Stochastic Cell Formation Problem within Queuing Theory and Considering Reliability

Document Type : Research Paper


1 Department of Industrial Engineering, Alzahra University, Tehran, Iran

2 Department of Industrial Engineering, Bu-Ali Sina University, Hamedan, Iran


In this study, the stochastic cell formation problem with developing model within queuing theory with stochastic demand, processing time and reliability has been presented. Machine as server and part as customer are assumed where servers should service to customers. Since, the cell formation problem is NP-Hard, therefore, deterministic methods need a long time to solve this model. In this study, genetic algorithm and modified particle swarm optimization algorithm are presented to solve problems. Because the metaheurstic algorithms quality depends strongly on selected operators and parameters, design of experiment is done for set parameters. The deterministic method of branch and bound algorithm is used to evaluate the results of modified particle swarm optimization algorithm and the genetic algorithm.Evaluates indicate better performance of the proposed algorithms in quality the metaheurstic algorithms final solution and solving time in comparing with the method of Lingo software’s branch and bound. Ultimately, the results of numerical examples indicate that considering reliability has significant effect on block structures of machine-part matrixes.


Main Subjects

1. Singh, N. and Rajamani, D. (1996). Cellular manufacturing systems: design, planning and control, 1th Ed, Chapter 1, Chapman & Hall Pub. Co., London.
2. Ahi, A., Aryanezhad, M. B., Ashtiani, B. and Makui, A. (2009). “A novel approach to determine cell formation, intracellular machine layout and cell layout in the CMS problem based on TOPSIS method”, Computers & Operations Research,Vol. 36, No. 5, PP. 1478- 1496.
3. Papaioannou, G. and Wilson, J. M. (2010). “The evolution of cell formation problem methodologies based on recent studies (1997-2008): Review and directions for future research”, European Journal of Operational Research,Vol. 206, No. 3, PP. 509- 521.
4. Ghezavati, V. R. and Saidi-Mehrabad, M. (2010). “Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time”, The International Journal of Advanced Manufacturing Technology, Vol. 48, No. 5- 8, PP. 701- 717.
5. 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, Vol. 38, No. 3, PP. 1326- 1335.
6. Das, K., Lashkari, R. S. and Sengupta, S. (2007a). “Machine reliability and preventive maintenance planning for cellular manufacturing systems”, European Journal of Operational Research, Vol. 183, No. 1, PP. 162-180.
7. Das, K., Lashkari, R. S. and Sengupta, S. (2007b). “Reliability consideration in the design and analysis of cellular manufacturing systems”, International Journal of Production Economics, Vol. 105, No1, PP. 243-262.
8. Das, K. (2008). “A comparative study of exponential distribution vs Weibull distribution in machine reliability analysis in a CMS design”, Computers & Industrial Engineering, Vol. 54, No. 1, PP. 12- 33.
9. Ameli, M. S. J., Arkat, J. and Barzinpour, F. (2008). “Modelling the effects of machine breakdowns in the generalized cell formation problem”, The International Journal of Advanced Manufacturing Technology, Vol. 39, No. 7- 8, PP. 838- 850.
10. Ameli, M. S. J. and Arkat, J. (2008). “Cell formation with alternative process routings and machine reliability consideration”, The International Journal of Advanced Manufacturing Technology, Vol. 35, No. 7-8, PP. 761- 768.
11. Chung, S. H., Wu, T. H. and Chang, C. C. (2011). “An efficient tabu search algorithm to the cell formation problem with alternative routings and machine reliability considerations”, Computers & Industrial Engineering, Vol. 60, No. 1, PP. 7- 15.
12. Rafiee, K., Rabbani, M., Rafiei, H. and Rahimi-Vahed, A. (2011). “A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system”, Applied Mathematical Modelling, Vol. 35, No. 4, PP. 1810- 1819.
13. Asgharpour, M. J. and Javadian, N. (2004). “Solving a stochastic cellular manufacturing model by using genetic algorithms”, International Journal of Engineering Transactions A, Vol. 17, No. 2, PP. 145- 156.
14. Tavakkoli-Moghaddam, R., Javadian, N., Javadi, B. and Safaei, N. (2007). “Design of a facility layout problem in cellular manufacturing systems with stochastic demands”, Applied Mathematics and Computation, Vol. 184, No. 2, PP. 721- 728.
15. Egilmez, G., Suer, G. A. and Huang, J. (2012). “Stochastic cellular manufacturing system design subject to maximum acceptable risk level”, Computers & Industrial Engineering, Vol. 63, No. 4, PP. 842- 854.
16. Frederick, G. J. L. and HillIer, S. (2001). Introduction to Operations Research, 7th Ed., Chapter 17, McGraw-Hill Pub. Co., New York.
17. Duran, O., Rodriguez, N. and Consalter, L. A. (2010). “Collaborative particle swarm optimization with a data mining technique for manufacturing cell design”, Expert Systems with Applications,Vol. 37, No. 2, PP. 1563- 1567.
18. Kennedy, J. and Eberhart, R. (1995). “Particle swarm optimization”, In Proceedings of the IEEE International Conference on Neural Networks IV., Perth, WA, Vol. 4, PP. 1942- 1948.
19. Eberhart, R. and Kennedy, J. (1995). “A new optimizer using particle swarm theory”, In Proceedings of the sixth international symposium on micro machine and human science., Nagoya, Japan. PP. 39- 43.
20. Mahdavi, I., Paydar, M. M., Solimanpur, M. and Heidarzade, A. (2009). “Genetic algorithm approach for solving a cell formation problem in cellular manufacturing”, Expert Systems with Applications, Vol. 36, No. 3, PP. 6598- 6604.