Akış Atölyesi Çizelgeleme Probleminin Sistematik Literatür Taraması ve Bütünsel Bir Çerçevesi

Yıl 2023, Cilt: 57 Sayı: 3, 577 - 594, 31.07.2023

Hatice Vurğun Koç , Ertan Güner

https://doi.org/10.51551/verimlilik.1207259

Öz

Amaç: Bu çalışmanın amacı, akış atölyesi çizelgeleme problemine dair farklı model türlerini oluşturmak için izlenen matematiksel programlama yöntemlerini, bunları çözme tekniklerini, bu problemleri çözmek için kullanılan yazılımları ve gelecek çalışmalara ilişkin önerileri sunmaktır.
Yöntem: Literatür araştırmasında 4 aşamalı yapılandırılmış bir metodoloji kullanılmıştır. Akış atölyesi çizelgeleme problemini karakterize eden en önemli hususları özetleyen bütünsel bir çerçeve önerilmiştir. 2000’den 2022 başlarına kadar toplam 73 makale gözden geçirilmiştir. Tüm makaleler önerilen bütünsel çerçeveye göre değerlendirilmiş ve kodlanmıştır.
Bulgular: Modelleme yaklaşımı belirtilen makalelerin %67’sinde karmaşık tam sayılı doğrusal programlama yaklaşımı benimsenmiştir. Referansların çoğu problem için çözüm yöntemlerinden birini (kesin çözüm algoritması, sezgisel algoritma ve metasezgisel algoritma) önermiştir. Programlama dili olarak C++ ve MATLAB ve çözücü olarak CPLEX’in ön planda olduğu görülmüştür.
Özgünlük: Çoğu yazarın burada önerilen çerçeveyi (modelleme ve çözüm yaklaşımı, programlama dili, çözüm aracı, amaç fonksiyonları) dikkate almadığı belirlenmiştir. Bu nedenle, bu inceleme akış atölyesi çizelgeleme problemlerinin temel unsurlarına genel bir bakış sağlamayı amaçlamaktadır.

Anahtar Kelimeler

Çizelgeleme, Akış Atölyesi, Permütasyon Akış Atölyesi

Destekleyen Kurum

Gazi Üniversitesi

A Systematic Literature Review and An Integrated Framework of the Flowshop Scheduling Problem

Öz

Purpose: The aim of this study is to present the mathematical programming methods followed to create different types of models for the flowshop scheduling problem, the techniques for solving them, and the software used to solve these problems.
Methodology: A 4-stage structured methodology was used in the literature search. A holistic framework is proposed that summarizes the most important aspects characterizing the flowshop scheduling problem. A total of 73 articles were reviewed from 2000 to early 2022. All articles were evaluated and coded according to the proposed holistic framework.
Findings: The MILP approach was adopted in 67% of the articles whose modeling approach was specified. Most of the references suggested solution methods (optimistic, heuristic and metaheuristic) for the problem. It has been seen that C++ and MATLAB as a programming language and CPLEX as a solver are at the forefront.
Originality: It has been determined that most authors do not consider the framework (modeling and solution approach, programming language, solution tool, model goals) proposed here. Therefore, this review aims to provide an overview of the key elements of flowshop scheduling problems.

Anahtar Kelimeler

Scheduling, Flowshop, Permutation Flowshop

Kaynakça

• Ahmadizar, F. (2012). “A New Ant Colony Algorithm for Makespan Minimization in Permutation Flowshops’’, Computers&Industrial Engineering, 63, 355-361, DOI: 10.1016/j.cie.2012.03.015.
• Ahmadizar, F. ve Barzinpour, F. (2012). “A Hybrid Algorithm to Minimize Makespan for the Permutation Flow Shop Scheduling Problem’’, International Journal of Computational Intelligence Systems, 3, 853-861.
• Akhshabi, M., Haddadnia, J. ve Akhshabi, M. (2012). “Solving Flow Shop Scheduling Problem Using a Parallel Genetic Algorithm’’, Procedia Technology, 1, 351-355, DOI: 10.1016/j.protcy.2012.02.073.
• Allahverdi, A. (1996). “Two-Machine Proportionate Flowshop Scheduling with Breakdowns to Minimize Maximum Lateness’’, Computers & Operations Research, 23, 909-916, DOI:10.1016/0305-0548(96)00012-3.
• Allahverdi, A., Pesch, E., Pinedo, M. ve Werner, F. (2018). “Scheduling in Manufacturing Systems: New Trends and Perspectives’’, International Journal of Production Research, 56, 6333-6335. DOI: 10.1080/00207543.2018.1504252.
• Anjana, V., Sridhanan, R. ve Ram Kumar, P.N. (2020). “Metaheuristics for Solving a Multi-Objective Flow Shop Scheduling Problem with Sequence-Dependent Setup Times’’, Journal of Scheduling, 23, 49-69.
• Arish, A., Young, P. ve El Baradie, M. (2002). “Flow Shop Scheduling Problem: a Computational Study’’, Sixth International Conference on Production Engineering and Design for Development, Cairo, Egypt, 543-557.
• Azad, T. ve Sarja, A.A. (2021). “A Comparative Analysis of Heuristic Metaheuristic and Exact Approach to Minimize Make Span of Permutation Flow Shop Scheduling’’, American Journal of Industrial Engineering, 8, 1-8. DOI: 10.12691/ajie-8-1-1.
• Bacha, S.Z.A., Belahdji, M.W., Benatchba, K. ve Tayeb, F.B. (2019). “A New Hyper-Heuristic to Generate Effective İnstance GA for the Permutation Flow Shop Problem’’, Procedia Computer Science, 159, 1365-1374, DOI: 10.1016/j.procs.2019.09.307.
• Balıkesir Üniversitesi Endüstri Mühendisliği Bölümü, (2020). “EMM4129 Çizelgeleme Ders Notları’’, http://ikucukkoc.baun.edu.tr/lectures/EMM4129/EMM4129-Cizelgeleme-BirlesikDersNotlari.pdf, (Erişim Tarihi: 11.03.2023).
• Bank, M., Ghomi, S.M.T.F., Jolai, F. ve Behnamian, J. (2012). “Applications of Particle Swarm Optimization and Simulated Annealing Algorithms in Flowshop Scheduling Problem Under Linear Deterioration’’, Advancesing Engineering Software, 47, 1-6, DOI: 10.1016/j.advengsoft.2011.12.001.
• Baskar, A., Anthony, X.M. ve Nithyanandan, N. (2018). “Analysis of a Few Simple Heuristics for the Permutation Flowshop Scheduling Problem for any Batch Processing Industry’’, Material Today: Proceedings, 5, 11762-11770.
• Başar, R. ve Engin, O. (2022). “Beklemesiz Akış Tipi Çizelgeleme Problemlerinin Analizi ve Hibrit Dağınık Arama Yöntemi ile Çözümü’’, Journal of Advanced Research in Natural and Applied Sciences, 8(2), 293-308, DOI: 10.28979/jarnas.936151.
• Belabid, J. Aqil, S. ve Allali, K. (2020). “Solving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Time’’, Journal of Applied Mathematics, DOI: 10.1155/2020/7132469.
• Benavides, A.J., Ritt, M. ve Miralles, C. (2014). “Flowshop Scheduling with Heterogeneous Workers’’, European Journal of Operational Research, 237, 713-720, DOI: 10.1016/j.ejor.2014.02.012.
• Bootaki, B. ve Paydar, M.M. (2018). “On the n-Job, m-Machine Permutation Flow Shop Scheduling Problems with Makespan Criterion and Rework’’, Scientia Iranica, 25(3), 1688-1700, DOI: 10.24200/sci.2017.4443.
• Chang, P., Chen, M., Tiwari, M.K. ve Iquebal, A.S. (2013). “A Block-Based Evolutionary Algorithm for Flow-Shop Scheduling Problem’’, Applied Soft Computing, 13, 4536-4547, DOI: 10.1016/j.asoc.2013.07.018.
• Chen, C., Tzeng, Y. ve Chen, C. (2015). “A New Heuristic Based on Local Best Solution for Permutation Flow Shop Scheduling’’, Applied Soft Computing, 29, 75-81, DOI: 10.1016/j.asoc.2014.12.011.
• Cheng, M., Tadikamalla, P.R., Shang, J. ve Zhang, B. (2015). “Two-Machine Flow Shop Scheduling with Deteriorating Jobs: Minimizing the Weighted Sum of Makespan and Total Completion Time’’, Journal of the Operational Research Society, 66, 709-719.
• Chiang, T., Cheng, H. ve Fu, L. (2011). “NNMA: an Effective Memetic Algorithm for Solving Multiobjective Permutation Flow Shop Scheduling Problems’’, Expert Systems with Applications, 38, 5986-5999, DOI: 10.1016/j.eswa.2010.11.022.
• Dağ, S. (2013). “Akış Tipi Çizelgeleme Üzerine Bir Uygulama’’, Alphanumeric Journal, 1(1), 47-56.
• Dasgupta, P. ve Das, S. (2015). “A Discrete İnter-Species Cuckoo Search for Flowshop Scheduling Problems’’, Computers&Operations Research, 60, 111-120, DOI: 10.1016/j.cor.2015.01.005.
• Deng, G. ve Gu, X. (2012). “A Hybrid Discrete Differential Evolution Algorithm for the No-Idle Permutationflow Shop Scheduling Problem with Makespan Criterion’’, Computers & Operations Research, 39, 2152-2160. DOI: 10.1016/j.cor.2011.10.024.
• Dong, X., Nowak, M., Chen, P. ve Lin, Y. (2015). “Self-Adaptive Perturbation and Multi-Neighborhood Search for Iterated Local Search on the Permutation Flow Shop Problem’’, Computers&Industrial Engineering, 87, 176-185, DOI: 10.1016/j.cie.2015.04.030.
• Doush, I.A., Al-Betar, M.A., Awadallah, M.A., Santos, E., Hammouri, A.I., Mafarjeh, M. ve AlMeraj, Z.(2019). “Flowshop Scheduling with Blocking Using Modified Harmony Search Algorithm with Neighboring Heuristics Methods’’, Applied Soft Computing Journal, 85, 105861, DOI: 10.1016/j.asoc.2019.105861.
• Dubois-Lacoste, J., Lopez-Ibanez, M. ve Stützle, T. (2011). “A Hybrid TP+PLS Algorithm for Bi-Objective Flow-Shop Scheduling Problems’’, Computers&Operations Research, 38, 1219-1236, DOI: 10.1016/j.cor.2010.10.008.
• Esmaeilbeigi, R., Charkhgard, P. ve Charkhgard, H. (2016). “Order Acceptance and Scheduling Problems in Two-Machine Flowshops: New Mixed İnteger Programming Formulations’’, European Journal of Operational Research, 251, 419-431, DOI: 10.1016/j.ejor.2015.11.036.
• Etiler, O., Toklu, B., Atak, M. ve Wilson, J. (2017). “A Genetic Algorithm for Flow Shop Scheduling Problem’’, Journal of the Operational Research Society, 55, 830-835, DOI: 10.1057/palgrave.jors.2601766.
• Gao, K-Z., Pan, Q-K. ve Li, J-Q. (2011). “Discrete Harmony Search Algorithm for the No-Wait Flow Shop Scheduling Problem with Total Flow Time Criterion’’, The International Journal of Advanced Manufacturing Technology, 56, 683-692.
• Geiger, M.J. (2011). “Decision Support for Multi-Objective Flow Shop Scheduling by the Pareto İterated Local Search Methodology’’, Computers&Industrial Engineering, 61, 805-812, DOI: 10.1016/j.cie.2011.05.013.
• Gemba Danışmanlık, (2023). “6 Sigma Danışmanlığı’’, https://gembadanismanlik.com/6-sigma-danismanligi/, (Erişim Tarihi: 11.03.2023).
• Gmys, J., Mezmaz, M., Melab, N. ve Tuyttens, D. (2020). “A Computationally Efficient Branch-and-Bound Algorithm for the Permutation Flow-Shop Scheduling Problem’’, European Journal of Operational Research, 284, 814-833. DOI: 10.1016/j.ejor.2020.01.039.
• Goli, A., Tirkolaee, E.B. ve Saltani, M. (2019). “A Robust Just In Time Flow Shop Scheduling Problem with Outsourcing Option on Subcontractors’’, Production & Manufacturing Research, 7, 294-315, DOI: 10.1080/21693277.2019.1620651.
• Goyal, B. ve Kaur, S. (2020). “Minimizing Waiting Time of Jobs in Flow-Shop Scheduling: a Heuristic Approach’’, Materials Today: Proceedings, DOI: 10.1016/j.matpr.2020.09.797.
• Grabowski, J. ve Wodecki, M. (2004). “A Very Fast Tabu Search Algorithm for the Permutation Flow Shop Problem with Makespan Criterion’’, Computers&Operations Research, 31, 1891-1909, DOI:10.1016/S0305-0548(03)00145-X.
• Guanlong, D., Zhenhao, X. ve Xingsheng, G. (2012). ‘’A Discrete Artificial Bee Colony Algorithm Forminimizing the Total Flow Time in the Blocking Flow Shop Scheduling’’, Chinese Journal of Chemical Engineering, 20 (6), 1067-1073.
• Guzman, E., Andres, B. ve Poler, R. (2022). “Models and Algorithms for Production Planning, Scheduling and Sequencing Problems: a Holistic Framework and a Systematic Review’’, Journal of Industrial Information Integration, DOI: 10.1016/j.jii.2021.100287.
• Harjunkoski, I., Maravelias, C.T., Bongers, P., Castro, P.M., Engell, S., Grossmann, I.E., Hooker, J., Mendez,C., Sand, G. ve Wassick, J. (2014). “Scope for İndustrial Applications of Production Scheduling Models and Solution Methods’’, Computers and Chemical Engineering, 62, 161-193, DOI: 10.1016/j.compchemeng.2013.12.001.
• Hwang, F.J., Kovalyov, M.Y. ve Lin, B.M.T. (2012). “Total Completion Time Minimization in Two-Machine Flowshop Scheduling Problems with a Fixed Job Sequence’’, Discrete Optimization, 9, 29-39, DOI: 10.1016/j.disopt.2011.11.001.
• Kalczynski, P.J. ve Kamburowski, J. (2008). “An Improved NEH Heuristic to Minimize Makespan in Permutation Flowshops’’, Computers&Operations Research, 35, 3001-3008, DOI: 10.1016/j.cor.2007.01.020.
• Kalir, A.A. ve Sarin, S.C. (2000). “Evaluation of the Potential Benefits of Lot Streaming in Flow-Shop Systems’’, International Journal of Production Economics, 66, 131-142, DOI: 10.1016/S0925-5273(99)00115-2.
• Khatami, M., Salehipour, A. ve Hwang, F.J. (2019). “Makespan Minimization for the M-Machine Ordered Flowshop Scheduling Problem’’, Computers and Operations Research, 111, 400-414, DOI: 10.1016/j.cor.2019.06.012.
• Kuo, I., Horng, S., Kao, T., Lin, T., Lee, C., Terano, T. ve Pan, Y. (2009). “An Efficient Flow-Shopscheduling Algorithm Based on a Hybrid Particle Swarm Optimization Model’’, Expert Systems with Applications, 36, 7027-7032, DOI: 10.1016/j.eswa.2008.08.054.
• Laha, D. ve Sarin, S.C. (2009). “A Heuristic to Minimize Total Flow Time in Permutation Flowshop’’, Omega, 37, 734-739, DOI: 10.1016/j.omega.2008.05.002.
• Lei, D. ve Wang, T. (2011). “An Effective Neighborhood Search Algorithm for Scheduling a Flow Shop of Batch Processing Machines’’, Computers&Industrial Engineering, 61, 739-743, DOI: 10.1016/j.cie.2011.05.005.
• Li, G., Li N., Sambandam, N., Sethi, S.P. ve Zhang, F. (2018). ‘’Flow Shop Scheduling with Jobs Arriving at Different Times’’, International Journal of Production Economics, 206, 250-260, DOI: 10.1016/j.ijpe.2018.10.010.
• Li, X. ve Yin, M. (2012). “A Discrete Artificial Bee Colony Algorithmwith Composite Mutation Strategies for Permutation Flowshop Scheduling Problem’’, Scientia Iranica, 19(6), 1921-1935, DOI: 10.1016/j.scient.2012.10.034.
• Li, X., Wang, Q. ve Wu, C. (2009). “Efficient Composite Heuristics for Total Flowtime Minimization in Permutation Flowshops’’, Omega, 37,155-164, DOI: 10.1016/j.omega.2006.11.003.
• Lian, Z., Gu, X. ve Jiao, B. (2008). “A Novel Particle Swarm Optimization Algorithm for Permutation Flow-Shop Scheduling to Minimize Makespan’’, Chaos, Solutions and Fractals, 35, 851-861, DOI: 10.1016/j.chaos.2006.05.082.
• Lin, Q., Gao, L., Li, X. ve Zhang, C. (2015). “A Hybrid Backtracking Search Algorithm for Permutation Flow-Shop Scheduling Problem’’, Computers&Industrial Engineering, 85, 437-446, DOI: 10.1016/j.cie.2015.04.009.
• Liu, X. ve Chung, T-P. (2017). “A Modified Immunoglobulin-Based Artificial Immune System Algorithm for Solving the Permutation Flow Shop Scheduling Problem’’, Journal of Industrial and Production Engineering, 34, 542-550, DOI:10.1080/21681015.2017.1383313.
• Liu,Y.,Yin, M. ve Gu, W. (2014). “An Effective Differential Evolution Algorithm for Permutation Flowshop Scheduling Problem’’, Applied Mathematics and Computation, 248, 143-159, DOI: 10.1016/j.amc.2014.09.010.
• Marichelvam, M.K., Tosun, Ö. ve Geetha, M. (2017). “Hybrid Monkey Search Algorithm for Flow Shop Scheduling Problem Under Makespan and Total Flowtime’’, Applied Soft Computing, 55,82-92, DOI: 10.1016/j.asoc.2017.02.003.
• Martin, C.H. (2009). “A Hybrid Genetic Algorithm/Mathematical Programming Approach to the Multi-Family Flowshop Scheduling Problem with Lot Streaming’’, Omega, 37, 126-137, DOI: 10.1016/j.omega.2006.11.002.
• Meng, T., Pan, Q., Li, J. ve Sang, H. (2018). “An İmproved Migrating Birds Optimization for an Integrated Lot-Streaming Flow Shop Scheduling Problem’’, Swarm and Evolutionary Computation, 38, 64-78. DOI: 10.1016/j.swevo.2017.06.003.
• Miyata, H.H. ve Nagano, M.S. (2019). “The Blocking Flow Shop Scheduling Problem: a Comperensive and Conceptual Review’’, Experts Systems With Applications, 137, 130-156, DOI: 10.1016/j.eswa.2019.06.069.
• Moslehi, G. ve Khorasanian, D. (2014). “A Hybrid Variable Neighborhood Search Algorithm for Solving the Limited-Buffer Permutation Flowshop Scheduling Problem with the Makespan Criterion’’, Computers&Operations Research, 52, 260-268. DOI: 10.1016/j.cor.2013.09.014.
• Moslehi, G. ve Khorasanian, D. (2013). “Optimizing Blocking Flow Shop Scheduling Problem with Total Completion Time Criterion’’, Computers&Operations Research, 40, 1874-1883. DOI: 10.1016/j.cor.2013.02.003.
• Pan, Q-K. ve Ruiz, R. (2012). “An Estimation of Distribution Algorithm for Lot-Streaming Flow Shop Problems with Setup Times’’, Omega, 40, 166-180, DOI: 10.1016/j.omega.2011.05.002.
• Pan, Q-K., Tasgetiren, M.F., Suganthan, P.N. ve Chua, T.J. (2011). ‘’A Discrete Artificial Bee Colony Algorithm for the Lot-Streaming Flow Shop Scheduling Problem’’, Information Sciences, 181, 2455-2468, DOI: 10.1016/j.ins.2009.12.025.
• Pan, Q., Wang, L. ve Gao, L. (2011). “A Chaotic Harmony Search Algorithm for the Flow Shop Scheduling Problem with Limited Buffers’’, Applied Soft Computing, 11, 5270-5280, DOI: 10.1016/j.asoc.2011.05.033.
• Pan, Q-K, Wang, L. ve Zhao, B-H. (2008). “An İmproved İterated Greedy Algorithm for the No-Wait Flow Shop Scheduling Problem with Makespan Criterion’’, The International Journal of Advanced Manufacturing Technology, 38, 778-786.
• Puka, R., Duda, J., Stawowy, A. ve Skalna, I. (2021). “N-NEH+ Algorithm for Solving Permutation Flowshop Problems’’, Computers and Operations Research, 132,105296, DOI: 10.1016/j.cor.2021.105296.
• Qian, B., Wang, L., Huang, D.X. ve Wang, X. (2008). “An Effective Hybrid DE-Based Algorithm for Flow Shop Scheduling with Limited Buffers’’, International Journal of Production Research, 47, 1-24. DOI: 10.1080/00207540701528750.
• Raguram, K.S. ve Jayanthi, G. (2021). “Implementation of Heijunka for Improving Performance Indicators: a Process Sector Case Study’’, Gorteria Journal, 34, 20-28.
• Rahman, H.F., Sarker, R. ve Essam, D. (2015). “A Genetic Algorithm for Permutation Flowshop Scheduling Under Make to Stock Production System’’, Computers & Industrial Engineering, 90, 12-24, DOI: 10.1016/j.cie.2015.08.006.
• Ramesh, C., Kamalakannan, R., Karthik, R., Pavin, C. ve Dhivaharan, S. (2021). “A Lot Streaming Based Flowshop Scheduling Problem Using Simulated Annealing Algorithm’’, Materials Today: Proceedings, 37, 241-244, DOI: 10.1016/j.matpr.2020.05.108.
• Ribas, I., Companys, R. ve Tort-Martorell, X. (2010). “Comparing Three-Step Heuristics for the Permutation Flow Shop Problem’’, Computers & Operations Research, 37, 2062-2070, DOI: 10.1016/j.cor.2010.02.006.
• Ribas, I. ve Companys, R. (2015). “Efficient Heuristic Algorithms for the Blocking Flowshop Scheduling Problem with Total Flowtime Minimization’’, Computers&Industrial Engineering, 87, 30-39, DOI: 10.1016/j.cie.2015.04.013.
• Sadaqa, M. ve Moraga, R.J. (2015). “Scheduling Blocking Flowshops Using Metaraps’’, Procedia Computer Science, 61, 533-538, DOI: 10.1016/j.procs.2015.09.211.
• Samarghandi, H. ve Behroozi, M. (2016). “On the Exact Solution of the No-Wait Flow Shop Problem with Due Date Constraints’’, Computers & Operations Research, 81, 141-159, DOI: 10.1016/j.cor.2016.12.013.
• Saraçoğlu, İ. ve Süer, G.A. (2018). “Multi-Objective Fuzzy Flowshop Scheduling Model in a Manufacturing Company’’, Procedia Manufacturing, 17, 214-221, DOI: 10.1016/j.promfg.2018.10.039.
• Schaller, J. ve Valente, J.M.S. (2020). “Minimizing Total Earliness and Tardiness in a Nowait Flow Shop’’, International Journal of Production Economics, 224, 107542, DOI: 10.1016/j.ijpe.2019.107542.
• Shao, W. ve Pi, D. (2016). “A Self-Guided Differential Evolution with Neighborhood Search for Permutation Flowshop Scheduling’’, Expert Systems with Applications, 51, 161-176, DOI: 10.1016/j.eswa.2015.12.001.
• Suliman, S.M.A. (2000). “A Two-Phase Heuristic Approach to the Permutation Flow-Shop Scheduling Problem’’, International Journal of Production Economics, 64,143-152.
• Svancara, J. ve Kralova, Z. (2012). “High-Mix Low-Volume Flow Shop Manufacturing System Scheduling’’, Proceedings of the 14th IFAC Symposium on Information Control Problems in Manufacturing, Romania.
• Tang, H-C. (2013). “A New Lower Bounding Rule for Permutation Flow Shop Scheduling’’, Journal of Information and Optimization Sciences, 22, 249-257. DOI:10.1080/02522667.2001.10699488.
• Tajbakhsh, Z., Fattahi, P. ve Behnamian, J. (2017). “Multi Objective Assembly Permutation Flow Shop Scheduling Problem: a Mathematical Model and a Meta-Heuristic Algorithm’’, Journal of the Operational Research Society, 65, 1580-1592, DOI:10.1057/jors.2013.105.
• Tomazella, C.P. ve Nagano, M.S. (2020). ‘’A Comprehensive Review of Branch-and-Bound Algorithms: Guidelines and Directions for Further Research on the Flowshop Scheduling Problem’’, Expert Systems with Applications, 158, 113556, DOI: 10.1016/j.eswa.2020.113556.
• Tseng, C-T. ve Liao, C-J. (2008). “A Discrete Particle Swarm Optimization for Lot-Streaming Flowshop Scheduling Problem’’, European Journal of Operational Research, 191, 360-373, DOI: 10.1016/j.ejor.2007.08.030.
• Umam, M.S., Mustafid, M. ve Suryono, S. (2021). “A Hybrid Genetic Algorithm and Tabu Search Forminimizing Makespan in Flow Shop Scheduling Problem’’, Journal of King Saud University-Computer and Information Sciences, DOI: 10.1016/j.jksuci.2021.08.025.
• Varmazyar, M. ve Salmasi, N. (2011). “Sequence-Dependent Flow Shop Scheduling Problem Minimising the Number of Tardy Jobs’’, International Journal of Production Research, 50, 5843-5858, DOI: 10.1080/00207543.2011.632385.
• Wang, W., Xu, Z. ve Gu, X. (2022). “A Two-Stage Discrete Water Wave Optimization Algorithm for the Flowshop Lot-Streaming Scheduling Problem with İntermingling and Variable Lot Sizes’’, Knowledge-Based Systems, 238, 107874, DOI: 10.1016/j.knosys.2021.107874.
• Yenisey, M.M. ve Yagmahan, B. (2014). “Multi-Objective Permutation Flow Shop Scheduling Problem: Literature Review, Classification and Current Trends’’, Omega, 45, 119-135, DOI: 10.1016/j.omega.2013.07.004.
• Yoon, S-H. ve Ventura, J.A. (2002). “Minimizing the Mean Weighted Absolute Deviation from Due Dates in Lot-Streaming Flow Shop Scheduling’’, Computers & Operations Research, 29, 1301-1315, DOI: 10.1016/S0305-0548(01)00032-6.
• Zhang, S-J. ve Gu, X-S. (2015). “An Effective Discrete Artificial Bee Colony Algorithm for Flow Shop Scheduling Problem with İntermediate Buffers’’, Journal of Central South University, 22, 3471-3484.
• Zhang, W., Wang, Y., Yang, Y. ve Gen, M. (2019). “Hybrid Multiobjective Evolutionary Algorithm Based on Differential Evolution for Flow Shop Scheduling Problems’’, Computers & Industrial Engineering, 130, 661-670, DOI: 10.1016/j.cie.2019.03.019.
• Zhao, F., Liu, Y., Zhang, Y., Ma, W. ve Zhang, C. (2017). “A Hybrid Harmony Search Algorithm with Efficient Job Sequence Scheme and Variable Neighborhood Search for the Permutation Flow Shop Scheduling Problems’’, Engineering Applications of Artificial Intelligence, 65, 178-199, DOI: 10.1016/j.engappai.2017.07.023.
• Zobolas, G.I., Tarantilis, C.D. ve Ioannou, G. (2009). “Minimizing Makespan in Permutation Flow Shop Scheduling Problems Using a Hybrid Metaheuristic Algorithm’’, Computers & Operations Research, 36, 1249-1267, DOI: 10.1016/j.cor.2008.01.007.