Document Type : Research Paper



This paper presents a mathematical model for solving dynamic cell formation problem, operator assignment and the inter-cellular and intra-cellular layouts simultaneously. The proposed model includes three objectives, the first objective seeks to minimize inter and intra-cell part movement, machine relocation, second objective minimize operator related cost, third objective maximize ratio of consecutive forward flows. The model is Multi-objective; therefore, the LP-metric approach is used to solve it. In order to validate the model, the proposed model has been solved by using Lingo software. Then, due to NP-hardness of the cell formation problem, for solving large scale problems, a multi-objective simulated annealing algorithm proposed. Several numerical examples solved by Lingo software and multi-objective simulated annealing algorithm. Results show that the proposed multi-objective simulated annealing algorithm solved considerably time less than the software Lingo and also none of the answers obtained by the two methods are not dominated


Arkat J., Hosseinabadi-Farahani M., Hosseini L., Integrating cell formation with cellular layout and operations scheduling, Int. J. Adv. Manuf. Technol. (2011) 61:637–647.
Aryanezhad M.B., Deljoo V., Mirzapour Al-e-hashem S.M.J., Dynamic cell formation and the worker assignment problem: a new model, Int. J. Adv. Manuf. Technol. (2009) 41:329–342.
Bagheri M., Bashiri M., A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment, Appl. Math. Model. (2013),
Burbidge J.L., Production flow analysis, Prod. Eng. (1963) 42:742–752
Chang C.-C., Wu T.-H., Wu C. W., An efficient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing, Computer & Industrial Engineering (2013) 66:438-450.
Chen M., A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environment, Ann Oper Res(1998) 77:109–128
Jolai F., Tavakkoli-mogaddam R., Golmohammadi A., Javadi B., An electromagnetism-like algorithm for cell formation and layout problem, Expert. Syst. Appl. (2011) 39:2172–2182.
458 مطالعات مدیریت صنعتی، سال سیزدهم، شماره 73 ، تابستان 49
Kia R., Baboli A., Javadian N., Tavakkoli-Moghaddam R., Kazemi M., Khorrami J., Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing, Comput. Oper. Res. (2012) 39:2642–2658.
Kia R., Shirazi H., Javadian N., Tavakkoli-Moghaddam R., A multi-objective model for designing a group layout of a dynamic cellular manufacturing system, J Ind Eng (2013) 9:8. Doi:10.1186/2251-712x-9-8
Kirkpatrick S., Gellat Jr CD, Vecchi MP., optimization by simulated annealing, Science, (1983) 220(6):71-80.
Krishnan K.K., Mirzaei S., Venkatasamy V., Pillai V.M., A comprehensive approach to facility layout design and cell formation, Int. J. Adv. Manuf. Technol. (2012) 59:737–753
Logendran R., Methodology for converting a functional manufacturing system into a cellular manufacturing system, Int J Prod Econ (1993) 29:27–41
Mahdavi I., Aalaei A., Paydar M.M., Solimanpur M., Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment, Comput. Math. Appl. (2010) 60:1014–1025.
Mahdavi I., Teymourian E., Tahami Bahar N., Keyvanfar V., An integrated model for solving cell formation and cell layout problem simultaneously considering new situations, J Manuf Syst (2013),
Majazi Delfard V., New mathematical model for problem of dynamic cell formation based on number and average length of intra and intercellular movements, Appl. Math. Model. (2013) 37:1884-1896.
Rafiei H., Ghodsi R., A bi-objective mathematical model toward dynamic cell formation considering labor utilization, Appl. Math. Model., (2013) 37:2308-2316
Safaei N., Tavakkoli-Moghaddam R., Integrated multi-period cell formation and subcontracting production planning in dynamic cellular manufacturing systems, Int. J. Prod. Econ. (2009) 120:301–314.
ارائه یک مدل ریاضی یکپارچه برای حل مسأله تشکیل سلول پویا.... 511
Satuglu S.I., Suresh N.C., A goal-programming approach for design of hybrid cellular manufacturing systems in dual resource constrained environment, Comput. Ind. Eng. (2009) 56: 560–575.
Tavakkoli-Moghaddam R., Aryanezhad M.B., Safaei N., Azaron A., Solving a dynamic cell formation problem using meta-heuristics, Appl. Math. Comput. (2005) 170:761–780.
Tavakkoli-Mogaddam R., Javadian N., Javadi B., Safaei N., Design of a facility layout problem in cellular manufacturing systems with stochastic demands, Appl. Math. Comput. (2007) 184:721–728.
Wu X., Chu C.-H., Wang Y., Yue D., Genetic algorithms for integrating cell formation with machine layout and scheduling, Comput. Ind. Eng. (2007) 53: 277–289.
Wang X., Tang J., Yung K.-L., Optimization of the multi-objective dynamic cell formation problem using a scatter search approach, Int. J. Adv. Manuf. Technol. (2009) 44 :318–329.
White S.R., Concept of Scale in Simulated Annealing, Proceeding IEEE International Conference on Computer Design, Portchester, (1983).