bychkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikhail Batsyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mikhail Batsyn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bychkov, I., Batsyn, M. & Pardalos, P.M. Exact model for the cell formation problem. Optim Lett 8, 2203–2210 (2014). https://doi.org/10.1007/s11590-014-0728-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-014-0728-8

Keywords

Search

Navigation