Document Type : Case Study

Authors

Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran.

Abstract

In this paper, a bi-objective mixed-integer mathematical model is presented for configuration of a dynamic cellular manufacturing system. In this model, dynamic changes and uncertainty in parts demand and machines reliability are considered. The first objective function minimizes total costs and the second one maximizes the machines reliability through minimizing machines failure. In addition, some routes are considered to produce each part based on operational requirements. An appropriate route is selected respect to the costs and operational time. Some parameters are considered under uncertainty in two categories. The first category such as demand is dependent on market condition and the uncontrolled competitive environment. The second one includes some parameters for production system and machines that are directly related to plans organized by production management. A robust optimization approach is used to deal with parameters uncertainty to produce feasible and optimal solutions. Furthermore, for validation and implementation of results in real world, a case study is investigated. Computational results show that the robust model reports better values for objective functions compared to the scenario-based model. In fact, Pareto-front which are resulted by robust model are dominated by scenario-based models’ Pareto front.  Sensitivity analyses on main parameters of the problem are performed to drive some managerial insights that help corresponding decision makers to provide suitable and homogenous decisions in a production system. 

Keywords

Agarwal, A., and Sarkis, J., (1998). "A review and analysis of comparative performance studies on functional and cellular manufacturing layouts", Computers and industrial engineering, Vol. 34, No.1, pp. 77-89.
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(7-8), pp. 761-768.
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(7-8), pp. 838-850.
Arıkan, F., and Güngör, Z., (2009). "Modeling of a manufacturing cell design problem with fuzzy multi-objective parametric programming", Mathematical and Computer Modelling, Vol. 50, No. 3, pp. 407-420.
Arkat, J., Naseri, F., and Ahmadizar, F., (2011). "A stochastic model for the generalised cell formation problem considering machine reliability", International Journal of Computer Integrated Manufacturing, Vol. 24, No. 12, pp. 1095-1102.
Askin, R. G., and Estrada, S., (1999). "Investigation of cellular manufacturing practices", Handbook of cellular manufacturing systems, pp. 25-34.
Babaee Tirkolaee, E., Alinaghian, M., Bakhshi Sasi, M., and Seyyed Esfahani, M., (2016). "Solving a robust capacitated arc routing problem using a hybrid simulated annealing algorithm: a waste collection application", Journal of Industrial Engineering and Management Studies, Vol. 3, No. 1, pp. 61-76.
Bedworth, D. D., Henderson, M. R., and Wolfe, P. M., (1991). Computer-integrated design and manufacturing: McGraw-Hill, Inc.
Ben-Tal, A., and Nemirovski, A., (1998). "Robust convex optimization", Mathematics of operations research, Vol. 23, No. 4, pp. 769-805.
Ben-Tal, A., and Nemirovski, A., (1999). "Robust solutions of uncertain linear programs", Operations research letters, Vol. 25, No. 1, pp. 1-13.
Ben-Tal, A., and Nemirovski, A., (2000). "Robust solutions of linear programming problems contaminated with uncertain data", Mathematical programming, Vol. 88, No. 3, pp. 411-424.
Cao, D., and Chen, M., (2005). "A robust cell formation approach for varying product demands", International journal of production research, Vol. 43, No. 8, pp. 1587-1605.
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 and industrial engineering, Vol. 60, No. 1, pp. 7-15.
Das, K., and Abdul-Kader, W., (2011). "Consideration of dynamic changes in machine reliability and part demand: a cellular manufacturing systems design model", International journal of production research, Vol.49, No. 7, pp. 2123-2142.
Das, K., Lashkari, R., and Sengupta, S., (2007). "Machine reliability and preventive maintenance planning for cellular manufacturing systems", European Journal of Operational Research, Vol. 183, No. 1, pp. 162-180.
Deep, K., and Singh, P. K., (2015). "Design of robust cellular manufacturing system for dynamic part population considering multiple processing routes using genetic algorithm", Journal of Manufacturing Systems, Vol. 35, pp. 155-163.
El Ghaoui, L., and Lebret, H., (1997). "Robust solutions to least-squares problems with uncertain data", SIAM Journal on matrix analysis and applications, Vol.18, No. 4, pp. 1035-1064.
Erenay, B., Suer, G. A., Huang, J., and Maddisetty, S., (2015). "Comparison of layered cellular manufacturing system design approaches", Computers and industrial engineering, Vol. 85, pp. 346-358.
Farughi, H., and Mostafayi, S., (2016). "Robust Optimization Approach for Design for a Dynamic Cell Formation Considering Labor Utilization: Bi-objective Mathematical Model", International Journal of Supply and Operations Management, Vol. 3, No. 1, pp. 1143-1167.
Ghezavati, V., 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.
Han, B. T., Zhang, C. B., Sun, C. S., and Xu, C. J., (2006). "Reliability analysis of flexible manufacturing cells based on triangular fuzzy number", Communications in Statistics-Theory and Methods, Vol. 35, No. 10, pp. 1897-1907.
Hazarika, M., and Laha, D., (2018). "Genetic algorithm approach for machine cell formation with alternative routings", Materials Today: Proceedings, Vol. 5, No. 1, pp. 1766-1775.
Hejazi, T., Soleimanmeigouni, I., (2014). "A novel approach in robust group decision making for supply strategic planning", Journal of Industrial Engineering and Management Studies, Vol. 1, No. 1, pp. 20-30.
Imran, M., Kang, C., Lee, Y. H., Jahanzaib, M., and Aziz, H., (2017). "Cell formation in a cellular manufacturing system using simulation integrated hybrid genetic algorithm", Computers and industrial engineering, Vol. 105, pp. 123-135.
Kia, R., Baboli, A., Javadian, N., Tavakkoli-Moghaddam, R., Kazemi, M., and Khorrami, J., (2012). "Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing", Computers and operations research, Vol. 39, No. 11, pp. 2642-2658.
Kia, R., Khaksar-Haghani, F., Javadian, N., and Tavakkoli-Moghaddam, R., (2014). "Solving a multi-floor layout design model of a dynamic cellular manufacturing system by an efficient genetic algorithm", Journal of Manufacturing Systems, Vol. 33, No. 1, pp. 218-232.
Kumar, R., and Singh, S. P., (2019). "Modified SA Algorithm for Bi-objective Robust Stochastic Cellular Facility Layout in Cellular Manufacturing Systems", Advanced Computing and Communication Technologies (pp. 19-33): Springer.
Lee, D.-T., (1980). "Two-dimensional Voronoi diagrams in the Lp-metric", J. ACM, Vol. 27, No. 4, pp. 604-618.
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, Vol.60, No. 4, pp. 1014-1025.
Mulvey, J. M., Vanderbei, R. J., and Zenios, S. A., (1995). "Robust optimization of large-scale systems", Operations Research, Vol. 43, No.2, pp. 264-281.
Nodem, F. D., Kenné, J., and Gharbi, A., (2011). "Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems", International Journal of Production Economics, Vol. 134, No. 1, pp. 271-282.
Noorossana, R., Niaki, S. T. A., and Ershadi, M. J., (2014).  "Economic and economic‐statistical designs of phase II profile monitoring", Quality and Reliability Engineering International, Vol. 30, No. 5, pp. 645-655.
Nsakanda, A. L., Diaby, M., and Price, W. L., (2006). "Hybrid genetic approach for solving large-scale capacitated cell formation problems with multiple routings", European Journal of Operational Research, Vol. 171, No. (3), pp. 1051-1070.
Paydar, M. M., Mahdavi, I., Sharafuddin, I., and Solimanpur, M., (2010). "Applying simulated annealing for designing cellular manufacturing systems using MDmTSP", Computers and industrial engineering, Vol. 59, No. 4, pp. 929-936.
Paydar, M. M., Saidi-Mehrabad, M., and Teimoury, E., (2014). "A robust optimisation model for generalised cell formation problem considering machine layout and supplier selection", International Journal of Computer Integrated Manufacturing, Vol. 27, No. 8, pp. 772-786.
Pillai, V. M., and Subbarao, K., (2008). "A robust cellular manufacturing system design for dynamic part population using a genetic algorithm", International journal of production research, Vol. 46, No. 18, pp. 5191-5210.
Renna, P., and Ambrico, M., (2015). "Design and reconfiguration models for dynamic cellular manufacturing to handle market changes", International Journal of Computer Integrated Manufacturing, Vol. 28, No. 2, pp. 170-186.
Safaei, N., Saidi-Mehrabad, M., Tavakkoli-Moghaddam, R., and Sassani, F., (2008). "A fuzzy programming approach for a cell formation problem with dynamic and uncertain conditions", Fuzzy Sets and Systems, Vol. 159, No. 2, pp. 215-236.
Safaei, N., and Tavakkoli-Moghaddam, R., (2009). "An extended fuzzy parametric programming-based approach for designing cellular manufacturing systems under uncertainty and dynamic conditions", International Journal of Computer Integrated Manufacturing, Vol. 22, No. 6, pp. 538-548.
Sakhaii, M., Tavakkoli-Moghaddam, R., Bagheri, M., and Vatani, B., (2016). "A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines", Applied Mathematical Modelling, Vol. 40, No. 1, pp. 169-191.
Seifoddini, H., and Djassemi, M., (2001). "The effect of reliability consideration on the application of quality index", Computers and industrial engineering,Vol. 40(1-2), pp. 65-77.
Solimanpur, M., Saeedi, S., and Mahdavi, I., (2010). "Solving cell formation problem in cellular manufacturing using ant-colony-based optimization", The International Journal of Advanced Manufacturing Technology, Vol. 50(9-12), pp. 1135-1144.
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.
Tavakkoli-Moghaddam, R., Ranjbar-Bourani, M., Amin, G. R., and Siadat, A., (2012). "A cell formation problem considering machine utilization and alternative process routes by scatter search", Journal of Intelligent Manufacturing, Vol. 23, No. 4, pp. 1127-1139.
Tavakkoli-Moghaddam, R., Sakhaii, M., and Vatani, B., (2013). "A robust model for a dynamic cellular manufacturing system with production planning", International Journal of Engineering-Transactions A: Basics, Vol. 27, No. 4, pp. 587-596.
Vakharia, A., and Kaku, B., (1993). "An investigation of the impact of demand changes on a cellular manufacturing system", Decision Sciences, Vol. 24, No. 5, pp. 909-930.
Wang, H., (2002). "A survey of maintenance policies of deteriorating systems", European Journal of Operational Research, Vol. 139, No. 3, pp. 469-489.
Wang, X., Tang, J., and Yung, K.-l., (2009). "Optimization of the multi-objective dynamic cell formation problem using a scatter search approach", The International Journal of Advanced Manufacturing Technology, Vol. 44(3-4), pp. 318-329.
Wemmerlöv, U., and Hyer, N. L., (1989). "Cellular manufacturing in the US industry: a survey of users", The international journal of production research, Vol. 27, No. 9, pp. 1511-1530.
Wemmerlov, U., and Johnson, D. J., (1997). "Cellular manufacturing at 46 user plants: implementation experiences and performance improvements", International journal of production research, Vol. 35, No. 1, pp. 29-49.
Wicks, E. M., and Reasor, R. J., (1999). "Designing cellular manufacturing systems with dynamic part populations", IIE transactions, Vol. 31, No. 1, pp. 11-20.
Yılmaz, E., and Erol, R., (2015). "A mathematical programming model for reconfiguration of flexible manufacturing cells", Engineering Optimization, Vol. 47, No. 2, pp. 184-203.
Yin, Y., Yasuda, K., and Hu, L., (2005). "Formation of manufacturing cells based on material flows", The International Journal of Advanced Manufacturing Technology, Vol. 27(1-2), pp. 159-165.
Yu, C.-S., and Li, H.-L., (2000). "A robust optimization model for stochastic logistic problems", International Journal of Production Economics, Vol. 64(1-3), pp. 385-397.