Dynamic cellular manufacturing systems design—a comprehensive model



This paper addresses the dynamic cell formation problem (DCF). In dynamic environment, the product demand and mix changes in each period of a multiperiod planning horizon. It causes need of reconfiguration of cells to respond to the product demand and mix change in each period. This paper proposes a mixed-integer nonlinear programming model to design the dynamic cellular manufacturing systems (DCMSs) under dynamic environment. The proposed model, to the best of the author’s knowledge, is the most comprehensive model to date with more integrated approach to the DCMSs. The proposed DCMS model integrates concurrently the important manufacturing attributes in existing models in a single model such as machine breakdown effect in terms of machine repair cost effect and production time loss cost effect to incorporate reliability modeling; production planning in terms of part inventory holding, part internal production cost, and part outsourcing; process batch size; transfer batch size for intracell travel; transfer batch size for intercell travel; lot splitting; alternative process plan, and routing and sequence of operation; multiple copies of identical copies; machine capacity, cutting tooling requirements, work load balancing, and machine in different cells constraint; machine in same cell constraint; and machine procurements and multiple period dynamic cell reconfiguration. Further, the objective of the proposed model is to minimize the sum of various costs such as intracell movement costs; intercell movement costs and machine procurement costs; setup cost; cutting tool consumption costs; machine operation costs; production planning-related costs such as internal part production cost, part holding costs, and subcontracting costs; system reconfiguration costs; and machine breakdown repair cost, production time loss cost due to machine breakdown, machine maintenance overheads, etc. ,in an integrated manner. Nonlinear terms of objective functions are transformed into linear terms to make mixed-integer linear programming model. The proposed model has been demonstrated with several problems, and results have been presented accordingly.


Mixed-integer programming DCMS Breakdown effects Production planning-part held outsourcing Alternative routings Transfer batch size Lot splitting Work load balancing 


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  1. 1.
    Ahkioon S, Bulgak AA, Bektas T (2009) Cellular manufacturing system design with routing flexibility, machine procurement, production planning & dynamic system reconfiguration. Int J Prod Res 47(6):1573–1600MATHCrossRefGoogle Scholar
  2. 2.
    Ahkioon S, Bulgak AA, Bektas T (2009) Integrated cellular manufacturing system design with production planning & dynamic system reconfiguration. Eur J Oper Res 192:414–428MathSciNetCrossRefGoogle Scholar
  3. 3.
    Akturk MS, Turkcan A (2000) Cellular manufacturing system design using a holonistic approach. Int J Prod Res 38:2327–2347MATHCrossRefGoogle Scholar
  4. 4.
    Alhourani F, Seifoddini H (2007) Machine cell formation for production management in cellular manufacturing systems. Int J Prod Res 45(4):913–934MATHCrossRefGoogle Scholar
  5. 5.
    Aljaber N, Baek W, Chen CL (1997) A tabu search approach to the cell formation problem. Comput Ind Eng 32(1):169–185CrossRefGoogle Scholar
  6. 6.
    Alkan M, Erkman AM, Erkman I (1994) Fuzzy dynamic programming. Proc Med Elecrotechnical Conf 2:723–726CrossRefGoogle Scholar
  7. 7.
    Arkat SMJ, Abbasi B (2007) Applying simulated annealing to cellular manufacturing system design. Int J Adv Manuf Technol 32:531–536CrossRefGoogle Scholar
  8. 8.
    Askin RG, Creswell JB, Goldberg JB, Vakharia AJ (1991) A Hamiltonian path approach to reordering the part-machine matrix for cellular manufacturing. Int J Prod Res 29:1081–1100CrossRefGoogle Scholar
  9. 9.
    Askin RG, Vakharia AJ (1991) Group technology—cell formation and operation. In: Cleland DI, Bidanda B (eds) The automated factory handbook: technology and management. TAB Books, New York, pp 317–366Google Scholar
  10. 10.
    Asokan P, Prabhakaran G, Kumar GS (2001) Machine-cell grouping in cellular manufacturing systems using non-traditional optimization techniques—a comparative study. Integr Manuf Syst 18:140–147Google Scholar
  11. 11.
    Balakrishnan J, Cheng C (2007) Multi-period planning and uncertainty issues in cellular manufacturing: a review and future directions. Eur J Oper Res 177:281–309MATHCrossRefGoogle Scholar
  12. 12.
    Balakrishnan J, Cheng CH (2005) Dynamic cellular manufacturing under multi period planning horizons. J Manuf Technol Manage 16:516–530CrossRefGoogle Scholar
  13. 13.
    Barker A (1970) Group technology and machining cells in the small-batch production valves. Mach Prod Eng 116:2–6Google Scholar
  14. 14.
    Baykasoglu A, Gindy NNZ, Cobb RC (2001) Capability based formulation and solution of multiple objective cell formation problems using simulated annealing. Integr Manuf Syst 12:258–274CrossRefGoogle Scholar
  15. 15.
    Boctor FF (1991) A linear formulation of the machine-part cell formation problem. Int J Prod Res 29:343–356CrossRefGoogle Scholar
  16. 16.
    Cao D, Chen M (2004) Using penalty function and tabu search to solve cell formation problems with fixed cell cost. Comput Oper Res 31:21–37MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Caux C, Bruniaux R, Pierreval H (2000) Cell formation with alternative process plans and machine capacity constraints: a new combined approach. Int J Prod Econ 64:179–284CrossRefGoogle Scholar
  18. 18.
    Chan HM, Milner DA (1982) Direct clustering algorithm for group formation in cellular manufacturing. J Manuf Syst 1:65–74CrossRefGoogle Scholar
  19. 19.
    Chandrasekharan MP, Rajagopalan R (1987) ZODIAC: an algorithm for concurrent formation of part families and machines cells. Int J Prod Res 25:835–850MATHCrossRefGoogle Scholar
  20. 20.
    Chandrasekharan MP, Rajagopalan R (1989) GROUPABILITY: an analysis of the properties of binary data for group technology. Int J Prod Res 27:1035–1052CrossRefGoogle Scholar
  21. 21.
    Chen CL, Cotruvo NA, Baek W (1995) A simulated annealing solution to the cell formation problem. Int J Prod Res 33(9):2601–2614MATHCrossRefGoogle Scholar
  22. 22.
    Chen M (1998) A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environment. Ann Oper Res 74:109–128CrossRefGoogle Scholar
  23. 23.
    Chen WH, Srivastava B (1994) Simulated annealing procedures for forming machine cells in group technology. Eur J Oper Res 75:100–111MATHCrossRefGoogle Scholar
  24. 24.
    Cheng CH, Goh CH, Lee A (1996) Solving the generalized machine assignment problem in group technology. J Oper Res Soc 47:794–802MATHGoogle Scholar
  25. 25.
    De Beer C, De Witte J (1978) Production flow synthesis. CIRP Annals 27:389–392Google Scholar
  26. 26.
    Defersha FM, Chen M (2006) A comprehensive mathematical model for the design of cellular manufacturing system. Int J Prod Econ 103:767–783CrossRefGoogle Scholar
  27. 27.
    Defersha FM, Chen M (2006) Machine Cell formation using a mathematical model and a genetic-algorithm-based heuristic. Int J Prod Res 44(12):2421–2444MATHCrossRefGoogle Scholar
  28. 28.
    Defersha FM, Chen M (2007) A parallel genetic algorithm for dynamic cell formation in cellular manufacturing systems. Int J Prod Res 46:6389–6413CrossRefGoogle Scholar
  29. 29.
    Defersha FM, Chen M (2008) A parallel multiple Markov chain simulated annealing for multi period manufacturing cell formation. Int J Adv Manuf Tech 37:140–156CrossRefGoogle Scholar
  30. 30.
    El-Essawy IFK, Torrance J (1972) Component flow analysis—an effective approach to production systems’ design. Prod Eng 51:165CrossRefGoogle Scholar
  31. 31.
    Gupta Y, Gupta M, Kumar A, Sundaram C (1996) A genetic algorithm based approach to cell composition and layout design problems. Int J Prod Res 34:447–482MATHCrossRefGoogle Scholar
  32. 32.
    Heragu SS, Chen JR (1998) Optimal solution of cellular manufacturing system design: benders’ decomposition approach. Eur J Oper Res 107:175–192MATHCrossRefGoogle Scholar
  33. 33.
    Jabal Ameli MS, Arkat J (2007) Cell formation with alternative process routings and machine reliability consideration. Int J Adv Manuf Technol 35:761–768. doi: 10.1007/s00170-006-0753-6 CrossRefGoogle Scholar
  34. 34.
    Jabal Ameli MS, Arkat J, Barzinpour F (2008) Modeling the effect of machine breakdowns in the generalized cell formation. Int J Adv Manuf Tech 39:838–850CrossRefGoogle Scholar
  35. 35.
    Jayaswal S, Adilz G (2004) Efficient algorithm for cell formation with sequence data, machine replications and alternative process routings. Int J Prod Res 42:2419–2433CrossRefGoogle Scholar
  36. 36.
    Joines JA, King RE, Culbreth CT (1996) A comprehensive review of production oriented manufacturing cell formation techniques. Int J Flex Autom Intell Manuf 3(3/4):120–161Google Scholar
  37. 37.
    Kaparthi S, Suresh NC (1992) Machine-component cell formation in group technology: a neural network approach. Int J Prod Res 30:1353–1367MATHCrossRefGoogle Scholar
  38. 38.
    Khator SK, Irani SA (1987) Cell formation in group technology: a new approach. Comput Ind Eng 12:131–142CrossRefGoogle Scholar
  39. 39.
    Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetCrossRefGoogle Scholar
  40. 40.
    Kumar KR, Kusiak A, Vannelli A (1986) Grouping of parts and components in flexible manufacturing systems. Eur J Oper Res 24:387–397CrossRefGoogle Scholar
  41. 41.
    Kusiak A, Chow WS (1988) Decomposition of manufacturing systems. IEEE J Robot Autom 4(5):457–471CrossRefGoogle Scholar
  42. 42.
    Kusiak A (1987) The generalized group technology concept. Int J Prod Res 25:561–569CrossRefGoogle Scholar
  43. 43.
    Logendran R (1990) A workload based model for minimizing total intercell and intracell moves in cellular manufacturing. Int J Prod Res 28:913–925CrossRefGoogle Scholar
  44. 44.
    Logendran R, Ramakrishna R, Srikandarajah C (1994) Tabu search based heuristics for cellular manufacturing system in the presence of alternative process plans. Int J Prod Res 32:273–297MATHCrossRefGoogle Scholar
  45. 45.
    Lokesh K, Jain PK (2008) Part-machine group formation with operation sequence, time and production volume. Int J Simul Model 7(4):198–209. doi: 10.2507/IJSIMM08(2)3.125, www.ijsimm.com CrossRefGoogle Scholar
  46. 46.
    Lokesh K, Jain PK (2009) Part-Machine group formation with ordinal-ratio level data and production volume. Int J Simul Model 8(2):90–101. doi: 10.2507/IJSIMM07(4)4.113, www.ijsimm.com CrossRefGoogle Scholar
  47. 47.
    Lokesh K, Jain PK (2010) Concurrently part-machine group formation with important production data. Int J Simul Model 9(1):5–16. doi: 10.2507/IJSIMM09(1)1.133, www.ijsimm.com, IJSIMM-133-2009CrossRefGoogle Scholar
  48. 48.
    Lokesh K, Jain PK (2010) Dynamic cellular manufacturing systems design—a comprehensive model & HHGA. Advances in Production Engineering & Management Journal 5(3):151–162. www.apem-journal.org
  49. 49.
    Lozano S, Adenso-Diaz B, Eguia I, Onieva L (1999) A one-step tabu search algorithm for manufacturing cell design. J Oper Res Soc 50:509–516MATHGoogle Scholar
  50. 50.
    Lozano S, Carlos A (2006) A particle swarm optimisation algorithm for part-machine grouping. Robot Comput Integr Manuf 22:468–474CrossRefGoogle Scholar
  51. 51.
    Lozano S, Canca D, Gueerro F, Garcia JM (2001) Machine grouping using sequence based similarity coefficient & neural networks. Robot Comput Integr Manuf 17:399–404CrossRefGoogle Scholar
  52. 52.
    Mansouri SA, Husseini SMM, Newman ST (2000) A review of modern approaches to multi-criteria cell design. Int J Prod Res 38(5):1201–1218MATHCrossRefGoogle Scholar
  53. 53.
    McAuley J (1972) Machine grouping for efficient production. Prod Eng 51:53–57CrossRefGoogle Scholar
  54. 54.
    Mitrafanov S (1966) Scientific principles of group technology. National Lending Library, LondonGoogle Scholar
  55. 55.
    Mungwattana A (2000) Design of cellular manufacturing systems for dynamic and uncertain production requirements with presence of routing flexibility. Ph.D. thesis, Virginia Polytechnic Institute and State University, Blackburg, VAGoogle Scholar
  56. 56.
    Nsakanda AL, Diaby M, Price WL (2006) Hybrid genetic approach for solving large scale capacitated cell formation problem with multiple routings. Eur J Oper Res 171:1058–1070CrossRefGoogle Scholar
  57. 57.
    Onwubolu GC, Mutingi M (2001) A genetic algorithm approach to cellular manufacturing systems. Comput Ind Eng 39:125–144CrossRefGoogle Scholar
  58. 58.
    Plaquin MF, Pierreval H (2000) Cell formation using evolutionary algorithms with certain constraints. Int J Prod Econ 64:267–278CrossRefGoogle Scholar
  59. 59.
    Purcheck GFK (1985) Machine-component group formation: a heuristic method for flexible production cells & flexible manufacturing systems. Int J Prod Res 23:911–943CrossRefGoogle Scholar
  60. 60.
    Rheault M, Drolet J, Abdulnour G (1995) Physically reconfigurable virtual cells: a dynamic model for a highly dynamic environment. Comput Ind Eng 29(1–4):221–225CrossRefGoogle Scholar
  61. 61.
    Safaei N, Saidi-Mehrabad N (2006) A new model of dynamic cell formation by a neural approach. Int J Adv Manuf Technol 33:1001–1009. doi: 10.1007/s00170-006-0518-2, Online FirstGoogle Scholar
  62. 62.
    Safaei N, Mehrabad SM, Ameli MSJ (2008) A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. Eur J Oper Res 185:563–592MATHCrossRefGoogle Scholar
  63. 63.
    Sankaran S (1990) Multiple objective decision making approach to cell formation a goal programming model. Math Comput Model 13:71–82MATHCrossRefGoogle Scholar
  64. 64.
    Shafer SM, Rogers DF (1991) A goal programmi9ng approach to cell formation problems. J Oper Manage 10:28–43CrossRefGoogle Scholar
  65. 65.
    Selim HM, Askin RG, Vakharia A (1998) Cell formation in group technology: review, evaluation and directions for future research. Comput Ind Eng 34(1):3–20CrossRefGoogle Scholar
  66. 66.
    Singh N (1993) Design of cellular manufacturing systems: an invited review. Eur J Oper Res 69:284–291CrossRefGoogle Scholar
  67. 67.
    Singh N, Rajamani D (1996) Cellular manufacturing systems: design, planning and control. Chapman & Hall, SuffolkGoogle Scholar
  68. 68.
    Spiliopoulos K, Sofianopoulou S (2008) An efficient ant colony optimization system for the manufacturing cells formation problem. Int J Adv Manuf Technol 36:589–597CrossRefGoogle Scholar
  69. 69.
    Sofianopoulou S (1999) Manufacturing cells design with alternative process zlans and or replicate machines. Int J Prod Res 37(3):707–720MATHCrossRefGoogle Scholar
  70. 70.
    Solimanpur M, Vrat P, Shankar R (2004) A multi-objective genetic algorithm approach to the design of cellular manufacturing systems. Int J Prod Res 42:1419–1441MATHCrossRefGoogle Scholar
  71. 71.
    Song S, Hitomi K (1992) GT cell formation for minimizing the intercell part flow. Int J Prod Res 30(12):1029–1036CrossRefGoogle Scholar
  72. 72.
    Srinivasan G, Narendran T (1991) GRAFICS—a nonhierarchical clustering algorithm for group technology. Int J Prod Res 29:463–478 [38]CrossRefGoogle Scholar
  73. 73.
    Su CT, Hsu CM (1998) Multi-objective machine-part cell formation through parallel simulated annealing. Int J Prod Res 36:2185–2207MATHCrossRefGoogle Scholar
  74. 74.
    Sule DR (1994) Manufacturing facilities: location, planning, and design. PWS, BostonGoogle Scholar
  75. 75.
    Sun D, Lin L, Batta R (1995) Cell formation using tabu search. Comput Ind Eng 28(3):485–494CrossRefGoogle Scholar
  76. 76.
    Taboun S, Merchawi N, Ulger T (1998) Part family and machine cell formation in multi-period planning horizons of cellular manufacturing systems. Prod Plan Control 9:561–571CrossRefGoogle Scholar
  77. 77.
    Tavakkoli-Moghaddam R, Aryanezhad MB, Safaei N, Azaron A (2005) Solving a dynamic cell formation problem using metaheuristics. Appl Math Comput 170:761–780MathSciNetMATHCrossRefGoogle Scholar
  78. 78.
    Tavakkoli-Moghaddam R, Safaei N, Babakhani M (2005) Solving a dynamic cell formation problem with machine cost and alternative process plan by mimetic algorithms. Lect Notes Comput Sci 3777:213–227CrossRefGoogle Scholar
  79. 79.
    Tompkins JA, White JA, Bozer YA, Tanchoco JMA (2003) Facility planning. Wiley, New YorkGoogle Scholar
  80. 80.
    Vakharia AJ, Wemmerlov U (1995) A comparative investigation of hierarchical clustering techniques and dissimilarity measures applied to the cell formation problem. J Oper Manage 13:117–138CrossRefGoogle Scholar
  81. 81.
    Venugopal V, Narendran TT (1994) Machine-cell formation through neural network models. Int J Prod Res 32:2105–2116MATHCrossRefGoogle Scholar
  82. 82.
    Wang X, Tang J, Yung KL (2008) Optimization of multi-objectives dynamic cell formation problem using a scatter search approach. Int J Adv Manuf Technol 44:318–329. doi: 10.1007/00170-008-1835-4 CrossRefGoogle Scholar
  83. 83.
    Wei JC, Kern GM (1989) Commonality analysis: a linear clustering algorithm for group technology. Int J Prod Res 12:2053–2062CrossRefGoogle Scholar
  84. 84.
    Wemmerlov U, Hyer NL (1986) Procedures for the part family machine group identification problem in cellular manufacturing. J Oper Manage 6(2):12–147CrossRefGoogle Scholar
  85. 85.
    Wicks EM, Reasor RJ (1999) Designing cellular manufacturing systems with dynamic part populations. IIE Trans 31:11–20Google Scholar
  86. 86.
    Xambre AR, Vilarinho PM (2003) A simulated annealing approach for manufacturing cell formation with multiple identical machines. Eur J Oper Res 151:434–446MathSciNetMATHCrossRefGoogle Scholar
  87. 87.
    Zhao C, Wu Z (2000) A genetic algorithm for manufacturing cell formation with multiple routes and multiple objectives. Int J Prod Res 38:385–395MATHCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJamia Millia IslamiaNew DelhiIndia
  2. 2.Department of Mechanical & Industrial EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia

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