Skip to main content

A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy


The cell formation problem determines decomposition of the manufacturing cells of a production system. Machines are assigned to the cells to process one or more part families so that each cell is operated independently and the inter-cellular movements are minimized. This paper proposes a new algorithm for grouping problems (bin packing, graph coloring, scheduling, etc.) which is a grouping version of an almost new algorithm (league championship algorithm (LCA)), and we used it to solve benchmarked instances of cell formation problem posing as a grouping problem. To evaluate the effectiveness of our approach, we borrow a set of 35 most widely used benchmark problem instances from literature and compare the performance of grouping LCA (GLCA) and several well-known algorithms published. The proposed algorithm can reach the best solution for 29 of the 35 benchmark problems and differs with the best-known solution of three benchmark problems only with 0.7 % average gap. We also used a new method to find the number of initial cells. The results show that GLCA may hopefully be a new approach for such kinds of difficult-to-solve problems. Moreover, a real-world industrial case is provided to show how the proposed algorithm works. Considering the performance of the GLCA algorithm on all test problems, the proposed algorithm should thus be useful to both practitioners and researchers.

This is a preview of subscription content, access via your institution.


  1. 1.

    Anvari M, Mehrabad M, Barzinpour F (2010) Machine-part cell formation using a hybrid particle swarm optimization. Int J Adv Manuf Technol 2010:745–754

    Article  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

    Ateme-Nguem B, Dao T (2007) Optimization of cellular manufacturing systems design using the hybrid approach based on the ant colony and tabu search techniques. In Proceedings of the IEEE IEEM, pages 668–673

  4. 4.

    Ateme-Nguema B, Dao T (2009) Quantized Hopfield networks and tabu search for manufacturing cell formation problems. Int J Prod Res 121:88–98

    Article  Google Scholar 

  5. 5.

    Batsyn M, Bychkov I, Goldengorin B, Pardalos P, Sukhov P (2013) Pattern-based heuristic for the cell formation problem in group technology. B. Goldengorin et al. (eds.), Models, algorithms, and technologies for network analysis, Springer Proceedings in Mathematics & Statistics, 32, 11-50

  6. 6.

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

    Article  Google Scholar 

  7. 7.

    Boe WJ, Cheng CH (1991) A close neighbor algorithm for designing cellular manufacturing systems. Int J Prod Res 29:2097–2116

    Article  MATH  Google Scholar 

  8. 8.

    Boulif M, Atif K (2006) A new branch-&-bound-enhanced genetic algorithm for the manufacturing cell formation problem. Comput Oper Res 33:2219–2245

    Article  MATH  Google Scholar 

  9. 9.

    Boutsinas B (2013) Machine-part cell formation using biclustering. Eur J Oper Res 230:563–572

    MathSciNet  Article  Google Scholar 

  10. 10.

    Brown E, James T (2007) A hybrid grouping genetic algorithm for the cell formation problem. Comput Oper Res 34:2059–2079

    Article  MATH  Google Scholar 

  11. 11.

    Brown E, Sumichrast R (2001) CF-GGA: a grouping genetic algorithm for the cell formation problem. Int J Prod Res 36:3651–3669

    Article  Google Scholar 

  12. 12.

    Carrie AS (1973) Numerical taxonomy applied to group technology and plant layout. Int J Prod Res 399-416

  13. 13.

    Chan HM, Milner DA (1982) Direct clustering algorithm for group formation in cellular manufacturing. Journal of Manufacturing Systems 1: 65–74

  14. 14.

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

    Article  Google Scholar 

  15. 15.

    Chandrasekharan MP, Rajagopalan R (1986) An ideal seed non-hierarchical clustering algorithm for cellular manufacturing. Int J Prod Res 24:451–463

    Article  MATH  Google Scholar 

  16. 16.

    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

    Article  Google Scholar 

  17. 17.

    Cheng C, Gupa Y, Lee WA (1998) TSP-based heuristic for forming machine groups and part families. Int J Prod Res 36:1325–1337

    Article  MATH  Google Scholar 

  18. 18.

    DeLit P, Falkenauer E, Delchambre A (2000) Grouping genetic algorithms: an efficient method to solve the cell formation problem. Math Comput Simul 51:257–271

    Article  Google Scholar 

  19. 19.

    Elbenani B, Ferland J, Bellemare J (2012) Genetic algorithm and large neighborhood search to solve the cell formation problem. Expert Syst Appl

  20. 20.

    Falkenauer E (1998) Genetic algorithm for grouping problems. Wiley, New York

    Google Scholar 

  21. 21.

    Ghosh T, Sengupta S, Chattopadhyay M, Dan KP (2011) Meta-heuristics in cellular manufacturing: a state-of-art review. Int J Ind EngComput 2:87–122

    Google Scholar 

  22. 22.

    Goldengorin B, Krushinsky D, Slomp J (2012) Flexible PMP approach for large size cell formation. Oper Res 60:1157–1166

    MathSciNet  Article  MATH  Google Scholar 

  23. 23.

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

    Article  Google Scholar 

  24. 24.

    Heragu SS (1997) Facility design. PWS Publishing Company, Boston

    Google Scholar 

  25. 25.

    Husseinzadeh Kashan A (2009) League championship algorithm: a new algorithm for numerical function optimization. International Conference of Soft Computing and Pattern Recognition

  26. 26.

    Husseinzadeh Kashan A, Karimi B, Jolai F (2006) Effective hybrid genetic algorithm for minimizing makespan on a single-batch-processing machine with non-identical job sizes. Int J Prod Res 44:2337–2360

    Article  Google Scholar 

  27. 27.

    Husseinzadeh Kashan A, Karimi B, Noktehdan A (2014) A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem. Int J Adv Manuf Technol

  28. 28.

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

  29. 29.

    King JR, Nakornchai V (1982) Machine-component group formation in group technology: review and extension. Int J Prod Res 20:117–131

    Article  Google Scholar 

  30. 30.

    Krushinsky D, Goldengorin B (2012) An exact model for cell formation in group technology. Comput Manag Sci 9:323–338

    MathSciNet  Article  MATH  Google Scholar 

  31. 31.

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

    Article  Google Scholar 

  32. 32.

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

    Article  Google Scholar 

  33. 33.

    Kusiak A, Cho M (1992) Similarity coefficient algorithm for solving the group technology problem. Int J Prod Res 30:2633–263346

    Article  Google Scholar 

  34. 34.

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

    Article  Google Scholar 

  35. 35.

    Lei D, Wu Z (2005) Tabu search approach based on a similarity coefficient for cell formation in generalized group technology. Int J Prod Res 19:4035–4047

    Article  Google Scholar 

  36. 36.

    Lei D, Wu Z (2006) Tabu search for multiple-criteria manufacturing cell design. Int J Adv Manuf Technol 28:950–956

    Article  Google Scholar 

  37. 37.

    McCormick WT, Schweitzer PJ, White TW (1972) Problem decomposition and data reorganization by a clustering technique. Oper Res 20:993–1009

    Article  MATH  Google Scholar 

  38. 38.

    Mosier CT, Taube L (1985) The facets of group technology and their impact on implementation. OMEGA

  39. 39.

    Mosier CT, Taube L (1985) Weighted similarity measure heuristics for the group technology machine clustering problem. OMEGA

  40. 40.

    Noktehdan A, Karimi B, Husseinzadehkashan A (2010) A differential evolution algorithm for the manufacturing cell formation problem using group based operators. Expert Syst Appl 37:4822–4829

    Article  Google Scholar 

  41. 41.

    Noktehdan A, Seyedhosseini SM, Saidi-Mehrabad M (2015) A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy. Int J Adv Manuf Technol

  42. 42.

    Pailla A, Trindade A, Parada V, Ochi L (2010) A numerical comparison between simulated annealing and evolutionary approaches to the cell formation problem. Expert Syst Appl 37:5476–5483

    Article  Google Scholar 

  43. 43.

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

    Article  Google Scholar 

  44. 44.

    Rao PK (2014) A multi stage heuristic for manufacturing cell formation. Int J Res EngTechnol 1163:2308–2321

    Google Scholar 

  45. 45.

    Roy N, Komma VR (2014) Cellular manufacturing through composite part formation: a genetic algorithm approach. International Conference on Industrial Engineering and Operations Management, Bali, Indonesia, January 7 – 9

  46. 46.

    Sarker B (2001) Measures of grouping efficacy in cellular manufacturing systems. Eur J Oper Res 130:588–611

    Article  MATH  Google Scholar 

  47. 47.

    Sayadi MK, Hafezalkotob A, Jalali naini SG (2013) Firefly-inspired algorithm for discrete optimization problems: an application to manufacturing cell formation. J Manuf Syst 32:78–84

    Article  Google Scholar 

  48. 48.

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

  49. 49.

    Seifoddini H, Wolf PM (1986) Application of the similarity coefficient method in group technology. IIIE Transaction 18: 271--277

  50. 50.

    Selim HM, Askin RG, Vakharia AJ (1998) Cell formation in group technology: evaluation and directions for future research. Comput Ind Eng 34:3–20

    Article  Google Scholar 

  51. 51.

    Solimanpur M, Saeedi S, Mahdavi I (2010) Solving cell formation problem in cellular manufacturing using ant-colony-based optimization. Int J Adv Manuf Technol 50:1135–1144

    Article  Google Scholar 

  52. 52.

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

    Article  Google Scholar 

  53. 53.

    Stawowy A (2006) Evolutionary strategy for manufacturing cell design. Omega, Int J Manag Sci 34:1–18

    Article  Google Scholar 

  54. 54.

    Sun D, Lin L, Batta R (1995) Cell formation using tabu search. Comput Ind Eng 28:485–494

    Article  Google Scholar 

  55. 55.

    Vin E, DeLit P, Delchamber A (2005) A multiple-objective grouping genetic algorithm for the cell formation problem with alternative routings. J Intell Manuf 16:189–205

    Article  Google Scholar 

  56. 56.

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

    Article  Google Scholar 

  57. 57.

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

    Article  Google Scholar 

  58. 58.

    Wu T, Chang C, Chung S (2008) A simulated annealing algorithm for manufacturing cell formation problems. Expert Syst Appl

  59. 59.

    Wu T, Chang C, Yeh J (2009) A hybrid heuristic algorithm adopting both Boltzmann function and mutation operator for manufacturing cell formation problems. Int J Prod Econ 120:669–688

    Article  Google Scholar 

  60. 60.

    Wu T, Chung S, Chang C (2010) A water flow-like algorithm for manufacturing cell formation problems. Eur J Oper Res 205:346–360

    Article  MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Seyedmohammad Seyedhosseini.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Noktehdan, A., Seyedhosseini, S. & Saidi-Mehrabad, M. A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy. Int J Adv Manuf Technol 82, 25–37 (2016).

Download citation


  • Cell formation problem
  • Grouping genetic algorithm
  • League championship algorithm