A Benders� Decomposition Approach for Dynamic Cellular Manufacturing System in the Presence of Unreliable Machines


1 Ph. D Student, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

2 MSc, Department of Industrial Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

3 Professor, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


In order to implement the cellular manufacturing system in practice, some essential factors should be taken into account. In this paper, a new mathematical model for cellular manufacturing system considering different production factors including alternative process routings and machine reliability with stochastic arrival and service times in a dynamic environment is proposed. Also because of the complexity of the given problem, a Benders’ decomposition approach is applied to solve the problem efficiently. In order to verify the performance of proposed approach, some numerical examples are generated randomly in hypothetical limits and solved by the proposed solution approach. The comparison of the implemented solution algorithm with the conventional mixed integer linear and mixed integer non linear models verifies the efficiency of Benders’ decomposition approach especially in terms of computational time.


Ameli, M. S. and Arkat, J. (2008). Cell formation with alternative process routings and machine reliability consideration. International Journal of Advanced Manufactirong Technology, 35, 761–768.
Aryanezhad, M. B., Deljoo, V. and Mirzapour Al-e-hashem, S. M. (2009). Dynamic cell formation and the worker assignment problem: a new model. International Journal of Advanced Manufacturing Technology, 41, 329–342.
Bagheri, M., Bashiri, M.  (2014). A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment. Applied Mathematical Modeling, 38, 1237-1254.
Bagheri, M., Bashiri, M.  (2014).  A hybrid Genetic and Imperialist Competitive Algorithms (GICA) approach to dynamic Cellular Manufacturing System . Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 228(3), 2014, 458-470.
Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4, 238–252.

Dimopoulos, C., Zalzala, A. (2000). Recent developments in evolutionary computations for manufacturing optimization: problems, solutions, and comparisons. IEEE Transactions on Evolutionary Computation, 4, 93–113.

Ghezavati, V. R., and Saidi-Mehrabad, M. (2011). An efficient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis. Expert Systems with Applications, 38, 1326-1335.
Ghotboddini, M., Rabbani, M., and Rahimian, H. (2011). A comprehensive dynamic cell formation design: Benders’ decomposition approach. Expert Systems with Applications, 38, 2478–2488.
Jolai, F., Tavakkoli-mogaddam, R., Golmohammadi, A. and Javadi, B. (2011). An Electromagnetism-like algorithm for cell formation and layout problem.  Expert System with Application, 39, 2172-2182.
Kia, R., Baboli, A., Javadian, N., Tavakkoli-Moghaddam, R., Kazemi, M. and Khorrami, J. (2012). Solving a group layout design model of a dynamic cellula rmanufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing. Computers & Operations Research, 39, 2642-2658.
kioon, S. A., Bulgak, A. A. and Bektas, T. (2009). Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration. European Journal of Operational Research, 192, 414–428.
Krishnan, K. k., Mirzaei, S., Venkatasamy, V., and  Pillai, V. M. (2012). A comprehensive approach to facility layout design and cell formation. International Journal of Advanced Manufacturing Technology , 59, 737-753.
Mahdavi, I., Aalaei, A., Paydar, M. M. and Solimanpur, M. (2010). Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment. Computers and Mathematics with Applications, 60, 1014-1025.
Onwubolu, G.C., and Mutingi, M. (2001). A genetic algorithm approach to cellular manufacturing Systems. Computers & industrial engineering, 39, 125-144.
Purcheck, G.F.K. (1974).  A mathematical classification as a basis for the design of group technology production cells.  Production Engineer, 54, 35–48.
Saidi-Mehrabad, M., and Mirnezami-ziabari, S. M. (2011). Developing a Multi-objective Mathematical Model for Dynamic Cellular Manufacturing Systems. Journal of Optimization in Industrial Engineering , 7, 1-9.
Satuglu, S. I. and Suresh, N. C. (2009). A goal-programming approach for design of hybrid cellular manufacturing systems in dual resource constrainted environment. Computers & Industrial Engineering, 56, 560-575.
Tavakkoli-Moghaddam, R., Aryanezhad, M. B., Safaei, N. and Azaron, A. (2005). Solving a dynamic cell formation problem using meta-heuristics. Applied Mathematics and Computation, 170, 761–780.
Tavakkoli-mogaddam, R., Javadian, N., Javadi, B. and Safaei, N. (2007). Design of a facility layout problem in cellular manufacturing systems with stochastic demands. Applied Mathematical Computions, 184, 721-728.
Wu, H., Chung, S-H. Chang, C-C. (2010). A water flow-like algorithm for manufacturing cell formation problems.  European Journal of Operations research, 205, 346-360.