PARALEL İŞLEMCİLİ ESNEK AKIŞ ATÖLYESİ ÇİZELGELEME PROBLEMLERİ İÇİN STOKASTİK ÇÖZÜM YAKLAŞIMI

Yıl 2023, , 69 - 90, 10.08.2023

Mehmet Ertem , Mujgan Sagir Ozdemir

https://doi.org/10.46465/endustrimuhendisligi.1244776

Öz

Bu çalışmada sıra bağımlı hazırlık zamanlı k kademeli esnek akış atölyesi çizelgeleme problemi için önceden geliştirilmiş bir matematiksel model revize edilerek, sıra bağımlı hazırlık sürelerinin stokastik olma durumu incelenmiştir. Çalışmada bu anlamda üç matematiksel modele yer verilmektedir. M1 modeli söz konusu problem için daha önce geliştirilen matematiksel modeldir. M2 modeli, M1 modeline göre daha büyük problemleri, daha hızlı çözebilecek revize modeldir. M3 modeli ise M2’nin stokastik parametreleri dikkate alan halidir. Test problemlerinin çözülmesi sonucunda; M2 modelinin, çözebildiği problem boyutu ve çözüm süresi bakımından M1’e göre üstünlüğü, M3 modelinin ise stokastik parametreleri ele alarak tamamlanma zamanı bakımından daha iyi sonuçlar verdiği gösterilmiştir.

Anahtar Kelimeler

Paralel işlemcili esnek akış atölyesi çizelgeleme, Karma Tamsayılı model, Stokastik sıra bağımlı hazırlık süresi, Stokastik çizelgeleme, Hybrid Flow Shop Scheduling, Mixed Integer Programming Model, Stochastic sequence dependent set-up times, Stochastic Scheduling

Destekleyen Kurum

Eskişehir Osmangazi Üniversitesi

Proje Numarası

201915053

A STOCHASTIC SOLUTION APPROACH TO FLEXIBLE FLOWSHOP SCHEDULING PROBLEMS

Öz

In this study, a previously developed mathematical model for the k-stage flexible flow workshop scheduling problem with sequence-dependent setup time was revised and the stochasticity of sequence-dependent setup times was investigated. In this sense, three mathematical models are included in the study. The M1 model is the mathematical model previously developed for the problem in question. The M2 model is a revised model that can solve larger-size problems faster than the M1 model. The M3 model, on the other hand, is the version of M2 that takes stochastic parameters into account. As a result of solving test problems, it has been shown that the M2 model is superior to M1 in terms of the problem size and solution time it can solve, while the M3 model gives better results in terms of completion time by taking stochastic parameters.

Anahtar Kelimeler

Hybrid Flow Shop Scheduling, Mixed Integer Programming Model, Stochastic sequence dependent set-up times, Stochastic Scheduling

Proje Numarası

201915053

Kaynakça

• Allahverdi, A. (2015). The third comprehensive survey on scheduling problems with setup times/costs. European Journal of Operational Research, 246 (2), 345–378. Doi: https://doi.org/10.1016/j.ejor.2015.04.004
• Avalos-Rosales, O., Angel-Bello, F. ve Alvarez, A. (2015). Efficient metaheuristic algorithm and re-formulations for the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times. The International Journal of Advanced Manufacturing Technology, 76, 1705-1718. Doi: https://doi.org/10.1007/s00170-014-6390-6
• Behnamian, J. ve Fatemi Ghomi, S.M.T. (2011). Hybrid flowshop scheduling with machine and resource-dependent processing times. Applied Mathematical Modelling, 35, 1107-1123. Doi: https://doi.org/10.1016/j.apm.2010.07.057
• Brah, S. A. (1996). A comparative analysis of due date based job sequencing rules in a flow shop with multiple processors. Production Planning & Control, 7(4), 362-373. DOI: https://doi.org/10.1080/09537289608930364
• Brah, S. A. ve Wheeler, G. E. (1998). Comparison of scheduling rules in a flow shop with multiple processors: A simulation. Simulation, 71(5), 302-311. DOI: https://doi.org/10.1177/003754979807100501
• Dessouky, M. M., Dessouky, M. I. ve Verma, S. K. (1998). Flowshop scheduling with identical jobs and uniform parallel machines. European Journal of Operational Research, 109(3), 620-631. DOI: https://doi.org/10.1016/ S0377-2217(97)00194-X
• Dudek, R., Smith, M. ve Panwalkar, S. (1974). Use of a case study in sequencing-scheduling research. Omega, 2, 253–261. DOI: https://doi.org/10.1016/0305-0483(74)90094-2.
• Ebrahimi, M., Ghomi, M. F. ve Karimi, B. (2014), Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates. Applied Mathematical Modelling, 38(9–10), 2490–2504. DOI: https://doi.org/10.1016/j.apm.2013.10.061
• Engin, O., ÖZMETE, A., İPEK, S. ve KAROĞLU, Y. (2023). Çizelgeleme Problemlerinin Çözümünde Hibrit Biyocoğrafya Tabanlı Optimizasyon Algoritmasının Kullanımı. Harran Üniversitesi Mühendislik Dergisi, 1(8), 68-77. Doi: https://doi.org/10.46578/humder.1256671
• Ertem, M., Ozcelik, F. ve Sarac, T. (2021), Stokastik İlişkisiz Paralel Makine Çizelgeleme Problemi için bir Matematiksel Model, Avrupa Bilim ve Teknoloji Dergisi, 29, 278-283. DOI: https://doi.org/10.31590/ejosat.1017475
• Gholami, Z., Seyed M., Hakimifar, M., Nazemi, N. ve Jolai, F. (2017). Robust and Fuzzy Optimisation Models for a Flow Shop Scheduling Problem with Sequence Dependent Set Up Times: A real case study on a PCB assembly company. International Journal of Computer Integrated Manufacturing, 30, 552-563. DOI: https://doi.org/10.1080/0951192X.2016.1187293
• Gupta, J.N.D. (1988). Two-stage, hybrid flow shop scheduling problem. Journal of the Operational Research Society, 39, 359-364. DOI: https://doi.org/10.1057/jors.1988.63
• Janiak, A., Kozan, E., Lichtenstein, M. ve Oğuz, C. (2007). Metaheuristic approach to the hybrid flow shop scheduling problem with a cost-related criterion. International Journal of Production Economics, 105, 407-424. DOI: https://doi.org/10.1016/j.ijpe.2004.05.027
• Lee, C. ve Kim, Y.D. (2009). A branch-and-bound algorithm for a two-stage hybrid flowshop scheduling problem minimizing total tardiness. International Journal of Production Research, 42(22):4731– 4743. DOI: https://doi.org/10.1080/0020754041233127044
• Marichelvam, M.K., Prabaharan, T. ve Yang, X.S. (2014). Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan. Applied Soft Computing, 19, 93-101. DOI: https://doi.org/10.1016/ j.asoc.2014.02.005
• Morais, M.D., Godinho, M. ve Boiko, T.J.P. (2013). Hybrid flow shop scheduling problems involving setup considerations: a literature review and analysis. International Journal of Industrial Engineering Theory Applications and Practice, 20, 614-630.
• Ozsoydan, B. ve Sagir, M. (2021). Iterated greedy algorithms enhanced by hyper-heuristic-based learning for hybrid flexible flowshop scheduling problem with sequence dependent setup times: A case study at a manufacturing plant. Computers & Operations Research, 125(1), 105044. DOI: https://doi.org/10.1016/j.cor.2020.105044
• Pan, Q.K., Gao, L., Li, X. ve Gao, K. (2017). Effective metaheuristics for scheduling a hybrid flowshop with sequence-dependent setup times. Applied Mathematics and Computation, 303, 89-112. DOI: https://doi.org/10.1016/j.amc.2017.01.004
• Rashidi, E., Jahandar, M. ve Zandieh, M. (2010), An improved hybrid multi-objective parallel genetic algorithm for hybrid flow shop scheduling with unrelated parallel machines. The International Journal of Advanced Manufacturing Technology, 49, 1129–1139. DOI: https://doi.org/10.1007/ s00170-009-2475-z
• Ribas, I., Leisten, R. ve Framinan, J.M. (2010). Review and classification of hybrid flow shop scheduling problems from a production system and a solutions procedure perspective. Computers and Operations Research, 37, 1439-454. DOI: https://doi.org/10.1016/j.cor.2009.11.001
• Ruiz, R., Şerifoğlu, F.S. ve Urlings, T. (2009). Modeling realistic hybrid flexible flow shop scheduling problems. Computers & Operations Research, 35, 1151-1175. DOI: https://doi.org/10.1016/j.cor.2006.07.014
• Sağır, M. ve Okul, H. D. (2020). Restricted Enumeration And Machine Grouping Based Approach for Hybrid Flexible Flow Shop Scheduling Problems With Sequence-Dependent Setup Times. Journal of Industrial Engineering (Turkish Chamber of Mechanical Engineers), 31(3). DOI: https://doi.org/10.46465/ endustrimuhendisligi. 706010
• Yang, X.S. ve Deb, S. (2009). Cuckoo search via Lévy flights, NaBIC 2009: Proceedings of the World Congress on Nature & Biologically Inspired Computing, Coimbatore, 210-214.