A Mathematical Model for the Type-II Assembly Line Balancing Problem with Hierarchical Worker Assignment

Yıl 2024, Cilt: 35 Sayı: 1, 1 - 21, 30.04.2024

Aslıhan Karaş Çelik , Feriştah Özçelik

https://doi.org/10.46465/endustrimuhendisligi.1333382

Öz

In the traditional assembly line balancing (ALB) problem, there is an assumption that the processing times of tasks are fixed and independent of the worker. However, the processing times vary due to factors such as experience and ability among workers. The type of problem in which workers are decoupled into hierarchical levels and their processing times and costs differ between the levels is known as the assembly line balancing with hierarchical worker assignment (ALBHWA) problem. In this study, for the first time in the literature, minimizing the cycle time and total worker cost is discussed in the case where the number of workstations is known for the ALBHWA problem. A mathematical modelling approach is developed for the solution of the problem and the performance of the proposed model is evaluated by adapting the test problems in the literature.

Anahtar Kelimeler

Assembly line, Line balancing, Hierarchical worker assignment, Mathematical modelling

HİYERARŞİK İŞÇİ ATAMASI İLE TİP-II MONTAJ HATTI DENGELEME PROBLEMİ İÇİN BİR MATEMATİKSEL MODEL

Öz

Geleneksel montaj hattı dengeleme (MHD) probleminde, görevlerin işlem sürelerinin sabit ve işçiden bağımsız olduğu varsayımı bulunmaktadır. Ancak, işlem süreleri; tecrübe ve yetenek gibi etmenler dolayısıyla işçiler arasında değişkenlik göstermektedir. İşçilerin hiyerarşik seviyelere ayrılarak işlem sürelerinin ve maliyetlerinin seviyeler arasında farklılık gösterdiği problem türü, hiyerarşik işçi ataması ile montaj hattı dengeleme (HİAMHD) problemi olarak bilinmektedir. Bu çalışmada, literatürde ilk kez HİAMHD problemi için iş istasyonu sayısının belirli olduğu durumda, çevrim süresinin ve toplam işçi maliyetinin enküçüklenmesi ele alınmaktadır. Problemin çözümü için bir matematiksel modelleme yaklaşımı geliştirilmiş ve literatürde bulunan test problemleri uyarlanarak önerilen modelin performansı değerlendirilmiştir.

Anahtar Kelimeler

Montaj hattı, Hat dengeleme, Hiyerarşik işçi ataması, Matematiksel modelleme

Kaynakça

• Araújo, F. F. B., Costa, A. M., & Miralles, C. (2012). Two extensions for the ALWABP: Parallel stations and collaborative approach. International Journal of Production Economics, 140(1), 483-495. Doi: https://doi.org/10.1016/j.ijpe.2012.06.032
• Araújo, F. F. B., Costa, A. M., & Miralles, C. (2015). Balancing parallel assembly lines with disabled workers. European Journal of Industrial Engineering, 9(3), 344–365. Doi: https://doi.org/10.1504/EJIE.2015.069343
• Baykasoğlu, A. ve Demirkol Akyol, Ş. (2014). Ergonomik montaj hattı dengeleme. Gazi Üniversitesi Mühendislik ve Mimarlık. Fakültesi Dergisi, 29(4), 785-792. Doi: https://doi.org/10.17341/gummfd.00296
• Blum, C. & Miralles, C. (2011). On solving the assembly line worker assignment and balancing problem via beam search. Computers & Operations Research, 38(1), 328-339. Doi: https://doi.org/10.1016/j.cor.2010.05.008
• Borba, L. & Ritt, M. (2014). A heuristic and a branch-and-bound algorithm for the assembly line worker assignment and balancing problem. Computers & Operations Research, 45, 87-96. Doi: https://doi.org/10.1016/j.cor.2013.12.002
• Campana, N. P., Iori, M., & Moreira, M. C. O. (2022). Mathematical models and heuristic methods for the assembly line balancing problem with hierarchical worker assignment. International Journal of Production Research, 60(7), 2193-2211. Doi: https://doi.org/10.1080/00207543.2021.1884767
• Chaves, A. A., Lorena, L. A. N., & Miralles, C. (2007). Clustering search approach for the assembly line worker assignment and balancing problem. Proceedings of the 37th International Conference on Computers & Industrial Engineering, 1469–1478, Alexandria, Egypt.
• Chaves, A. A., Lorena, L. A. N., & Miralles, C. (2009). Hybrid metaheuristic for the assembly line worker assignment and balancing problem. Proceedings of the 6th International Workshop on Hybrid Metaheuristics, 1–14, Udine, Italy. Doi: https://doi.org/10.1007/978-3-642-04918-7_1
• Costa, A. M. & Miralles, C. (2009). Job rotation in assembly lines employing disabled workers. International Journal of Production Economics, 120(2), 625–632. Doi: https://doi.org/10.1016/j.ijpe.2009.04.013
• Demirkol Akyol, S. & Baykasoğlu, A. (2019a). A multiple-rule based constructive randomized search algorithm. Journal of Intelligent Manufacturing, 30(2), 557-573. Doi: https://doi.org/10.1007/s10845-016-1262-6
• Demirkol Akyol, S. & Baykasoglu, A. (2019b). ErgoALWABP: A multiple-rule based constructive randomized search algorithm for solving assembly line worker assignment and balancing problem under ergonomic risk factors. Journal of Intelligent Manufacturing, 30(1), 291-302. Doi: https://doi.org/10.1007/s10845-016-1246-6
• Efe, B., Kremer G. E. O., & Kurt, M. (2018). Age and gender-based workload constraint for assembly line worker assignment and balancing problem in a textile firm. International Journal of Industrial Engineering, 25(1), 1-17. Erişim adresi: https://eds.p.ebscohost.com/eds/pdfviewer/pdfviewer?vid=0&sid=82051d6d-1d31-4836-abf6-d3b82821d70b%40redis
• Janardhanan, M. N., Li, Z., & Nielsen, P. (2019). Model and migrating birds optimization algorithm for two-sided assembly line worker assignment and balancing problem. Soft Computing, 23(21), 11263-11276. Doi: https://doi.org/10.1007/s00500-018-03684-8
• Janardhanan, M. N., Li Z., Nielsen P., & Tang Q. (2018). Artificial bee colony algorithms for two-sided assembly line worker assignment and balancing problem. Advances in Intelligent Systems and Computing, 620, 11–18. Doi: https://doi.org/10.1007/978-3-319-62410-5_2
• Karas, A. & Ozcelik, F. (2021). Assembly line worker assignment and rebalancing problem: A mathematical model and an artificial bee colony algorithm. Computers & Industrial Engineering, 156, 107195. Doi: https://doi.org/10.1016/j.cie.2021.107195
• Liu, M., Liang, B., & Chu, F. (2019). A risk-averse assembly line worker assignment and balancing problem with uncertain processing time. Proceedings of the 2019 International Conference on Industrial Engineering and Systems Management, IESM, 266-271, Shanghai, China. Doi: https://doi.org/10.1109/IESM45758.2019.8948211
• Liu, M., Liu, R., & Chu, F. (2019). An improved model for assembly line worker assignment and balancing problem considering stochastic worker availability. Proceedings of the 2019 International Conference on Industrial Engineering and Systems Management, IESM, 731-736, Shanghai, China. Doi: https://doi.org/10.1109/IESM45758.2019.8948125
• Liu, M., Liu, Z., Chu, F., Liu, R., Zheng, F., & Chu, C. (2022). Risk-averse assembly line worker assignment and balancing problem with limited temporary workers and moving workers. International Journal of Production Research, 60(23), 7074–7092. Doi: https://doi.org/10.1080/00207543.2021.2002960
• Liu, R., Liu, M., Chu, F., Zheng, F., & Chu, C. (2021). Eco-friendly multi-skilled worker assignment and assembly line balancing problem. Computers & Industrial Engineering, 151, 106944. Doi: https://doi.org/10.1016/j.cie.2020.106944
• Miralles, C., Garcia-Sabater, J. P., Andres, C., & Cardós, M. (2007). Advantages of assembly lines in sheltered work centres for disabled. A case study. International Journal of Production Economics, 110(1-2), 187-197. Doi: https://doi.org/10.1016/j.ijpe.2007.02.023
• Miralles, C., Garcia-Sabater, J. P., Andres, C., & Cardós, M. (2008). Branch and bound procedures for solving the assembly line worker assignment and balancing problem: Application to sheltered work centers for disabled. Discrete Applied Mathematics, 156(3), 352–367. Doi: https://doi.org/10.1016/j.dam.2005.12.012
• Moreira, M. C. O. & Costa, A. M. (2009). A minimalist yet efficient tabu search algorithm for balancing assembly lines with disabled workers. Proceedings of the XLI Simpósio Brasileiro de Pesquisa Operacional, 660–671, Porto Seguro, Bahia, Brazil.
• Moreira, M. C. O., Ritt, M., Costa, A. M., & Chaves, A. A. (2012). Simple heuristics for the assembly line worker assignment and balancing problem. Journal of Heuristics, 18(3), 505-524. Doi: https://doi.org/10.1007/s10732-012-9195-5
• Mutlu, O., Polat, O., & Supciller, A. A. (2013). An iterative genetic algorithm for the assembly line worker assignment and balancing problem of type-II. Computers & Operations Research, 40(1), 418-426. Doi: https://doi.org/10.1016/j.cor.2012.07.010
• Oksuz, M. K., Buyukozkan, K., & Itir Satoglu, S. (2017). U-shaped assembly line worker assignment and balancing problem: A mathematical model and two meta-heuristics. Computers & Industrial Engineering, 112, 246–263. Doi: https://doi.org/10.1016/j.cie.2017.08.030
• Pereira, J. (2018). The robust (minmax regret) assembly line worker assignment and balancing problem. Computers & Operations Research, 93, 27-40. Doi: https://doi.org/10.1016/j.cor.2018.01.009
• Polat, O., Kalayci, C. B., Mutlu, O., & Gupta, S. M. (2016). A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: An industrial case study. International Journal of Production Research, 54(3), 722-741. Doi: https://doi.org/10.1080/00207543.2015.1055344
• Ramezanian, R. & Ezzatpanah, A. (2015). Modeling and solving multi-objective mixed-model assembly line balancing and worker assignment problem. Computers & Industrial Engineering, 87, 74-80. Doi: https://doi.org/10.1016/j.cie.2015.04.017
• Ritt, M., Costa, A. M., & Miralles, C. (2016). The assembly line worker assignment and balancing problem with stochastic worker availability. International Journal of Production Research, 54(3), 907-922. Doi: https://doi.org/10.1080/00207543.2015.1108534
• Sungur, B. & Yavuz, Y. (2015). Assembly line balancing with hierarchical worker assignment. Journal of Manufacturing Systems, 37, 290-298. Doi: https://doi.org/10.1016/j.jmsy.2014.08.004
• Topaloglu Yildiz, S., Yildiz, G., & Okyay, R. (2020). Assembly line balancing problem with hierarchıcal worker assignment, positional constraints, task assignment restrictions and parallel workstations. International Journal of Industrial Engıneering-Theory Applications and Practice, 27(3), 345-377. Doi: https://doi.org/10.23055/ijietap.2020.27.3.5953
• Vilà, M. & Pereira, J. (2014). A branch-and-bound algorithm for assembly line worker assignment and balancing problems. Computers & Operations Research, 44, 105-114. Doi: https://doi.org/10.1016/j.cor.2013.10.016
• Yang, H., Lee, J. H., & Kim, H. J. (2021). Assembly line worker assignment and balancing problem with positional constraints. Proceedings of the International-Federation-of-Information-Processing-Working-Group-5.7 (IFIP WG 5.7) International Conference on Advances in Production Management Systems (APMS), 3-11, Nantes, France. Doi: https://doi.org/10.1007/978-3-030-85914-5_1
• Yilmaz, H. (2021). Modeling and solving assembly line worker assignment and balancing problem with sequence-dependent setup times. Soft Computing, 25(20), 12899–12914. Doi: https://doi.org/10.1007/s00500-021-06107-3
• Yilmaz, O. F. (2020) Robust optimization for U–shaped assembly line worker assignment and balancing problem with uncertain task times. Croatian Operational Research Review, 11(2), 229–239. Doi: https://doi.org/10.17535/crorr.2020.0018
• Zacharia, P. T. & Nearchou, A. C. (2016). A population-based algorithm for the biobjective assembly line worker assignment and balancing problem. Engineering Applications of Artificial Intelligence, 49, 1-9. Doi: https://doi.org/10.1016/j.engappai.2015.11.007
• Zacharia, P. T. & Nearchou, A. C. (2020). The fuzzy assembly line worker assignment and balancing problem. Cybernetics and Systems, 52(3), 221–243. Doi: https://doi.org/10.1080/01969722.2020.1840144
• Zhang, Z., Tang, Q., Han, D., & Li, Z. (2019). Enhanced migrating birds optimization algorithm for U-shaped assembly line balancing problems with workers assignment. Neural Computing & Applications, 31(11), 7501-7515. Doi: https://doi.org/10.1007/s00521-018-3596-9
• Zhang, Z., Tang, Q., Ruiz, R., & Zhang, L. (2020). Ergonomic risk and cycle time minimization for the U-shaped worker assignment assembly line balancing problem: A multi-objective approach. Computers & Operations Research, 118, 104905. Doi: https://doi.org/10.1016/j.cor.2020.104905