Time Prediction Using Artificial Neural Networks for the Permutation Flow Shop Problem: Predict-Then-Optimize Framework
DOI:
https://doi.org/10.20961/performa.v25i2.3246Keywords:
Artificial Neural Network, Backpropagation, Gradient Descent , NEH Algorithm , Permutation Flow Shop SchedulingAbstract
This study introduces the implementation of predict-then-optimize (PTO) as a revolution in operational research (OR) in the industrial engineering field. In this contribution, we proposed an artificial neural network (ANN) model with a 4-20-4 multi-layer perceptron (MLP) using training and learning gradient descent with momentum under the backpropagation process as a prediction framework. Meanwhile, for the optimized model, we proposed mixed integer linear programming (MILP) for the permutation flow shop scheduling problem PFSP case using the NEH algorithm. Subsequently, we tested momentum, gradient, and learning rate parameters to validate the best performance of MSE in the ANN model. The best solution with the highest accuracy is used to simulate a scheduling prediction. Moreover, in the scheduling case, we compare the general flow shop FIFO model based on existing conditions with the proposed PFSP model, using the results of ANNs that consist of 4 machines and 4 jobs, based on the ANNs' prediction simulation. Furthermore, we proposed a PFSP model that can re-sequence jobs using the NEH algorithm with aims for minimize makespan. The results show that in the PTO framework, adaptive prediction and optimal conditions can achieve the best decision solution. Ultimately, this study successfully proves, in both practical and theoretical aspects, that the two biggest topics in the current era, that is, machine learning (ML) and operational research (OR), can work together under the PTO framework model.
References
Anis Lahoud, A., Khan, A. S., Schaffernicht, E., Trincavelli, M., & Stork, J. A. (2025). Predict-and-Optimize Techniques for Data-Driven Optimization Problems: A Review. Neural Processing Letters, 57(2), 1–28. https://doi.org/10.1007/s11063-025-11746-w
Badan Pusat Statistik. (2026). BPS: Manufacturing Products Support the Continued Growth of Non-Oil and Gas Exports. https://www.bps.go.id/en/news/2026/03/03/871/bps--manufacturing-products-support-the-continued-growth-of-non-oil-and-gas-exports.html
Belabid, J., Aqil, S., & Allali, K. (2020). Solving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Time. Journal of Applied Mathematics, 2020. https://doi.org/10.1155/2020/7132469
Cáceres-Gelvez, S., Dang, T. H., & Letchford, A. N. (2026). MIP-based local search for permutation flowshop scheduling with makespan objective. Computers and Operations Research, 186(February 2025), 107309. https://doi.org/10.1016/j.cor.2025.107309
Chen, X., Yang, H., Zhang, H., & Wong, C. U. I. (2025). Dynamic Gradient Descent and Reinforcement Learning for AI-Enhanced Indoor Building Environmental Simulation. Buildings, 15(12), 1–25. https://doi.org/10.3390/buildings15122044
Du, K. L., Leung, C. S., Mow, W. H., & Swamy, M. N. S. (2022). Perceptron: Learning, Generalization, Model Selection, Fault Tolerance, and Role in the Deep Learning Era. Mathematics, 10(24), 1–46. https://doi.org/10.3390/math10244730
Elissaouy, O., & Allali, K. (2024). Minimizing the Maximum Tardiness for a Permutation Flow Shop Problem Under the Constraint of Sequence Independent Setup Time. RAIRO - Operations Research, 58(1), 373–395. https://doi.org/10.1051/ro/2024001
Elmachtoub, A. N., & Grigas, P. (2022). Smart “Predict, then Optimize.” Management Science, 68(1), 9–26. https://doi.org/10.1287/mnsc.2020.3922
Fernandez-Viagas, V., Sanchez-Mediano, L., Angulo-Cortes, A., Gomez-Medina, D., & Molina-Pariente, J. M. (2022). The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm. Mathematics, 10(19). https://doi.org/10.3390/math10193446
Gao, R. X., Krüger, J., Merklein, M., Möhring, H. C., & Váncza, J. (2024). Artificial Intelligence in manufacturing: State of the art, perspectives, and future directions. CIRP Annals, 73(2), 723–749. https://doi.org/10.1016/j.cirp.2024.04.101
Grumbach, F., Müller, A., Reusch, P., & Trojahn, S. (2024). Robust-stable scheduling in dynamic flow shops based on deep reinforcement learning. Journal of Intelligent Manufacturing, 35(2), 667–686. https://doi.org/10.1007/s10845-022-02069-x
Gupta, J. N. D., Majumder, A., & Laha, D. (2020). Flowshop scheduling with artificial neural networks. Journal of the Operational Research Society, 71(10), 1619–1637. https://doi.org/10.1080/01605682.2019.1621220
Hoffmann, J., Neufeld, J. S., & Buscher, U. (2025). Customer order scheduling in a permutation flow shop environment. Operations Research Perspectives, 15(November). https://doi.org/10.1016/j.orp.2025.100362
Lapucci, M., Liuzzi, G., Lucidi, S., Pucci, D., & Sciandrone, M. (2025). A globally convergent gradient method with momentum. Computational Optimization and Applications. https://doi.org/10.1007/s10589-025-00741-5
Lee, H. (2025). Fault-Resilient Manufacturing Scheduling with Deep Learning and Constraint Solvers. Applied Sciences (Switzerland), 15(4), 1–24. https://doi.org/10.3390/app15041771
Li, X., Yu, J., Wang, X., & Lu, H. (2026). Balanced Smart Predict-Then-Optimize Framework for Container Yard Intelligent Retrofit Decision-Making. Journal of Advanced Transportation, 2026(1), 1–20. https://doi.org/10.1155/atr/8856441
Li, Y., & Yu, C. (2025). Flexible Job Shop Scheduling with Job Precedence Constraints: A Deep Reinforcement Learning Approach. Journal of Manufacturing and Materials Processing, 9(7), 1–21. https://doi.org/10.3390/jmmp9070216
Liu, R., Piplani, R., & Toro, C. (2022). Deep reinforcement learning for dynamic scheduling of a flexible job shop. International Journal of Production Research, 60(13), 4049–4069. https://doi.org/10.1080/00207543.2022.2058432
Mao, S., Wang, B., Tang, Y., & Qian, F. (2019). Opportunities and Challenges of Artificial Intelligence for Green Manufacturing in the Process Industry. Engineering, 5(6), 995–1002. https://doi.org/10.1016/j.eng.2019.08.013
Mu, H., Wang, Z., Chen, J., Zhang, G., Wang, S., & Zhang, F. (2024). A Flow Shop Scheduling Method Based on Dual BP Neural Networks with Multi-Layer Topology Feature Parameters. Systems, 12(9), 1–18. https://doi.org/10.3390/systems12090339
Nasseri, M., Falatouri, T., Brandtner, P., Darbanian, F., & Mirshahi, S. (2025). Enhancing Resource Assignment Efficiency in Service Industry: A Predict-then-Optimize Approach with XGBoost. Procedia Computer Science, 253, 644–653. https://doi.org/10.1016/j.procs.2025.01.126
Prastiya, D. S., & Wahyuni, R. S. (2024). Artificial Neural Network Model For Optimization of Forecasting Material Inventory. Jurnal Teknik Industri, 25(2), 173–188. https://doi.org/10.22219/jtiumm.vol25.no2.173-188
Puka, R., Duda, J., Stawowy, A., & Skalna, I. (2021). N-NEH+ algorithm for solving permutation flow shop problems. Computers and Operations Research, 132(October 2020). https://doi.org/10.1016/j.cor.2021.105296
Ren, F., & Liu, H. (2024). Dynamic scheduling for flexible job shop based on MachineRank algorithm and reinforcement learning. Scientific Reports, 14(1), 1–17. https://doi.org/10.1038/s41598-024-79593-8
Singh, A., Kushwaha, S., Alarfaj, M., & Singh, M. (2022). Comprehensive Overview of Backpropagation Algorithm for Digital Image Denoising. Electronics (Switzerland), 11(10). https://doi.org/10.3390/electronics11101590
Tang, H., & Dong, J. (2024). Solving Flexible Job-Shop Scheduling Problem with Heterogeneous Graph Neural Network Based on Relation and Deep Reinforcement Learning. Machines, 12(8). https://doi.org/10.3390/machines12080584
Xin, X., Jiang, Q., Li, C., Li, S., & Chen, K. (2023). Permutation flow shop energy-efficient scheduling with a position-based learning effect. International Journal of Production Research, 61(2), 382–409. https://doi.org/10.1080/00207543.2021.2008041
Yan, Q., Wu, W., & Wang, H. (2022). Deep Reinforcement Learning for Distributed Flow Shop Scheduling with Flexible Maintenance. Machines, 10(3). https://doi.org/10.3390/machines10030210
Zhang, H., & Liu, H. (2025). Real-Time Power System Optimization Under Typhoon Weather Using the Smart “Predict, Then Optimize” Framework. Energies, 18(3). https://doi.org/10.3390/en18030615
Zhou, T., Luo, L., Ji, S., & He, Y. (2023). A Reinforcement Learning Approach to Robust Scheduling of Permutation Flow Shop. Biomimetics, 8(6). https://doi.org/10.3390/biomimetics8060478
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Performa: Media Ilmiah Teknik Industri
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
