Çeşitli makine kısıtlarını içeren optimum hücre tasarım problemi için matematik programlama modeli

Yıl 2020, Cilt: 32 Sayı: 2, 172 - 179, 30.06.2020

Onur Derse , Ebru Yılmaz

https://doi.org/10.7240/jeps.592213

Öz

Hücresel üretim sistemleri, firmaların sürekli gelişen teknolojiye ve rekabete adaptasyon sağlayabilmesi amacıyla kullanılan ve benzer işlemlerin benzer ortamlarda üretilmesi esasına dayalı olan sistemlerdir. Hücresel üretim sistemlerinin etkin bir şekilde kurulması ve tasarlanması ile işlemlerin daha hızlı ve daha az maliyetle gerçekleşmesi sağlanabilmektedir. Bu çalışmada, kalemleri, üretim maliyeti, makinelerin hazırlık maliyeti, makinelerin bakım maliyeti ve personel maliyeti olan en uygun toplam tasarım maliyetini hedefleyen bir matematik programlama modeli oluşturulmaktadır. Bu modelde, makinelerin kapasiteleri, hücreyi oluşturmak için gerekli olan en az makine sayısı, her makine türünün en fazla atanabileceği hücre sayısı, parçaların en az kaç makinede işlem görebileceği, parçaların en fazla kaç makinede işlem görebileceği ve parçaların hangi makinelerde işlem göremeyeceği gibi çeşitli kısıtlar dikkate alınmaktadır. Önerilen bu model, geliştirilen beş farklı parçadan ve dokuz farklı olmak üzere toplamda on bir makineden oluşan bir örnek problem üzerinde uygulanmaktadır. Bu problemin çözümünde GAMS optimizasyon programı kullanılmış olup bir saniyeden daha kısa bir sürede toplam tasarım maliyetini en küçükleyen hücre tasarımı sonuçları ortaya çıkmaktadır.

Anahtar Kelimeler

Hücresel üretim sistemleri, Hücre tasarımı, Optimizasyon, Matematik programlama modeli

Kaynakça

• [1] Luong, L., He, J., Abhary, K., & Qiu, L., (2002). A Decision Support System for Cellular Manufacturing System Design. Computers & Industrial Engineering, 42(2-4), 457-470.
• [2] Raminfar, R., Zulkifli, N., Vasili, M., & Hong, T.S., (2013). An Integrated Model for Production Planning and Cell Formation in Cellular Manufacturing Systems. Journal of Applied Mathematics, 10 pages.
• [3] Imran, M., Kang, C., Lee, Y.H., Jahanzaib, M., & Aziz, H., (2017). Cell Formation in a Cellular Manufacturing System Using Simulation Integrated Hybrid Genetic Algorithm. Computers & Industrial Engineering, 105, 123-135.
• [4] Hazarika, M., & Laha, D., (2018). Genetic Algorithm Approach for Machine Cell Formation with Alternative Routings. Materials Today: Proceedings, 5(1), 1766-1775.
• [5] Srinivasan, G., Narendran, T.T., & Mahadevan, B., (1990). An Assignment Model for the Part-families Problem in Group Technology. International Journal of Production Research, 28(1), 145-152.
• [6] Shafer, S.M., & Rogers, D.F., (1991). A Goal Programming Approach to the Cell Formation Problem. Journal of Operations Management, 10(1), 28-43.
• [7] Adil, G.K., Rajamani, D., & Strong, D., (1993). A Mathematical Model for Cell Formation Considering Investment and Operational Costs. European Journal of Operational Research, 69(3), 330-341.
• [8] Heragu, S.S., & Chen, J.-S., (1998). Optimal Solution of Cellular Manufacturing System Design: Benders' Decomposition Approach. European Journal of Operational Research, 107(1), 175-192.
• [9] Wang, J., (2003). Formation of Machine Cells and Part Families in Cellular Manufacturing Systems Using a Linear Assignment Algorithm. Automatica, 39(9), 1607-1615.
• [10] Öztürk, G., & Öztürk, Z.K., (2005). A Competitive Neural Network Approach to Manufacturing Cell Formation. Proceedings of the 35th International Conference on Computers & Industrial Engineering, Istanbul, Turkey, June 19-22, 1549-1554.
• [11] Prabhaharan, G., Muruganandam, A., Asokan, P., & Girish, B.S., (2005). Machine Cell Formation for Cellular Manufacturing Systems Using an Ant Colony System Approach. Int J Adv Manuf Technol, 25, 1013-1019.
• [12] 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.
• [13] Ozturk, G., Ozturk, Z.K., & Islier, A.A., (2006). A Comparison of Competitive Neural Network with Other AI Techniques in Manufacturing Cell Formation. In: Jiao, L., Wang, L., Gao, X., Liu, J., Wu, F. (eds.), Advances in Natural Computation, ICNC 2006, Lecture Notes in Computer Science, vol. 4221, Springer, Berlin, Heidelberg, pp. 575-583.
• [14] Mahdavi, I., Javadi, B., Fallah-Alipour, K., & Slomp, J., (2007). Designing a New Mathematical Model for Cellular Manufacturing System Based on Cell Utilization. Applied Mathematics and Computation, 190(1), 662-670.
• [15] Ameli, M.S.J., & Arkat, J., (2008). Cell Formation with Alternative Process Routings and Machine Reliability Consideration. Int J Adv Manuf Technol, 35(7-8), 761-768.
• [16] Fan, J., & Feng, D., (2013). Design of Cellular Manufacturing System with Quasi-dynamic Dual Resource Using Multi-objective GA. International Journal of Production Research, 51(14), 4134-4154.
• [17] Erenay, B., Suer, G.A., Huang, J., & Maddisetty, S., (2015). Comparison of Layered Cellular Manufacturing System Design Approaches. Computers & Industrial Engineering, 85, 346-358.
• [18] Paydar, M.M., & Saidi-Mehrabad, M., (2015). Revised Multi-choice Goal Programming for Integrated Supply Chain Design and Dynamic Virtual Cell Formation with Fuzzy Parameters. International Journal of Computer Integrated Manufacturing, 28(3), 251-265.
• [19] Rafiei, H., Rabbani, M., Nazaridoust, B., & Ramiyani, S.S., (2015). Multi-objective Cell Formation Problem Considering Work-in-process Minimization. Int J Adv Manuf Technol, 76(9-12), 1947-1955.
• [20] Aghajani, M., Keramati, A., Tavakkoli-Moghaddam, R., & Mirjavadi, S.S., (2016). A Mathematical Programming Model for Cellular Manufacturing System Controlled by Kanban with Rework Consideration. The International Journal of Advanced Manufacturing Technology, 83(5-8), 1377-1394.
• [21] Alhourani, F., (2016). Cellular Manufacturing System Design Considering Machines Reliability and Parts Alternative Process Routings. International Journal of Production Research, 54(3), 846-863.
• [22] Aljuneidi, T., & Bulgak, A.A., (2017). Designing a Cellular Manufacturing System Featuring Remanufacturing, Recycling, and Disposal Options: A Mathematical Modeling Approach. CIRP Journal of Manufacturing Science and Technology, 19, 25-35.
• [23] Feng, H., Da, W., Xi, L., Pan, E., & Xia, T., (2017). Solving the Integrated Cell Formation and Worker Assignment Problem Using Particle Swarm Optimization and Linear Programming. Computers & Industrial Engineering, 110, 126-137.
• [24] Kazemi, M., Gol, S.S., Tavakkoli-Moghaddam, R., Kia, R., & Khorrami, J., (2017). A Mathematical Model for Assessing the Effects of a Lot Splitting Feature on a Dynamic Cellular Manufacturing System. Production Engineering, 11(4-5), 557-573.
• [25] Sadeghi, S., Forghani, M.A., & Seidi, M., (2017). Integrated Dynamic Cell Formation with Operator Assignment and Inter-cell Layout Problems: A Mathematical Model. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 231(9), 1658-1669.
• [26] Soolaki, M., & Arkat, J., (2018). Incorporating Dynamic Cellular Manufacturing into Strategic Supply Chain Design. Int J Adv Manuf Technol, 95(5-8), 2429-2447.
• [27] Feng, H., Xi, L., Xia, T., & Pan, E., (2018). Concurrent Cell Formation and Layout Design Based on Hybrid Approaches. Applied Soft Computing, 66, 346-359.
• [28] Maleki, R., Ketabi, S., & Rafiei, F.M., (2018). Grouping Both Machines and Parts in Cellular Technology by Genetic Algorithm. Journal of Industrial and Production Engineering, 35(2), 91-101.
• [29] Mahmoodian, V., Jabbarzadeh, A., Rezazadeh, H., & Barzinpour, F., (2019). A Novel Intelligent Particle Swarm Optimization Algorithm for Solving Cell Formation Problem. Neural Comput & Applic, 31(2), 801-815.
• [30] Shashikumar, S., Raut, R.D., Narwane, V.S., Gardas, B.B., Narkhede, B.E., & Awasthi, A., (2019). A Novel Approach to Determine the Cell Formation Using Heuristics Approach. OPSEARCH, 56, 628-656.