MAKİNE VE KALIP BAKIMLARININ DAHİL EDİLDİĞİ ÜRETİM ÇİZELGELEME PROBLEMİ

Yıl 2025, Cilt: 36 Sayı: 2, 119 - 143, 31.08.2025

Büşra Tutumlu , Tuğba Saraç

Öz

Plastik enjeksiyon, seramik ve metal döküm dahil olmak üzere birçok üretim sürecinde kalıplar kullanılmaktadır ve belirli zamanlarda bu kalıplara bakım yapılması gerekmektedir. Üretim sürecinde aksamalar yaşanmaması için, işler çizelgelenirken, makine ve kalıp bakımları da dikkate alınmalıdır. Literatürde çoğunlukla sadece makine bakımları ele alınmaktadır. Oysaki bir makine bakımda iken o makinedeki kalıp başka bir makineye monte edilerek kullanılabilir veya bir kalıp bakımda ise makineye başka bir kalıp monte edilerek makine kullanılabilmektedir. Bu nedenle üretim çizelgesine hem makine hem de kalıp bakımlarının dahil edilmesi önemlidir. Bu çalışmada, makinelerin ve kalıpların planlı bakımlarının dahil edildiği üretim çizelgeleme problemi ele alınmıştır. Ele alınan problemde her iş belirli bir kalıp tipi ve belirli makinelerde gerçekleştirilmektedir. Hazırlık süreleri sıraya bağımlıdır ve hammadde değişimi gibi işlemler için geçiş süresi ve kalıp değişim süresi olmak üzere iki aşamadan oluşmaktadır. Planlı bakımlar, bir zaman penceresi içerisinde başlamalıdır. Ele alınan problemin çözümü için bir matematiksel model önerilmiştir. Planlı bakım başlama zamanlarının bir zaman penceresi içinde esnek olmasının katkısını gösterebilmek için önerilen matematiksel model bakım zamanlarının sabit alındığı ve bakımların çizelgeye sonradan dahil edildiği durumlarla kıyaslanmıştır.

Anahtar Kelimeler

Planlı bakım , Kalıp bakımları , Çizelgeleme problemi , Karma tamsayılı matematiksel model

Destekleyen Kurum

TÜBİTAK 2211-A

Teşekkür

Bu çalışmanın 1. Yazarı TÜBİTAK 2211-A Yurt İçi Doktora Burs Programı tarafından desteklenmektedir. Ancak yayın ile ilgili tüm sorumluluk yayının sahibine aittir. Yayının içeriğinin bilimsel anlamda TÜBİTAK tarafından onaylandığı anlamına gelmemektedir.

Kaynakça

• Agárdi, A., ve Nehéz, K. (2021). Parallel machine scheduling with Monte Carlo Tree Search. Acta Polytechnica, 61(2), 307-312. Doi: https://doi.org/10.14311/AP.2021.61.0307
• Al-Shayea, A. M., Saleh, M., Alatefi, M., ve Ghaleb, M. (2020). Scheduling two identical parallel machines subjected to release times, delivery times and unavailability constraints. Processes, 8(9), 1025. Doi: https://doi.org/10.3390/pr8091025
• Babaeimorad, S., Fatthi, P., ve Fazlollahtabar, H. (2021). A joint optimization model for production scheduling and preventive maintenance interval. International Journal of Engineering, 34(11), 2508-2516. Doi: https://doi.org/10.5829/ije.2021.34.11b.13
• Berrichi, A., ve Yalaoui, F. (2013). Efficient bi-objective ant colony approach to minimize total tardiness and system unavailability for a parallel machine scheduling problem. The International Journal of Advanced Manufacturing Technology, 68, 2295-2310. Doi: https://doi.org/10.1007/s00170-013-4841-0
• Chen, J. S. (2006). Optimization models for the machine scheduling problem with a single flexible maintenance activity. Engineering Optimization, 38(1), 53-71. Doi: https://doi.org/10.1080/03052150500270594
• Chen, L., Yang, W., Qiu, K., ve Dauzère-Pérès, S. (2023). A lexicographic optimization approach for a bi-objective parallel-machine scheduling problem minimizing total quality loss and total tardiness. Computers & Operations Research, 155, 106245. Doi: https://doi.org/10.1016/j.cor.2023.106245
• Chen, Y. Y., Huang, P. Y., Huang, C. J., Huang, S. Q., ve Chou, F. D. (2021). Makespan minimization for scheduling on two identical parallel machiens with flexible maintenance and nonresumable jobs. Journal of Industrial and Production Engineering, 38(4), 271-284. Doi: https://doi.org/10.1080/21681015.2021.1883131
• Chen, Y., Guan, Z., Wang, C., Chou, F., ve Yue, L. (2022). Bi-objective optimization of identical parallel machine scheduling with flexible maintenance and job release times. International Journal of Industrial Engineering Computations, 13(4), 457-472. Doi: https://doi.org/10.5267/j.ijiec.2022.8.003
• Chen, Y., Zhong, L., Shena, C., Mumt, J., ve Chou, F. (2023). Joint optimization of production and maintenance scheduling for unrelated parallel machine using hybrid discrete spider monkey optimization algorithm. International Journal of Industrial Engineering Computations, 14(3), 539-554. Doi: https://doi.org/10.5267/j.ijiec.2023.4.001
• Cheng, T. E., Hsu, C. J., ve Yang, D. L. (2011). Unrelated parallel-machine scheduling with deteriorating maintenance activities. Computers & Industrial Engineering, 60(4), 602-605. Doi: https://doi.org/10.1016/j.cie.2010.12.017
• Fu, B., Huo, Y., ve Zhao, H. (2011). Approximation schemes for parallel machine scheduling with availability constraints. Discrete Applied Mathematics, 159(15), 1555-1565. Doi: https://doi.org/10.1016/ j.dam.2011.06.007
• Furugi, A. (2021). A tabu search algorithm for the unrelated parallel machine scheduling problem with machine availability constraint and sequence-dependent setup time. Journal of the Faculty of Engineering and Architecture of Gazi University, 36(3). Doi: https://doi.org/10.17341/gazimmfd.806641
• Geurtsen, M., Didden, J. B., Adan, J., Atan, Z., ve Adan, I. J. B. F. (2023). Production, maintenance and resource scheduling: A review. European Journal of Operational Research, 305(2), 501-529. Doi: https://doi.org/10.1016/ j.ejor.2022.03.045
• He, J., Li, Q., ve Xu, D. (2016). Scheduling two parallel machines with machine-dependent availabilities. Computers & Operations Research, 72, 31-42. Doi: https://doi.org/10.1016/j.cor.2016.01.021
• He, X., Wang, Z., Li, Y., Khazhina, S., Du, W., Wang, J., ve Wang, W. (2022). Joint decision-making of parallel machine scheduling restricted in job-machine release time and preventive maintenance with remaining useful life constraints. Reliability Engineering & System Safety, 222, 108429. Doi: https://doi.org/10.1016/j.ress.2022.108429
• Hu, C., Lu, S., Kong, M., Liu, X., ve Pardalos, P. M. (2023). Parallel machine scheduling with linearly increasing energy consumption cost. Annals of Mathematics and Artificial Intelligence, 91(2), 239-258. Doi: https://doi.org/10.1007/s10472-022-09810-5
• Krim, H., Zufferey, N., Potvin, J. Y., Benmansour, R., ve Duvivier, D. (2022). Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times. Journal of Scheduling, 1-17. Doi: https://doi.org/10.1007/s10951-021-00711-9
• Kurt, A., ve Çetinkaya, F. C. (2024). Unrelated parallel machine scheduling under machine availability and eligibility constraints to minimize the makespan of non-resumable jobs. International Journal of Industrial Engineering and Management, in-press. Doi: https://doi.org/10.24867/IJIEM-2024-1-345
• Lee, D., Lee, D., ve Kim, K. (2023). Self-growth learning-based machine scheduler to minimize setup time and tardiness in OLED display semiconductor manufacturing. Applied Soft Computing, 145, 110600. Doi: https://doi.org/10.1016/j.asoc.2023.110600
• Lee, J. Y., ve Kim, Y. D. (2015). A branch and bound algorithm to minimize total tardiness of jobs in a two identical-parallel-machine scheduling problem with a machine availability constraint. Journal of the Operational Research Society, 66(9), 1542-1554. Doi: https://doi.org/10.1057/jors.2014.122
• Lei, D., ve He, S. (2022). An adaptive artificial bee colony for unrelated parallel machine scheduling with additional resource and maintenance. Expert Systems with Applications, 205, 117577. Doi: https://doi.org/10.3390/ sym14071380
• Lei, D., ve Liu, M. (2020). An artificial bee colony with division for distributed unrelated parallel machine scheduling with preventive maintenance. Computers & Industrial Engineering, 141, 106320. Doi: https://doi.org/10.1016/j.cie.2020.106320
• Lei, D., ve Yang, H. (2022). Scheduling unrelated parallel machines with preventive maintenance and setup time: Multi-sub-colony artificial bee colony. Applied Soft Computing, 125, 109154. Doi: https://doi.org/10.1016/j.asoc.2022.109154
• Lei, D., ve Yi, T. (2021). A novel shuffled frog-leaping algorithm for unrelated parallel machine scheduling with deteriorating maintenance and setup time. Symmetry, 13(9), 1574. Doi: https://doi.org/10.3390/sym13091574
• Li, G., Liu, M., Sethi, S. P., ve Xu, D. (2017). Parallel-machine scheduling with machine-dependent maintenance periodic recycles. International Journal of Production Economics, 186, 1-7. Doi: https://doi.org/10.1016/j.ijpe.2017.01.014
• Li, M., Xiong, H., ve Lei, D. (2022). An artificial bee colony with adaptive competition for the unrelated parallel machine scheduling problem with additional resources and maintenance. Symmetry, 14(7), 1380. Doi: https://doi.org/10.3390/sym14071380
• Lu, S., Liu, X., Pei, J., Thai, M. T., ve Pardalos, P. M. (2018). A hybrid ABC-TS algorithm for the unrelated parallel-batching machines scheduling problem with deteriorating jobs and maintenance activity. Applied Soft Computing, 66, 168-182. Doi: https://doi.org/10.1016/j.asoc.2018.02.018
• Mellouli, R., Kacem, I., Sadfi, C., ve Chu, C. (2013). Lagrangian relaxation and column generation-based lower bounds for the Pm, hj1‖∑ wiCi scheduling problem. Applied Mathematics and Computation, 219(22), 10783-10805. Doi: https://doi.org/10.1016/j.amc.2013.05.004
• Moradi, E., ve Zandieh, M. (2010). Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm. The International Journal of Advanced Manufacturing Technology, 51, 829-840. Doi: https://doi.org/10.1007/s00170-010-2666-7
• Saraç, T., ve Özçelik, F. (2023). Bozulma etkili ve tek bakım ekipli bakım çizelgeleme problemi için bir matematiksel model. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, 31(3), 882-892. Doi: https://doi.org/10.31796/ogummf.1247165
• Santoro, M. C., ve Junqueira, L. (2023). Unrelated parallel machine scheduling models with machine availability and eligibility constraints. Computers & Industrial Engineering, 179, 109219. Doi: https://doi.org/10.1016/j.cie.2023.109219
• Sharifi, M., Ghaleb, M., ve Taghipour, S. (2023). Joint parallel-machine scheduling and maintenance planning optimisation with deterioration, unexpected breakdowns, and condition-based maintenance. International Journal of Systems Science: Operations & Logistics, 10(1), 2200888. Doi: https://doi.org/10.1080/23302674.2023.2200888
• Sheen, G. J., ve Liao, L. W. (2007). Scheduling machine-dependent jobs to minimize lateness on machines with identical speed under availability constraints. Computers & Operations Research, 34(8), 2266-2278. Doi: https://doi.org/10.1016/j.cor.2005.09.002
• Shen, J., ve Zhu, Y. (2019). A parallel-machine scheduling with periodic constraints under uncertainty. Advances in Mechanical Engineering, 11(12), 1687814019892430. Doi: https://doi.org/10.1177/1687814019892430
• Su, L. H., Hsiao, M. C., Zhou, H., ve Chou, F. D. (2018). Minimizing the number of tardy jobs on unrelated parallel machines with dirt consideration. Journal of Industrial and Production Engineering, 35(6), 383-393. Doi: https://doi.org/10.1080/21681015.2018.1508082
• Sun, L., Zhang, X. H., ve Ning, L. (2021). Results of parallel-machine scheduling model with maintenance activity considering time-dependent deterioration, delivery times, and resource allocation. Mathematical Problems in Engineering, 2021, 1-14. Doi: https://doi.org/10.1155/2021/8826345
• Tan, Z., Chen, Y., ve Zhang, A. (2011). Parallel machines scheduling with machine maintenance for minsum criteria. European Journal of Operational Research, 212(2), 287-292. Doi: https://doi.org/10.1016/j.ejor.2011.02.006
• Wang, L. Y., Huang, X., Ji, P., ve Feng, E. M. (2014). Unrelated parallel-machine scheduling with deteriorating maintenance activities to minimize the total completion time. Optimization letters, 8, 129-134. Doi: https://doi.org/10.1007/s11590-012-0472-x
• Wang, M., ve Pan, G. (2019). A novel imperialist competitive algorithm with multi-elite individuals guidance for multi-object unrelated parallel machine scheduling problem. IEEE Access, 7, 121223-121235. Doi: https://doi.org/10.1109/ACCESS.2019.2937747
• Wang, S., ve Liu, M. (2015). Multi-objective optimization of parallel machine scheduling integrated with multi-resources preventive maintenance planning. Journal of Manufacturing Systems, 37, 182-192. Doi: https://doi.org/10.1016/j.jmsy.2015.07.002
• Xu, D., Sun, K., ve Li, H. (2008). Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan. Computers & operations research, 35(4), 1344-1349. Doi: https://doi.org/10.1016/ j.cor.2006.08.015
• Yang, D. L., Cheng, T. C. E., Yang, S. J., ve Hsu, C. J. (2012). Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities. Computers & Operations Research, 39(7), 1458-1464. Doi: https://doi.org/10.1016/j.cor.2011.08.017
• Yang, S. J. (2011). Parallel machines scheduling with simultaneous considerations of position-dependent deterioration effects and maintenance activities. Journal of Industrial and Production Engineering, 28(4), 270-280. Doi: https://doi.org/10.1080/10170669.2011.573006
• Yin, Y., Wang, Y., Cheng, T. C. E., Liu, W., ve Li, J. (2017). Parallel-machine scheduling of deteriorating jobs with potential machine disruptions. Omega, 69, 17-28. Doi: https://doi.org/10.1016/ j.omega.2016.07.006 Yoo, J., ve Lee, I. S. (2016). Parallel machine scheduling with maintenance activities. Computers & Industrial Engineering, 101, 361-371. Doi: https://doi.org/10.1016/j.cie.2016.09.020
• Zhang, X., ve Chen, L. (2022). A general variable neighborhood search algorithm for a parallel-machine scheduling problem considering machine health conditions and preventive maintenance. Computers & Operations Research, 143, 105738. Doi: https://doi.org/10.1016/j.cor.2022.105738
• Zhang, X., Liu, S. C., Lin, W. C., ve Wu, C. C. (2020). Parallel-machine scheduling with linear deteriorating jobs and preventive maintenance activities under a potential machine disruption. Computers & Industrial Engineering, 145, 106482. Doi: https://doi.org/10.1016/j.cie.2020.106482