Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On some measures for grouping efficiency

  • 134 Accesses

  • 6 Citations


The problem of grouping has attracted the attention of researchers and practitioners both. They have proposed number of schemes for classification of part-types into part-families and machines into machine-cells based on machine-requirement data. Real issue lies in judging objectively the relative merit of the varying grouping solutions that are obtained from their schemes. To this end, many measures have already been suggested by several researchers. In the present paper, these measures have been summarised, and their suitability is discussed. In particular, the measure due to Chandrasekharan and Rajagopalan (Int J Prod Res 24(2):451–464, 1986) has been analysed in details. Identifying the weakness of their measure, two new efficiency measures have been proposed in the present paper that relate grouping efficiency not only with exceptional elements and voids but also with the number of groups formed and size of the grouping problem. It has been shown by taking several examples from literature that the proposed measures have much better characteristics of discriminating good groups from bad ones.

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


  1. 1.

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

  2. 2.

    Wemmerlov U, Hyer NL (1989) Cellular manufacturing in the US industry: a survey of users. Int J Prod Res 27(9):1511–1530

  3. 3.

    Burbidge JL (1963) Production flow analysis. Prod Eng 42(12):42–752

  4. 4.

    El-Essawy IFK, Torrance J (1972) Component flow analysis-an effective approach to production systems design. Prod Eng 51:165–170

  5. 5.

    Ham I, Hitomi K, Yoshida T (1985) Group technology-applications to production management (Kluwer Nijhoff Publishing)

  6. 6.

    Kusiak A (1988) EXGT-S: a knowledge based system for group technology. Int J Prod Res 26:887–904

  7. 7.

    Suresh N (1996) Towards an integrated evaluation of flexible automation investments. Int J Prod Res 28:1657–1672

  8. 8.

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

  9. 9.

    Mukhopadhyay S, Babu KA, Sai KVV (2000) Modified Hamilton chain: a graph theoretic approach to group technology. Int J Prod Res 38:2459–2470

  10. 10.

    Rajagopalan R, Batra JL (1975) Design of cellular production systems: a graph theoretic approach. Int J Prod Res 13(6):567–579

  11. 11.

    Abduelmola AI, Taboun SM (2000) A simulated annealing algorithm for designing cellular manufacturing system with productivity considerations. Prod Plan Control 11:589–597

  12. 12.

    Lei D, Wu Z (2005) Tabu search approach based on a similarity coefficient for cell formation in generalized group technology. Int J Prod Res 43:4035–4047

  13. 13.

    Uddin MK, Shanker K (2002) Grouping of parts and machines in presence of alternative process route by genetic algorithm. Int J Prod Res 76:219–228

  14. 14.

    Won Y, Currie KR (2007) Fuzzy ART/RRR-RSS: a two phase neural network algorithm for part-machine grouping in cellular manufacturing. Int J Prod Res 9:2073–2104

  15. 15.

    Adil GK, Rajamani D, Strong D (1996) Cell formation considering alternate routeings. Int J Prod Res 34:1361–1380

  16. 16.

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

  17. 17.

    Mazzola JB, Neebe AW, Dunn CVR (1987) Production planning of a flexible manufacturing system in a material requirement planning environment. Working Paper No. 8608, Fuqua School of Business, Duke University, 1986, Revised 1987

  18. 18.

    Prabhakaran G, Muruganandam A, Asokan P, Girish BS (2005) Machine cell formation for cellular manufacturing system using ant colony system approach. Int J Adv Manuf Technol 25:1013–1019

  19. 19.

    Islier AA (2005) Group technology by an ant system algorithm. Int J Prod Res 43(5):913–932

  20. 20.

    Spiliopoulos K, Sofianopoulou S (2008) An efficient ant colony optimization system for the manufacturing cell formation problem. Int J Adv Manuf Technol 36:589–597

  21. 21.

    Fox B, Xiang W, Lee HP (2007) Industrial application of the ant colony optimization algorithm. Int J Adv Manuf Technol 31:805–814

  22. 22.

    Bhardwaj P (2007) Group technology applications for flexible manufacturing systems: some models and methodologies. Unpublished Ph.D. Thesis, Mechanical Engineering Department, Institute of Technology, Banaras Hindu University, India

  23. 23.

    Shtub A (1989) Modeling group technology cell formation as a generalized assignment problem. Int J Prod Res 27(5):775–782

  24. 24.

    Sarker BR, Mondal S (1999) Grouping efficiency measures in cellular manufacturing: a survey and critical review. Int J Prod Res 37(2):285–314

  25. 25.

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

  26. 26.

    Sandbothe RA (1998) Two observations on the grouping efficacy measure for goodness of block diagonal forms. Int J Prod Res 36:3217–3222

  27. 27.

    Zolfaghari S, Liang M (2003) A new genetic algorithm for the machine/part grouping problem in involving processing times and lot sizes. Comput Ind Eng 45:713–731

  28. 28.

    Hsu CP (1990) Similarity coefficient approaches to machine-component cell formation in cellular manufacturing: a comparative study. Ph.D. Thesis, Department of Industrial and Systems Engineering, University of Wisconsin, Milwaukee, WI

  29. 29.

    Harhalakis G, Nagi R, Proth JM (1990) An efficient heuristic in manufacturing cell formation for group technology applications. Int J Prod Res 28:185–198

  30. 30.

    Miltenburg J, Zhang W (1991) A comparative evaluation of nine well-known algorithms for solving the cell formation problem in group technology. Oper Manage 10:44–72

  31. 31.

    Ng SM (1993) Worst-case analysis of an algorithm for cellular manufacturing. Eur J Oper Res 69:384–398

  32. 32.

    Kandiller L (1994) A comparative study of cell formation in cellular manufacturing system. Int J Prod Res 32:2395–2429

  33. 33.

    Shargal G, Shekhar S, Trani SA (1995) Evaluation of search algorithms and clustering efficiency measures for machine-part matrix clustering. IIE Trans 27:43–59

  34. 34.

    Rogers DF, Shafer SM (1995) Measuring cellular manufacturing performance, In: Kamrani AK, Parsaei HR, Liles DH (eds) Planning, design and analysis of cellular manufacturing systems. Elsevier Science, pp 147–165

  35. 35.

    Mosier CT (1989) An experiment investigating the application of clustering procedures and similarity coefficients to the GT machine cell formation problem. Int J Prod Res 27(10):1811–1835

  36. 36.

    Li M-L (2006) Efficiency measure for multi-dimensional group technology. Int J Adv Manuf Technol 35:621–632

  37. 37.

    Seifoddini H, Djassemi M (1996) The threshold value of a quality index for formation of cellular manufacturing systems. Int J Prod Res 34:3401–3416

  38. 38.

    Sarker BR, Li Z (1998) Measuring matrix based cell formation considering alternative routings. J Oper Res Soc 49(9):953–965

  39. 39.

    Badhai RK (1998) A genetic algorithm approach for group technology applications. Unpublished M. Tech. Thesis, Department of Mechanical Engineering, Institute of Technology, Banaras Hindu University, Varanasi, India

  40. 40.

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

  41. 41.

    Askin RG, Subramanian SP (1987) A cost based heuristic for group technology configuration. Int J Prod Res 25(1):101–113

  42. 42.

    Seifoddini H (1989) Single linkage versus average linkage clustering in machine cells formation applications. Comput Ind Eng 16(3):419–426

  43. 43.

    McAuley J (1972) Machine grouping for efficient production. Prod Eng 51(2):53–57

  44. 44.

    Seifoddini H, Wolfe PM (1986) Selection of a threshold value based on the material handling cost in machine-component grouping. IIE Trans 19(3):266–270

  45. 45.

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

  46. 46.

    Pannerselvam R, Balasubramanian KN (1985) Algorithm grouping of operation sequences. Eng Cost Prod Econ 13(6):567–579

  47. 47.

    King JR, Nakornchai V (1982) Machine-component group formation in group technology: review and extension. Int J Prod Res 20(2):117–123

Download references

Author information

Correspondence to Prabhas Bhardwaj.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Agrawal, A.K., Bhardwaj, P. & Srivastava, V. On some measures for grouping efficiency. Int J Adv Manuf Technol 56, 789–798 (2011). https://doi.org/10.1007/s00170-011-3201-1

Download citation


  • Group technology
  • Cellular manufacturing
  • Grouping efficiency
  • Ant colony optimization