Optimization Letters

, Volume 8, Issue 8, pp 2203–2210 | Cite as

Exact model for the cell formation problem

  • Ilya Bychkov
  • Mikhail BatsynEmail author
  • Panos M. Pardalos
Original Paper


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.


Cell formation problem Exact model Grouping efficacy  Fractional objective function 



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


  1. 1.
    Askin, R.G., Subramanian, S.P.: A cost-based heuristic for group technology configuration. Int. J. Prod. Res. 25(1), 101–113 (1987)CrossRefGoogle Scholar
  2. 2.
    Boctor, F.F.: A linear formulation of the machine-part cell formation problem. Int. J. Prod. Res. 29(2), 343–356 (1991)CrossRefGoogle Scholar
  3. 3.
    Boe, W., Cheng, C.H.: A close neighbor algorithm for designing cellular manufacturing systems. Int. J. Prod. Res. 29(10), 2097–2116 (1991)zbMATHCrossRefGoogle Scholar
  4. 4.
    Carrie, S.: Numerical taxonomy applied to group technology and plant layout. Int. J. Prod. Res. 11, 399–416 (1973)CrossRefGoogle Scholar
  5. 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. 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)CrossRefGoogle Scholar
  7. 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)zbMATHCrossRefGoogle Scholar
  8. 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)zbMATHCrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    Elbenani, B., Ferland, J.A.: Cell Formation Problem Solved Exactly with the Dinkelbach Algorithm. Montreal. Quebec. CIRRELT-2012-07, pp. 1–14 (2012)Google Scholar
  11. 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)zbMATHCrossRefGoogle Scholar
  12. 12.
    Goncalves, J.F., Resende, M.G.C.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)CrossRefGoogle Scholar
  13. 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)zbMATHCrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 18.
    Kumar, K.R., Vannelli, A.: Strategic subcontracting for efficient disaggregated manufacturing. Int. J. Prod. Res. 25(12), 1715–1728 (1987)Google Scholar
  19. 19.
    Kusiak, A.: The generalized group technology concept. Int. J. Prod. Res. 25(4), 561–569 (1987)CrossRefGoogle Scholar
  20. 20.
    Kusiak, A., Chow, W.S.: Efficient solving of the group technology problem. J. Manuf. Syst. 6(2), 117–124 (1987)CrossRefGoogle Scholar
  21. 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)zbMATHCrossRefGoogle Scholar
  22. 22.
    Mosier, C.T., Taube, L.: The facets of group technology and their impact on implementation. OMEGA 13(6), 381–391 (1985a)CrossRefGoogle Scholar
  23. 23.
    Mosier, C.T., Taube, L.: Weighted similarity measure heuristics for the group technology machine clustering problem. OMEGA 13(6), 577–583 (1985b)CrossRefGoogle Scholar
  24. 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)MathSciNetCrossRefGoogle Scholar
  25. 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)CrossRefGoogle Scholar
  26. 26.
    Seifoddini, H., Wolfe, P.M.: Application of the similarity coefficient method in group technology. IIE Trans. 18(3), 271–277 (1986)CrossRefGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 28.
    Stanfel, L.: Machine clustering for economic production. Eng. Costs Prod. Econ. 9, 73–81 (1985)CrossRefGoogle Scholar
  29. 29.
    Waghodekar, P.H., Sahu, S.: Machine-component cell formation in group technology MACE. Int. J. Prod. Res. 22, 937–948 (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ilya Bychkov
    • 1
  • Mikhail Batsyn
    • 1
    Email author
  • Panos M. Pardalos
    • 1
    • 2
  1. 1.Laboratory of Algorithms and Technologies for Network AnalysisNational Research University Higher School of EconomicsNizhniy NovgorodRussian Federation
  2. 2.Center of Applied OptimizationUniversity of FloridaGainesvilleUSA

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