Impact of queuing theory and alternative process routings on machine busy time in a dynamic cellular manufacturing system

Document Type : Research Paper


1 Department of Industrial Engineering, IlamBranch, Islamic Azad university,Ilam, Iran

2 Faculty of Engineering, Ilam university, Ilam, Iran

3 Department of Industrial Engineering, Ilam Branch, Islamic Azad university,Ilam, Iran


A new mathematical model based on the alternative process routings in presence of a queuing system in a dynamic cellular manufacturing system has been proposed in this paper.This model integrates two problems of cell formation and inter-cell layout and also an efficiency factor which is defined for minimizing the cell load variation through the maximizing the busy time for all machine types. In order to evaluate the performance of proposed model, some numerical examples are generated randomly and solved using GAMS optimization software suitable for MIP and MINLP models. The Baron solver which is capable of solving both linear and nonlinear model is implemented. Experimental results verify the applicability of proposed model in every industrial plant which implements a CMS. Moreover, based on the sensitivity analysis, the queue system has significant impact on overall system efficiency. In other words by increasing the part arrival rate the machine busy time is increased strictly.


Main Subjects

Arani, S. D., & Mehrabad, M. S. (2014). A two stage model for Cell Formation Problem (CFP) considering the inter-cellular movements by AGVs. Journal of Industrial and Systems Engineering, 7(1), 43-55.
Arkat, J., Farahani, M. H., & Hosseini, L. (2012). Integrating cell formation with cellular layout and operations scheduling. The International Journal of Advanced Manufacturing Technology, 61(5-8), 637-647.
Bagheri, M., & Bashiri, M. (2014a). A hybrid genetic and imperialist competitive algorithm approach to dynamic cellular manufacturing system. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 228(3), 458-470.
Bagheri, M., & Bashiri, M. (2014b). A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment. Applied Mathematical Modelling, 38(4), 1237-1254.
Bashiri, M., & Bagheri, M. (2013). A Two Stage Heuristic Solution Approach for Resource Assignment during a Cell Formation Problem. International Journal of Engineering-Transactions C: Aspects, 26(9), 943.
Chung, S.-H., Wu, T.-H., & Chang, C.-C. (2011). An efficient tabu search algorithm to the cell formation problem with alternative routings and machine reliability considerations. Computers & Industrial Engineering, 60(1), 7-15.
Dalfard, V. M. (2013). New mathematical model for problem of dynamic cell formation based on number and average length of intra and intercellular movements. Applied Mathematical Modelling, 37(4), 1884-1896.
Defersha, F. M., & Chen, M. (2006). A comprehensive mathematical model for the design of cellular manufacturing systems. International Journal of Production Economics, 103(2), 767-783.
Elbenani, B., Ferland, J. A., & Bellemare, J. (2012). Genetic algorithm and large neighbourhood search to solve the cell formation problem. Expert Systems with Applications, 39(3), 2408-2414.
Ghezavati, V., & Saidi-Mehrabad, M. (2011). An efficient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis. Expert Systems with Applications, 38(3), 1326-1335.
Ilić, O. R. (2014). An e-Learning tool considering similarity measures for manufacturing cell formation. Journal of Intelligent Manufacturing, 25(3), 617-628.
Saraç, T., & Ozcelik, F. (2012). A genetic algorithm with proper parameters for manufacturing cell formation problems. Journal of Intelligent Manufacturing, 23(4), 1047-1061.
Niakan, F., Baboli, A., Moyaux, T., & Botta-Genoulaz, V. (2015). A new multi-objective mathematical model for dynamic cell formation under demand and cost uncertainty considering social criteria. Applied Mathematical Modelling. doi:
Tavakkoli-Moghaddam, R., Javadian, N., Javadi, B., & Safaei, N. (2007). Design of a facility layout problem in cellular manufacturing systems with stochastic demands. Applied Mathematics and Computation, 184(2), 721-728.
Tavakkoli-Moghaddam, R., Minaeian, S., & Rabbani, S. (2008). A new multi-objective model for dynamic cell formation problem with fuzzy parameters. International Journal of Engineering—Transactions A: Basic, 21(2), 159-172.
Tavakkoli-Moghaddam, R., Ranjbar-Bourani, M., Amin, G. R., & Siadat, A. (2012). A cell formation problem considering machine utilization and alternative process routes by scatter search. Journal of Intelligent Manufacturing, 23(4), 1127-1139.
Tavakoli-Moghadam, R., Javadi, B., Jolai, F., & Mirgorbani, S. (2006). An efficient algorithm to inter and intra-cell layout problems in cellular manufacturing systems with stochastic demands. INTERNATIONAL JOURNAL OF ENGINEERING-MATERIALS AND ENERGY RESEARCH CENTER-, 19(1), 67.
Ulutas, B. (2015). Assessing the number of cells for a cell formation problem. IFAC-PapersOnLine, 48(3), 1122-1127. doi:
Wu, X., Chu, C.-H., Wang, Y., & Yue, D. (2007). Genetic algorithms for integrating cell formation with machine layout and scheduling. Computers & Industrial Engineering, 53(2), 277-289.