Production
http://www.production.periodikos.com.br/article/doi/10.14488/1980-5411.20260050
Production
Research Article

Energy-efficient flexible job-shop scheduling with transportation times and selectable speeds

Khaled Abdelaziz Mili; Majdi Argoubi

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Abstract

Paper aims: This study addresses an extended FJSP that simultaneously incorporates inter-machine workpiece transportation times and selectable machine processing speeds within a unified multi-objective framework.

Originality: A multi-objective mixed-integer model is formulated to jointly minimize makespan, total machine workload, and total energy consumption — decomposed into processing, idle, and transportation phases. An Improved Multi-Objective Jaya Algorithm (IMOJA) is proposed, featuring a three-layer encoding scheme, a transportation-aware insertion-based decoding method, four discrete update strategies, a Pareto-ranked external archive, and five tailored neighborhood search structures.

Research method: IMOJA is benchmarked against NSGA-II and SPEA2 on the ten extended Brandimarte instances (MK01–MK10) using Coverage (C) and Inverted Generational Distance (IGD) indicators over ten independent runs.

Main findings: IMOJA consistently dominates both competitors across all instances, achieving Coverage values close to 1.0 and IGD values up to two orders of magnitude smaller, including zero on four instances. On MK05, IMOJA yields a best makespan of 72.87 versus 80.00 and 83.37 for NSGA-II and SPEA2.

Implications for theory and practice: IMOJA offers a reliable decision-support tool for energy-conscious shop-floor scheduling where transportation logistics and speed flexibility must be jointly managed.

Keywords

Flexible job-shop scheduling, Multi-objective optimization, Energy-efficient manufacturing, Jaya algorithm, Transportation time, Selectable processing speeds

References

Abreu, A., & Fuchigami, H. Y. (2026). Optimising manufacturing schedules with tailored metrics to reduce unproductive times. Production, 36, e20250004. https://doi.org/10.1590/0103-6513.20250004.

Ahmadipour, M., Abadi, M. S. S., & Ahmadi, M. (2024). MG-Jaya: an advanced multi-objective Jaya algorithm for optimal microgrid energy management. Applied Soft Computing, 163, 111924. https://doi.org/10.1016/j.asoc.2024.111924.

Berterottière, L., Dauzère-Pérès, S., & Yugma, C. (2024). Flexible job-shop scheduling with transportation resources. European Journal of Operational Research, 312(3), 890-909. https://doi.org/10.1016/j.ejor.2023.07.036.

Brandimarte, P. (1993). Routing and scheduling in a flexible job shop by tabu search. Annals of Operations Research, 41(3), 157-183. https://doi.org/10.1007/BF02023073.

Brucker, P., & Schlie, R. (1990). Job-shop scheduling with multi-purpose machines. Computing, 45(4), 369-375. https://doi.org/10.1007/BF02238804.

Caldeira, R. H., & Gnanavelbabu, A. (2021). A Pareto based discrete Jaya algorithm for multi-objective flexible job shop scheduling problem. Expert Systems with Applications, 170, 114567. https://doi.org/10.1016/j.eswa.2021.114567.

Camargo, F. G., Rossomando, F. G., Gandolfo, D. C., Sarroca, E. A., Faure, O. R., & Sosa, G. (2025). A novel hybrid methodology for multi-objective optimisation of dual-axis solar tracking systems with artificial intelligence. Production, 35, e20240139. https://doi.org/10.1590/0103-6513.20240139.

Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. https://doi.org/10.1109/4235.996017.

He, P., Jiang, X., Wang, Q., & Zhang, B. (2025). Multi-objective human-robot collaborative batch scheduling in distributed hybrid flowshop via automatic design of local search-reconstruction-feedback algorithm. Computers & Industrial Engineering, 203, 110983. https://doi.org/10.1016/j.cie.2025.110983.

Li, Z., & Chen, Y. (2023). Minimizing the makespan and carbon emissions in the green flexible job shop scheduling problem with learning effects. Scientific Reports, 13(1), 6369. https://doi.org/10.1038/s41598-023-33615-z. PMid:37076558.

Li, S., Han, K., Pei, Z., Yi, W., & Lv, R. (2026). Green flexible job shop integrated scheduling optimization for machines and AGVs based on the INSGA-II algorithm. Proceedings of the Institution of Mechanical Engineers. Part B, Journal of Engineering Manufacture, 240(4), 477-494. https://doi.org/10.1177/09544054251327439.

Luo, S., Zhang, L., & Fan, Y. (2019). Energy-efficient scheduling for multi-objective flexible job shops with variable processing speeds by grey wolf optimization. Journal of Cleaner Production, 234, 1365-1384. https://doi.org/10.1016/j.jclepro.2019.06.151.

Nabati, E. G., Alvela Nieto, M. T., Bode, D., Schindler, T. F., Decker, A., & Thoben, K.-D. (2022). Challenges of manufacturing for energy efficiency: towards a systematic approach through applications of machine learning. Production, 32, e20210147. https://doi.org/10.1590/0103-6513.20210147.

Rao, R. V. (2016). Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7, 19-34. https://doi.org/10.5267/j.ijiec.2015.8.004.

Rao, R. V. (2019). Jaya: an advanced optimization algorithm and its engineering applications. Cham: Springer.

Rao, R. V., & Rai, D. P. (2017). Optimization of submerged arc welding process parameters using quasi-oppositional based Jaya algorithm. Journal of Mechanical Science and Technology, 31(5), 2513-2522. https://doi.org/10.1007/s12206-017-0449-x.

Pal, M., Mittal, M. L., Soni, G., Chouhan, S. S., & Kumar, M. (2023). A multi-agent system for FJSP with setup and transportation times. Expert Systems with Applications, 216, 119474. https://doi.org/10.1016/j.eswa.2022.119474.

Shen, L., Dauzère-Pérès, S., & Maecker, S. (2023). Energy cost efficient scheduling in flexible job-shop manufacturing systems. European Journal of Operational Research, 310(3), 992-1016. https://doi.org/10.1016/j.ejor.2023.03.041.

Vishnu, M., & Kumar, S. (2022). Hybrid Firefly–JAYA algorithm for complex engineering design optimization problems. Applied Sciences, 12(14), 7193. https://doi.org/10.3390/app12147193.

Wei, Z., Liao, W., & Zhang, L. (2022). Hybrid energy-efficient scheduling measures for flexible job-shop problem with variable machining speeds. Expert Systems with Applications, 197, 116785. https://doi.org/10.1016/j.eswa.2022.116785.

Xu, G. J., Bao, Q., & Zhang, H. L. (2023). Multi-objective green scheduling of integrated flexible job shop and automated guided vehicles. Engineering Applications of Artificial Intelligence, 126, 106864. https://doi.org/10.1016/j.engappai.2023.106864.

Yuan, Y., Xu, H., & Yang, J. (2013). A hybrid harmony search algorithm for the flexible job shop scheduling problem. Applied Soft Computing, 13(7), 3259-3272. https://doi.org/10.1016/j.asoc.2013.02.013.

Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: improving the strength Pareto evolutionary algorithm (TIK-Report, No. 103). Zurich: ETH Zurich.

Zhang, G., Gao, L., & Shi, Y. (2011). An effective genetic algorithm for the flexible job-shop scheduling problem. Expert Systems with Applications, 38(4), 3563-3573. https://doi.org/10.1016/j.eswa.2010.08.145.

Zhang, F., Li, R., & Gong, W. (2024). Deep reinforcement learning-based memetic algorithm for energy-aware flexible job shop scheduling with multi-AGV. Computers & Industrial Engineering, 189, 109917. https://doi.org/10.1016/j.cie.2024.109917.

Zhang, B., Wang, Z.-X., Meng, L.-L., Sang, H.-Y., & Jiang, X.-C. (2025). Multi-objective scheduling for surface mount technology workshop: automatic design of two-layer decomposition-based approach. International Journal of Production Research, 63(20), 7570-7590. https://doi.org/10.1080/00207543.2025.2502106.
 


Submitted date:
04/10/2026

Accepted date:
08/17/2026

6aa9781da953955273185ddf production Articles
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