A Mixed-Integer Programming Model for Skill-Aware Multi-Task Simultaneous Supervision Dual Resource-Constrained Scheduling on Unrelated Parallel Machines
DOI:
https://doi.org/10.9744/jti.28.2.%25pKeywords:
MTSSDRC, operator skill, unrelated parallel machines, makespan, schedulingAbstract
In semi-automated manufacturing systems, operators are required to perform manual tasks while simultaneously supervising multiple unrelated parallel machines. Consequently, effective scheduling requires the integrated allocation of machines and operators as dual-capacitated resources. This study introduces a multi-task simultaneous supervision dual resource-constrained scheduling model for unrelated parallel machine environments. The proposed model incorporates machine heterogeneity, operator skill heterogeneity, and operator movement time between machines, with the objective of minimizing makespan. The scheduling problem is formulated as a mixed-integer linear programming model and solved using Gurobi Optimizer on synthetically generated benchmark instances. All six small instances were solved to optimality, while the medium instances produced feasible solutions within the specified time limit. Under the same average workforce skill, the heterogeneous scenario reduced makespan in all small instances by an average of 8.95%. The average reduction in true machine idle time was 22.29%, although the effect was not consistent across all instances. The results demonstrate that operator skill heterogeneity influences machine assignment, manual-operation sequencing, and workload distribution. The model generally assigns faster operators to critical setup and unloading activities, but this allocation may create workload imbalance. Therefore, practical implementation should consider the trade-off between production efficiency and equitable operator workload distribution.
Downloads
References
[1] S. Zhang, H. Du, S. Borucki, S. Jin, T. Hou, and Z. Li, “Dual resource constrained flexible job shop scheduling based on improved quantum genetic algorithm,” Machines, vol. 9, no. 6, p. 108, 2021, doi: https://doi.org/10.3390/machines9060108.
[2] G. Yang, B. Do Chung, and S. J. Lee, “Limited search space-based algorithm for dual resource constrained scheduling problem with multilevel product structure,” Appl. Sci., vol. 9, no. 19, p. 4005, 2019, doi: https://doi.org/10.3390/app9194005.
[3] Z. Gao and H. Qiao, “A study of flexible job-shop scheduling with dual constraints,” Processes, vol. 12, p. 2649, 2024, doi: https://doi.org/10.3390/pr12122649.
[4] X. Gong, Q. Deng, G. Gong, W. Liu, and Q. Ren, “A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility,” Int. J. Prod. Res., vol. 56, no. 7, pp. 2506–2522, 2017, doi: https://doi.org/10.1080/00207543.2017.1388933.
[5] M. Akbar and T. Irohara, “Dual resource constrained scheduling considering operator working modes and moving in identical parallel machines using a permutation-based genetic algorithm,” IFIP Adv. Inf. Commun. Technol., vol. 535, pp. 464–472, 2018, doi: https://doi.org/10.1007/978-3-319-99704-9_57.
[6] A. Elidrissi, R. Benmansour, K. Hasani, and F. Werner, “Minimizing the makespan on two parallel machines with a common server in charge of loading and unloading operations,” Comput. Oper. Res., vol. 167, p. 106638, 2024, doi: https://doi.org/10.1016/j.cor.2024.106638.
[7] P. Baptiste, D. Rebaine, and M. Zouba, “FPTAS for the two identical parallel machine problem with a single operator under the free changing mode,” Eur. J. Oper. Res., vol. 256, no. 1, pp. 55–61, 2017, doi: https://doi.org/10.1016/j.ejor.2016.05.062.
[8] M. Akbar and T. Irohara, “Metaheuristics for the multi-task simultaneous supervision dual resource-constrained scheduling problem,” Eng. Appl. Artif. Intell., vol. 96, p. 104004, 2020, doi: https://doi.org/10.1016/j.engappai.2020.104004.
[9] M. Akbar and T. Irohara, “NSGA-II variants for solving a social-conscious dual resource-constrained scheduling problem,” Expert Syst. Appl., vol. 162, p. 113754, 2020, doi: https://doi.org/10.1016/j.eswa.2020.113754.
[10] M. Akbar and T. Irohara, “NSGA families for solving a dual resource-constrained problem to optimize the total tardiness and labor productivity in the spirit of sustainability,” Comput. Ind. Eng., vol. 188, p. 109883, 2024, doi: https://doi.org/10.1016/j.cie.2024.109883.
[11] Z. He, B. Tang, and F. Luan, “An improved African vulture optimization algorithm for dual-resource constrained multi-objective flexible job shop scheduling problems,” Sensors, vol. 23, no. 1, p. 90, 2023, doi: https://doi.org/10.3390/s23010090.
[12] X. Zhu, J. Xu, J. Ge, Y. Wang, and Z. Xie, “Multi-task multi-agent reinforcement learning for real-time scheduling of a dual-resource flexible job shop with robots,” Processes, vol. 11, no. 1, p. 267, 2023, doi: https://doi.org/10.3390/pr11010267.
[13] K. A. Larasati, Sukoyo, and M. Akbar, “A dual resource constrained unrelated parallel machine scheduling model considering tardiness and workload balance,” Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri, vol. 26, no. 2, pp. 87–102, 2024, doi: https://doi.org/10.9744/jti.26.2.87-102.
[14] I. M. Al-harkan, A. A. Qamhan, A. Badwelan, A. Alsamhan, and L. Hidri, “Modified harmony search algorithm for resource-constrained parallel machine scheduling problem with release dates and sequence-dependent setup times,” Processes, vol. 9, no. 4, p. 654, 2021, doi: https://doi.org/10.3390/pr9040654.
[15] A. Rizka, Sukoyo, and M. Akbar, “Multi-task simultaneous supervision: Dual resource-constrained scheduling problem in identical parallel machines considering differences in operator skill levels,” Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri, vol. 26, no. 2, pp. 119–130, 2024, doi: https://doi.org/10.9744/jti.26.2.119-130.
[16] C. Wang, D. Fan, Y. Liu, S. Ren, and J. Wang, “Dual-resource flexible job shop scheduling considering worker proficiency differences,” Comput. Oper. Res., vol. 184, p. 107216, 2025, doi: https://doi.org/10.1016/j.cor.2025.107216.
[17] L. Zhang, Q. Deng, R. Lin, G. Gong, and W. Han, “A combinatorial evolutionary algorithm for unrelated parallel machine scheduling problem with sequence and machine-dependent setup times, limited worker resources and learning effect,” Expert Syst. Appl., vol. 175, p. 114843, 2021, doi: https://doi.org/10.1016/j.eswa.2021.114843.
[18] F. Costa, M. Thürer, and A. Portioli‑Staudacher, “Heterogeneous worker multi‑functionality and efficiency in dual resource constrained manufacturing lines: an assessment by simulation,” Oper. Manag. Res., vol. 16, pp. 1476–1489, 2023, doi: https://doi.org/10.1007/s12063-023-00371-2.
[19] J. I. Vázquez-Serrano, L. E. Cárdenas-Barrón, and R. E. Peimbert-García, “Agent scheduling in unrelated parallel machines with sequence-and agent–machine–dependent setup time problem,” Mathematics, vol. 9, no. 22, p. 2955, 2021, doi: https://doi.org/10.3390/math9222955.
[20] A. Costa, F. A. Cappadonna, and S. Fichera, “A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times,” Int. J. Adv. Manuf. Technol., vol. 69, no. 9–12, pp. 2799–2817, 2013, doi: https://doi.org/10.1007/s00170-013-5221-5.
[21] P. Heuser, P. Letmathe, and T. Vossen, “Skill development in the field of scheduling: A structured literature review,” Eur. J. Oper. Res., vol. 321, no. 3, pp. 697–716, 2025, doi: https://doi.org/10.1016/j.ejor.2024.04.005.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 adi candra, Anas Ma'ruf, Muhammad Akbar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in the Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri will be Open-Access articles distributed under the terms and conditions of the Creative Commons Attribution License (CC BY).
This work is licensed under a Creative Commons Attribution License (CC BY).
