Robust Optimization Approach for Design for a Dynamic Cell Formation Considering Labor Utilization: Bi-objective Mathematical Model

Document Type: Research Paper


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


In this paper, robust optimization of a bi-objective mathematical model in a dynamic cell formation problem considering labor utilization with uncertain data is carried out. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. In this research, cost parameters of the cell formation and demand fluctuations are subject to uncertainty and a mixed-integer programming (MIP) model is developed to formulate the related robust dynamic cell formation problem. Then the problem is transformed into a bi-objective linear one. The first objective function seeks to minimize relevant costs of the problem including machine procurement and relocation costs, machine variable cost, inter-cell movement and intra-cell movement costs, overtime cost and labor shifting cost between cells, machine maintenance cost, inventory, holding part cost. The second objective function seeks to minimize total man-hour deviations between cells or indeed labor utilization of the modeled.


Main Subjects

Aalaei, Amin, and Hamid Davoudpour. (2015) "Revised multi-choice goal programming for incorporated dynamic virtual cellular manufacturing into supply chain management: A case study." Engineering Applications of Artificial Intelligence.

Ben-Tal, Aharon, Laurent El Ghaoui, and Arkadi Nemirovski. Robust optimization. Princeton University Press, 2009.

Bertsimas, Dimitris, and Aurélie Thiele.(2004) "A robust optimization approach to supply chain management." Integer programming and combinatorial optimization. Springer Berlin Heidelberg, pp. 86-100.

Burbridge, J.L., Production flow analysis Prod. Eng.(April/May 1971), pp.139-152.

Dantzig, George B. (1955) "Linear programming under uncertainty." Management science, Vol. 1.3-4, pp. 197-206.

Deep, Kamal, and Pardeep K. Singh. "Design of robust cellular manufacturing system for dynamic 

part population considering multiple processing routes using genetic algorithm. (2015)" Journal of Manufacturing Systems, Vol. 35, pp. 155-163.

Defersha, Fantahun M., and Mingyuan Chen. (2008) "A linear programming embedded genetic algorithem for an integrated cell formation and lot sizing considering product quality." European Journal of Operational Research, Vol. 187(1), pp. 46-69.

FahimehKhaksar-Haghani& Reza Kia &IrajMahdavi& Mohammad Kazemi ,(2013) "A genetic algorithm for solving a multi-floor layout design model of a cellular manufacturing system with alternative process routings and flexible configuration", Int J AdvManufTechnol, Vol. 66, pp. 845–865.

Feizollahi, Mohammad Javad, and Mohammad Modarres.(2012) "The robust deviation redundancy allocation problem with interval component reliabilities." Reliability, IEEE Transactions on, Vol. 61(4), pp. 957-965.

Kia, Reza, et al. (2012) "Designing an intra-cell layout model in dynamic cellular manufacturing systems with unequal-area facilities." International Journal of Management Science and Engineering Management, Vol. 7(1), pp. 10-19.

Lokesh Kumar Saxena, Promod Kumar Jain, 2011"Dynamic cellular manufacturing systems design—a comprehensive model", The International Journal of Advanced Manufacturing Technology, Vol. 53 (1-4), pp 11-34.

Mulvey, John M., Robert J. Vanderbei, and Stavros A. Zenios. (1995) "Robust optimization of large-scale systems." Operations research, Vol. 43(2), pp. 264-281.

Pan, Feng, and Rakesh Nagi. (2010) "Robust supply chain design under uncertain demand in agile manufacturing." Computers & Operations Research, Vol. 37(4), pp. 668-683.

Paydar, M.M., M .Saidi-Mehrabad, and E. Teimoury, (2104) "A robust optimization model for generalized cell formation problem considering machine layout and supplier selection". International Journal of Computer Integrated Manufacturing, Vol. 27(8), pp. 772-786.

Rahmani, Donya, Reza Ramezanian, Parviz Fattahi, and Mahdi Heydari.  (2013) "A robust optimization model for multi-product two-stage capacitated production planning under uncertainty." Applied Mathematical Modelling, Vol. 37(20), pp. 8957-8971.

Rheault, Martin, Jocelyn R. Drolet, and Georges Abdulnour. (1995) "Physically reconfigurable virtual cells: a dynamic model for a highly dynamic environment." Computers & Industrial Engineering, Vol. 29(1), pp. 221-225.

Saffarian, Mohsen, Farnaz Barzinpour, and Mohammad Ali Eghbali. (2015) "A robust programming approach to bi-objective optimization model in the disaster relief logistics response phase." International Journal of Supply and Operations Management, Vol. 2(1), pp. 595-616.

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, Vol. 40(1), pp. 169-191. 

Shishebori, Davood, and Abdolsalam Ghaderi. (2015) "An integrated approach for reliable facility location/network design problem with link disruption." International Journal of Supply and Operations Management, Vol. 2(1), pp. 640-661.

Singh, C. (1982) "Convex programming with set-inclusive constraints and its applications to generalized linear and fractional programming." Journal of Optimization Theory and Applications, Vol. 38(1), pp. 33-42.

Vafaeinezhad, Moghadaseh, Reza Kia, and Parisa Shahnazari-Shahrezaei. (2016) "Robust optimization of a mathematical model to design a dynamic cell formation problem considering labor utilization." Journal of Industrial Engineering International, Vol. 129(1), pp. 45-60.

Venugopal, V., and T. T. Narendran. (1992) "A genetic algorithm approach to the machine-component grouping problem with multiple objectives." Computers & Industrial Engineering, Vol. 22(4), pp. 469-480.

Wemmerlöv, Urban, and Nancy L. Hyer. (1989) "Cellular manufacturing in the US industry: a survey of users." The International Journal of Production Research, Vol. 27(9), pp. 1511-1530.

Wemmerlöv, Urban, and Nancy Lea Hyer. (1986) "Procedures for the part family/machine group identification problem in cellular manufacturing." Journal of Operations Management, Vol. 6(2), pp. 125-147.

Y. Gupta, M. Gupta, A. Kumar, C. Sundram,(1995) "Minimizing total inter-cell and intra-cell moves in cell formation: a genetic algorithm", International Journal of Computer Integrated Manufacturing, Vol. 8(2), pp. 92–101.

Zanjani, Masoumeh Kazemi, Daoud Ait-Kadi, and Mustapha Nourelfath. (2010) "Robust production planning in a manufacturing environment with random yield: A case in sawmill production planning." European Journal of Operational Research, Vol. 201(3), pp. 882-891.
Zhang, Zhifeng, and Renbin Xiao. (2009)"Empirical study on entropy models of cellular manufacturing systems." Progress in Natural Science, Vol. 19(3), pp. 389-395.