A Mathematical Model for Dynamic Cell Formation Problem Based on Scheduling, Worker Allocation, and Financial Resources Constraint

Document Type : Research Paper

Authors

1 Associate Prof., Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran.

2 MSc., Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran.

3 Assistant Prof., Department of Industrial Engineering, Faculty of Engineering, Meybod University, Meybod, Iran.

Abstract

Objective: Cellular production is one of the important applications of group technology in production. With the development of modern industrial technology, many manufacturers use it as a solution to implement complex and realistic scenarios that increase the productivity and flexibility of a production system. Cellular production includes cell formation, cellular and intracellular arrangement, operation scheduling, and resource allocation. The process of formation and grouping of machines to produce families of parts to minimize the cost of moving materials among cells is called cell formation. In other words, cell formation in cell production systems and assignment of machine groups and family of parts to these cells is done to minimize the total cost and increase flexibility and productivity in production. The layout design is also related to the position of the cells relative to each other and the position of the machines in each cell relative to each other. In some production units, the placement of cells in relation to each other and even the placement of devices in each cell is not done properly, which increases the movement of materials, semi-finished parts, and consequently, production costs. On the other hand, with changes in customer needs and demand and competitive market conditions, the combination of existing cells and their arrangement in one period may not be appropriate for another period, and it is necessary to make changes to reply to customer needs and remain competitive. The possibility of making changes in cells combination, placement inside and between cells is called dynamic cell formation. In other words, dynamic cell formation involves changing the position of the cells relative to each other and the proper placement of the machines in one cell so that it is possible to move the machines to a new position or another cell and increase or decrease them.
Methods: Operation scheduling and assigning human resources incurring a notable proportion of expenses in the cell formation. These issues seem more important when financial resources are limited. In this research, dynamic cell formation problems based on scheduling, allocation of workers, and constraints of financial resources on machines and workers are simultaneously investigated, Accordingly, the present study seeks to minimize the total costs, including the costs of machines, workers, and transportation of parts. At first, a mathematical model was presented. The model was then linearized and validated. After that, a genetic algorithm was proposed to solve the problem where the parameters were adjusted and selected by using the Taguchi method. Sensitivity analysis was also performed based on the related parameters in constraints of financial resources of machines and workers.
Results: The results showed the accuracy of the model and its validation. It was also shown that the proposed algorithm is highly efficient and can be used for medium and large-sized problems where it is not impossible to find the optimal solution.
Conclusion: Sensitivity analysis showed that the constraints of financial resources for purchasing machines have a greater impact on the objective function than workers' financial constraints, which is of high importance.

Keywords


Alimian, M., Ghezavati, V., Tavakkoli-Moghaddam, R. (2020). New integration of preventive maintenance and production planning with cell formation and group scheduling for dynamic cellular manufacturing systems. Journal of Manufacturing Systems, 56, 341-358.
Aminpour, S., Irajpour, A., Yazdani, M., Mohtashami, A. (2020). The Design of a Multi-directional Network Chain Model Offering a Closed Loop in the Automotive Industry by Providing Energy and Time Efficiency Programs. Industrial Management Journal. 12(2), 319-343. (in Persian)
Arkat, J., Hosseinabadi Farahani, M., Hosseini, L. (2011). Integrating cell formation with cellular layout and operations scheduling. The International Journal of Advanced Manufacturing Technology, 61(5), 637-647.
Aryanezhad, M.B., Deljoo, V., Mirzapour Al-e-hashem, S.M.J. (2009). Dynamic cell formation and the worker assignment problem: a new model. The International Journal of Advanced Manufacturing Technology, 41(3), 329-342.
Bagheri, M., Bashiri, M. (2013). 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.
Bouaziz, H., Berghida, M., Lemouari, A. (2020). Solving the generalized cubic cell formation problem using discrete flower pollination algorithm. Expert Systems with Applications, 150, 13345.
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.
Chiniforooshan, P., Pourghannad, B., Shahraki, N. (2011). A New Approach for Solving Cell Formation Problem Considering Alternative Process Routings. Journal of Industrial Management Studies, 9(23), 209-231. (in Persian)
Chu, X., Gao, D., Cheng, S., Wu, L., Chen, J., Shi, Y., Qin, Q. (2019). Worker assignment with learning-forgetting effect in cellular manufacturing system using adaptive memetic differential search algorithm. Computers & Industrial Engineering, 136, 381-396.
Danilovic, M., Ilic, O. (2019). A novel hybrid algorithm for manufacturing cell formation problem. Expert Systems with Applications, 135(30), 327-350.
Deljoo, V., Mirzapour Al-e-hashem, S.M.J., Deljoo, F., Aryanezhad, M.B. (2010). Using genetic algorithm to solve dynamic cell formation problem. Applied Mathematical Modelling, 34(4), 1078-1092.
Jolai, F., Tavakkoli-Moghaddam, R., Golmohammadi, A., Javadi, B. (2012). An Electromagnetism-like algorithm for cell formation and layout problem. Expert Systems with Applications, 39(2), 2172-2182.
Kia, R., Baboli, A., Javadian, N., Tavakkoli-Moghaddam, R., Kazemi, M., 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 & Operations Research, 39(11), 2642-2658.
Kia, R., Shirazi, H., Javadian, N., Tavakkoli-Moghaddam, R. (2013). A multi-objective model for designing a group layout of a dynamic cellular manufacturing system. Journal of Industrial Engineering International, 9(1), 1-14.
Kong, T., Seong, K., Song, K., Lee, K. (2018). Two-mode Modularity Clustering of Parts and Activities for Cell Formation Problems. Computers & Operations Research, 100, 77-88.
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), 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., Teymourian, E., Tahami Baher, N., 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.
Mehdizadeh, E., Daei Niaki, S.V., Rahimi, V. (2016). A vibration damping optimization algorithm for solving a new multi-objective dynamic cell formation problem with workers training. Computers & Industrial Engineering, 101, 35-52.
Mehdizadeh, E., Rahimi, V. (2016). An integrated mathematical model for solving dynamic cell formation problem considering operator assignment and inter/intra cell layouts. Applied Soft Computing, 42, 325-341.
Mohammadi, M., Forghani, K. (2017) A hybrid method based on genetic algorithm and dynamic programming for solving a bi-objective cell formation problem considering alternative process routings and machine duplication. Applied Soft Computing, 53, 97-110.
Mohammadi, M., Forghani, K. (2018). Solving an Integrated Cell Formation, Group Layout and Routing Problem Using Dynamic Programming Based MetaheuristicAlgorithms. Journal of Industrial Management Studies, 16(49), 67-104. (in Persian)
Niakan, F., Baboli, A., Moyaux, T., Botta-Genoulaz, V. (2016). A bi-objective model in sustainable dynamic cell formation problem with skill-based worker assignment. Journal of Manufacturing Systems, 38, 46-62.
Rafiei, H., Ghodsi, R. (2013). A bi-objective mathematical model toward dynamic cell formation considering labor utilization. Applied Mathematical Modelling, 37(4) 2308-2316.
Rajesh, K.V.D., Abid Ali, M.D., Chalapathi, P.V. (2018). Voids Based Approach for Solving Cell Formation Problems. Materials Today: Proceedings, 5(13), 27185–27192.
Salimpour, S., Pourvaziri, H., Azab, A. (2021). Semi-robust layout design for cellular manufacturing in a dynamic environment. Computers & Operations Research, 133, 105367.
Satuglu, S., Suresh, N.C. (2009). A goal-programming approach for design of hybrid cellular manufacturing systems in dual resource constrainted environment. Computers & Industrial Engineering, 56, 560-575.
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.
Teymouri, E., Amiri, M., Olfat, L., Zandieh, M. (2020). Presenting a Supplier Selection, Order Allocation, and Pricing Model in Multi-item, Single-Period, and Multi-Supplier Supply Chain Management with Surface Response Methodology and Genetic Algorithm Approach. Industrial Management Journal. 12(1), 1-23. (in Persian)
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.
Xue, G., Offodile, O.F. (2020). Integrated optimization of dynamic cell formation and hierarchical production planning problems. Computers & Industrial Engineering, 139, 106155.
Zohrevand, A.M., Rafiei, H., Zohrevand, A.H. (2016). Multi-objective dynamic cell formation problem: A stochastic programming approach. Computers & Industrial Engineering, 98, 323-332.