Document Type : Research Paper

**Authors**

**Abstract**

Abstract

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

**Keywords**

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), http://dx.doi.org/10.1016/j.apm.2013.08.026

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), http://dx.doi.org/10.1016/j.jmsy.2013.02.003

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).