A New Mathematical Model in Cell Formation Problem with Consideration of Inventory and Backorder: Genetic and Particle Swarm Optimization Algorithms

Document Type : Research Paper


1 Faculty of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Faculty of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran


Cell Formation (CF) is the initial step in the configuration of cell assembling frameworks. This paper proposes a new mathematical model for the CF problem considering aspects of production planning, namely inventory, backorder, and subcontracting. In this paper, for the first time, backorder is considered in cell formation problem. The main objective is to minimize the total fixed and variable costs, including the machine related costs, intercellular movements, deviation between the levels of cell utilizations, inventory, backorder, and sub-contracting costs. The presented mathematical model is validated using GAMS software, and various test problems are solved by Genetic Algorithm (GA) and Discrete Particle Swarm Optimization (DPSO) algorithm. The performance of the algorithms is compared with the results obtained by the GAMS. The results demonstrate, there is no significant difference between the results of algorithms. Finally, some sensitive analyses are carried out to analyze the effects of backorder and inventory holding costs. 


Main Subjects

Arkat, J., Saidi, M., & Abbasi, B. (2007). Applying simulated annealing to cellular manufacturing system design. The International Journal of Advanced Manufacturing Technology, 32(5-6), 531-536.
Azadeh, A., Ravanbakhsh, M., Rezaei-Malek, M., Sheikhalishahi, M., & Taheri-Moghaddam, A. (2017). Unique NSGA-II and MOPSO algorithms for improved dynamic cellular manufacturing systems considering human factors. Applied Mathematical Modelling, 48, 655-672.
Chang, C.-C., Wu, T.-H., & Wu, C.-W. (2013). An efficient approach to determine cell formation, cell layout and intracellular machine sequence in cellular manufacturing systems. Computers & Industrial Engineering, 66(2), 438-450.
Chattopadhyay, M., Sengupta, S., Ghosh, T., Dan, P. K., & Mazumdar, S. (2013). Neuro-genetic impact on cell formation methods of Cellular Manufacturing System design: A quantitative review and analysis. Computers & Industrial Engineering, 64(1), 256-272.
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). Machine cell formation using a mathematical model and a genetic-algorithm-based heuristic. International Journal of Production Research, 44(12), 2421-2444.
Delgoshaei, A., & Gomes, C. (2016). A multi-layer perceptron for scheduling cellular manufacturing systems in the presence of unreliable machines and uncertain cost. Applied Soft Computing, 49, 27-55.
Durán, O., Rodriguez, N., & Consalter, L. A. (2010). Collaborative particle swarm optimization with a data mining technique for manufacturing cell design. Expert Systems with Applications, 37(2), 1563-1567.
Eguia, I., Molina, J. C., Lozano, S., & Racero, J. (2017). Cell design and multi-period machine loading in cellular reconfigurable manufacturing systems with alternative routing. International Journal of Production Research, 55(10), 2775-2790.
Hassan Zadeh, A., Afshari, H., & Ramazani Khorshid-Doust, R. (2014). Integration of process planning and production planning and control in cellular manufacturing. Production Planning & Control, 25(10), 840-857.
Holland, J. H. (1975). Adaptation in natural and artificial systems. An introductory analysis with application to biology, control, and artificial intelligence. Ann Arbor, MI: University of Michigan Press.
Kennedy, J., Eberhart, R., & Shi, Y. (2001). Swarm intelligence. San Francisco, CA: Morgan Kaufmann.
Kennedy, J., & Eberhart, R. C. (1997). A discrete binary version of the particle swarm algorithm. Proceedings from 1997 IEEE International Conference on the Systems, Man, and Cybernetics, Computational Cybernetics and Simulation.
Krishnan, K. K., Mirzaei, S., Venkatasamy, V., & Pillai, V. M. (2012). A comprehensive approach to facility layout design and cell formation. The International Journal of Advanced Manufacturing Technology, 59(5-8), 737-753.
Mahdavi, I., Aalaei, A., Paydar, M. M., & Solimanpur, M. (2010). Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment. Computers & Mathematics with Applications, 60(4), 1014-1025.
Mahdavi, I., Aalaei, A., Paydar, M. M., & Solimanpur, M. (2012). A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system. Journal of Manufacturing Systems, 31(2), 214-223.
Mahdavi, I., Teymourian, E., Baher, N. T., & Kayvanfar, V. (2013). An integrated model for solving cell formation and cell layout problem simultaneously considering new situations. Journal of Manufacturing Systems, 32(4), 655-663.
Rabbani, M., Farrokhi-Asl, H., Rafiei, H., & Khaleghi, R. (2017). Using metaheuristic algorithms to solve a dynamic cell formation problem with consideration of intra-cell layout design. Intelligent Decision Technologies, 11(1), 109-126.
Rabbani, M., Taheri, M., & Ravanbakhsh, M. (2016). A Bi-Objective Vehicle Routing Problem with Time Window by Considering Customer Satisfaction. International Journal of Strategic Decision Sciences (IJSDS), 7(2), 16-39.
Rafiee, K., Rabbani, M., Rafiei, H., & Rahimi-Vahed, A. (2011). A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system. Applied Mathematical Modelling, 35(4), 1810-1819.
Rezazadeh, H., & Khiali-Miab, A. (2017). A two-layer genetic algorithm for the design of reliable cellular manufacturing systems. International Journal of Industrial Engineering Computations, 8(3), 315-332.
Safaei, N., Saidi-Mehrabad, M., & Jabal-Ameli, M. (2008). A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. European Journal of Operational Research, 185(2), 563-592.
Saidi-Mehrabad, M., & Safaei, N. (2007). A new model of dynamic cell formation by a neural approach. The International Journal of Advanced Manufacturing Technology, 33(9), 1001-1009.
Sakhaii, M., Tavakkoli-Moghaddam, R., Bagheri, M., & Vatani, B. (2016). A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines. Applied Mathematical Modelling, 40(1), 169-191.
Shirzadi, S., Tavakkoli-Moghaddam, R., Kia, R., & Mohammadi, M. (2017). A multi-objective imperialist competitive algorithm for integrating intra-cell layout and processing route reliability in a cellular manufacturing system. International Journal of Computer Integrated Manufacturing, 30(8), 839-855.
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.
Venugopal, V., & Narendran, T. (1992). A genetic algorithm approach to the machine-component grouping problem with multiple objectives. Computers & Industrial Engineering, 22(4), 469-480.
Wu, T.-H., Chang, C.-C., & Chung, S.-H. (2008). A simulated annealing algorithm for manufacturing cell formation problems. Expert Systems with Applications, 34(3), 1609-1617.
Yousefi, H., Tavakkoli-Moghaddam, R., Oliaei, M., Mohammadi, M., & Mozaffari, A. (2017). Solving a bi-objective vehicle routing problem under uncertainty by a revised multi-choice goal programming approach. International Journal of Industrial Engineering Computations, 8(3), 283-302.