*Result*: Fuzzy-based multi-objective scheduling for human-robot manufacturing systems.
Title:
Fuzzy-based multi-objective scheduling for human-robot manufacturing systems.
Authors:
Deng Y; College of Packaging Design and Art, Hunan University of Technology, Zhuzhou, 412000, Hunan, China., Huang B; College of Packaging Design and Art, Hunan University of Technology, Zhuzhou, 412000, Hunan, China., Lai S; College of Packaging Design and Art, Hunan University of Technology, Zhuzhou, 412000, Hunan, China. laishouliang@hut.edu.cn.
Source:
Scientific reports [Sci Rep] 2026 Feb 27. Date of Electronic Publication: 2026 Feb 27.
Publication Model:
Ahead of Print
Publication Type:
Journal Article
Language:
English
Journal Info:
Publisher: Nature Publishing Group Country of Publication: England NLM ID: 101563288 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 2045-2322 (Electronic) Linking ISSN: 20452322 NLM ISO Abbreviation: Sci Rep Subsets: MEDLINE
Imprint Name(s):
Original Publication: London : Nature Publishing Group, copyright 2011-
References:
Akbari, M. & Ghasemi, M. Scheduling employees with different skill levels in small clothing workshops. J. Ind. Manag. Perspect. 11(3), 153–180 (2021).
Lohmer, J. & Lasch, R. Production planning and scheduling in multi-factory production networks: A systematic literature review. Int. J. Prod. Res. 59(7), 2028–2054 (2020).
Yazdani, M., Amiri, M. & Zandieh, M. Flexible job-shop scheduling with parallel variable neighborhood search algorithm. Expert Syst. Appl. 37(1), 678–687 (2010).
Zu, L., Liao, W. & Yang, X. An optimization model for production scheduling in parallel machine systems. Axioms 13 848 (2024).
Löffler, M., Boysen, N. & Schneider, M. Human-robot cooperation: Coordinating autonomous mobile robots and human order pickers. Transp. Sci. 57(4), 979–998 (2023).
Seyed Bathaee, M. S., Ghahremani-Nahr, J., Nozari, H. & Najafi, S. E. Designing a mathematical model of a collaborative production system based on make to order under uncertainty. J. Ind. Manag. Perspect. 12(1), 193–224 (2022).
Xu, W., Sun, H. Y., Awaga, A. L., Yan, Y. & Cui, Y. Optimization approaches for solving production scheduling problem: A brief overview and a case study for hybrid flow shop using genetic algorithms. Adv. Prod. Eng. Manag. 17(1), 45–56 (2022).
Faraji Amiri, M. & Behnamian, J. A simulation based genetic algorithm for flowshop scheduling problem considering energy cost under uncertainty. J. Ind. Manag. Perspect. 10(2), 9–32 (2020).
Fattahi, P., Mohammadi, E. & Daneshamooz, F. Providing a harmony search algorithm for solving multi objective job shop scheduling problem with considering an assembly stage and lot streaming. J. Ind. Manag. Perspect. 61(86), 61–86 (2019).
Shakeri, Z., Benfriha, K., Varmazyar, M., Talhi, E. & Quenehen, A. Production scheduling with multirobot task allocation in a real industry 4.0 setting. Sci. Rep. 15, 1795 (2025).
Bogner, K., Pferschy, U., Unterberger, R. & Zeiner, H. Optimised scheduling in human–robot collaboration—A use case in the assembly of printed circuit boards. Int. J. Prod. Res. 56(16), 5522–5540 (2018).
Vital-Soto, A., Baki, M. F. & Azab, A. A multi-objective mathematical model and evolutionary algorithm for the dual-resource flexible job-shop scheduling problem with sequencing flexibility. Flex. Serv. Manuf. J. 35(3), 626–668 (2023).
Vahedi-Nouri, B., Tavakkoli-Moghaddam, R., Hanzálek, Z. & Dolgui, A. Production scheduling in a reconfigurable manufacturing system benefiting from human-robot collaboration. Int. J. Prod. Res. 62(3), 767–783 (2024).
Khadivi, M., Abbasi, M., Charter, T., & Najjaran, H. A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling. arXiv, vol. 15670, pp. 1–24 (2024).
Alimian, M., Ghezavati, V. & Tavakkoli-Moghaddam, R. New integration of preventive maintenance and production planning with cell formation and group scheduling for dynamic cellular manufacturing systems. J. Manuf. Syst. 56, 341–358 (2020).
Liu, Q., Li, X. & Gao, L. Mathematical modeling and a hybrid evolutionary algorithm for process planning. J. Intell. Manuf. 32, 781–797 (2021).
Ghaleb, M., Taghipour, S. & Zolfagharinia, H. Real-time integrated production-scheduling and maintenance-planning in a flexible job shop with machine deterioration and condition-based maintenance. J. Manuf. Syst. 61, 423–449 (2021).
Gharoun, H., Hamid, M. & Torabi, S. A. An integrated approach to joint production planning and reliability-based multi-level preventive maintenance scheduling optimisation for a deteriorating system considering due-date satisfaction. Int. J. Syst. Sci. Oper. Logist. 9(4), 489–511 (2022).
Goli, A., Ala, A. & Hajiaghaei-Keshteli, M. Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem. Expert Syst. Appl. 213, 119077 (2023).
Zhang, B., Wang, Z. X., Meng, L. L., Sang, H. Y., & Jiang, X. C. Multi-objective scheduling for surface mount technology workshop: automatic design of two-layer decomposition-based approach. Int. J. Prod. Res. 63(20), 7570–7590 (2025).
Zhang, B., Sang, H., Meng, L., Jiang, X., & Lu, C. Knowledge- and data-driven hybrid method for lot streaming scheduling in hybrid flowshop with dynamic order arrivals. Comput. Oper. Res. 184, 107244. https://doi.org/10.1016/j.cor.2025.107244 (2025).
Xu, W. et al. Blockchain-Based Verifiable Decentralized Identity for Intelligent Flexible Manufacturing. IEEE Internet Things J. 12(16), 32366–32378. https://doi.org/10.1109/JIOT.2025.3576735 (2025).
Hari, S. K. K., Nayak, A. & Rathinam, S. An approximation algorithm for a task allocation, sequencing and scheduling problem involving a human-robot team. IEEE Robot. Autom. Lett. 5(2), 2146–2153 (2020).
Yu, T., Huang, J. & Chang, Q. Optimizing task scheduling in human-robot collaboration with deep multi-agent reinforcement learning. J. Manuf. Syst. 60, 487–499 (2021).
Maderna, R., Pozzi, M., Zanchettin, A. M., Rocco, P. & Prattichizzo, D. Flexible scheduling and tactile communication for human–robot collaboration. Robot. Comput. Integr. Manuf. 73, 102233 (2022).
Xie, W., Song, D., Tang, W., Ma, J., & Li, J. Auxiliary support path planning for robot-assisted machining of thin-walled parts with non-uniform thickness and closed cross-section based on a neutral surface. J. Manuf. Process. 147, 16–28. https://doi.org/10.1016/j.jmapro.2025.05.002 (2025).
Wang, D. & Zhang, J. Flow shop scheduling with human–robot collaboration: A joint chance-constrained programming approach. Int. J. Prod. Res. 62(4), 1297–1317 (2024).
Aerts, D., et al. The origin of quantum mechanical statistics: Some insights from the research on human language. arXiv preprint arXiv, vol. 2407, p. 14924 (2024).
Bazargan-Lari, M. R., Taghipour, S., Zaretalab, A. & Sharifi, M. Production scheduling optimization for parallel machines subject to physical distancing due to COVID-19 pandemic. Oper. Manag. Res. 15(1), 503–527 (2022).
Baroud, M. M. et al. A new method for solving the flow shop scheduling problem on symmetric networks using a hybrid nature-inspired algorithm. Symmetry 15(7), 1409 (2023).
Yu, F., Lu, C., Zhou, J. & Yin, L. Mathematical model and knowledge-based iterated greedy algorithm for distributed assembly hybrid flow shop scheduling problem with dual-resource constraints. Expert Syst. Appl. 239, 122434 (2024).
Zacharia, P. T., Xidias, E. K. & Nearchou, A. C. The fuzzy human–robot collaboration assembly line balancing problem. Comput. Ind. Eng. 187, 109774 (2024).
Hashemi-Petroodi, S. E., Mezghani, Y., Thevenin, S. & Dolgui, A. An adversarial approach for the mixed-model assembly line design with new product variants in production generations. IFAC-PapersOnLine 58(19), 97–102 (2024).
Shao, S., Tian, Y., Zhang, Y., & Zhang, X. Knowledge Learning-Based Dimensionality Reduction for Solving Large-Scale Sparse Multiobjective Optimization Problems. IEEE Trans. Cybern. 55(7), 3471–3484. https://doi.org/10.1109/TCYB.2025.3558354 (2025).
Jia, Z., Xie, S. & Zhang, W. Flexible task assignment and assembly scheduling for human–robot collaboration cell considering uncertainty. Int. J. Prod. Res. 63(16), 6134–6154 (2025).
Sadik, A. R. & Urban, B. Flow shop scheduling problem and solution in cooperative robotics case-study: One cobot in cooperation with one worker. Future Internet 9(3), 48 (2017).
Qin, W., Zhang, J. & Song, D. An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time. J. Intell. Manuf. 29, 891–904 (2018).
Lu, C., Gao, L., Pan, Q., Li, X. & Zheng, J. A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution. Appl. Soft Comput. 75, 728–749 (2019).
Shao, W., Shao, Z. & Pi, D. Modeling and multi-neighborhood iterated greedy algorithm for distributed hybrid flow shop scheduling problem. Knowl. Based Syst. 194, 105527 (2020).
Ham, A. & Park, M. J. Human–robot task allocation and scheduling: Boeing 777 case study. IEEE Robot. Autom. Lett. 6(2), 1256–1263 (2021).
Vieira, M. et al. A two-level optimisation-simulation method for production planning and scheduling: The industrial case of a human–robot collaborative assembly line. Int. J. Prod. Res. 60(9), 2942–2962 (2022).
Guo, X. et al. Human–robot collaborative disassembly line balancing problem with stochastic operation time and a solution via multi-objective shuffled frog leaping algorithm. IEEE Trans. Autom. Sci. Eng. 21(3), 4448–4459 (2023).
Amirnia, A. & Keivanpour, S. A context-aware real-time human-robot collaborating reinforcement learning-based disassembly planning model under uncertainty. Int. J. Prod. Res. 62(11), 3972–3993 (2024).
Guo, D. Fast scheduling of human-robot teams collaboration on synchronised production-logistics tasks in aircraft assembly. Robot. Comput.-Integr. Manuf. 85, 102620 (2024).
Nourmohammadi, A., Fathi, M. & Ng, A. H. Balancing and scheduling human-robot collaborated assembly lines with layout and objective consideration. Comput. Ind. Eng. 187, 109775 (2024).
Liu, B. & Liu, Y. K. Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10(4), 445–450 (2002).
Roshanaei, V., Azab, A. & ElMaraghy, H. Mathematical modelling and a meta-heuristic for flexible job shop scheduling. Int. J. Prod. Res. 51(20), 6247–6274 (2013).
Rastgar, I., Rezaeian, J., Mahdavi, I. & Fattahi, P. A novel mathematical model for integration of production planning and maintenance scheduling. Int. J. Ind. Eng. Manag. 14(2), 122–137 (2023).
Yao, M., Zhao, T., Cao, J., & Li, J. Hierarchical Fuzzy Topological System for High-Dimensional Data Regression Problems. IEEE Trans. Fuzzy Syst. 33(7), 2084–2095. https://doi.org/10.1109/TFUZZ.2025.3549791 (2025).
Tasgetiren, M. F., Kizilay, D. & Pan, Q. K. A new iterated greedy algorithm for the no-idle permutation flowshop scheduling problem with makespan criterion. Int. J. Prod. Res. 55(16), 4509–4526 (2017).
Deb, k, Pratap, A., Agarwal, S. & Meyarivan, T. A. M. T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
Yang, Z. et al. Observer-Based Fuzzy Adaptive Dynamic Surface Force Control for Pneumatic Polishing System End-Effector With Uncertain Contact Environment Model. IEEE Trans. Autom. Sci. Eng. 22, 17898–17913. https://doi.org/10.1109/TASE.2025.3585136 (2025).
Lohmer, J. & Lasch, R. Production planning and scheduling in multi-factory production networks: A systematic literature review. Int. J. Prod. Res. 59(7), 2028–2054 (2020).
Yazdani, M., Amiri, M. & Zandieh, M. Flexible job-shop scheduling with parallel variable neighborhood search algorithm. Expert Syst. Appl. 37(1), 678–687 (2010).
Zu, L., Liao, W. & Yang, X. An optimization model for production scheduling in parallel machine systems. Axioms 13 848 (2024).
Löffler, M., Boysen, N. & Schneider, M. Human-robot cooperation: Coordinating autonomous mobile robots and human order pickers. Transp. Sci. 57(4), 979–998 (2023).
Seyed Bathaee, M. S., Ghahremani-Nahr, J., Nozari, H. & Najafi, S. E. Designing a mathematical model of a collaborative production system based on make to order under uncertainty. J. Ind. Manag. Perspect. 12(1), 193–224 (2022).
Xu, W., Sun, H. Y., Awaga, A. L., Yan, Y. & Cui, Y. Optimization approaches for solving production scheduling problem: A brief overview and a case study for hybrid flow shop using genetic algorithms. Adv. Prod. Eng. Manag. 17(1), 45–56 (2022).
Faraji Amiri, M. & Behnamian, J. A simulation based genetic algorithm for flowshop scheduling problem considering energy cost under uncertainty. J. Ind. Manag. Perspect. 10(2), 9–32 (2020).
Fattahi, P., Mohammadi, E. & Daneshamooz, F. Providing a harmony search algorithm for solving multi objective job shop scheduling problem with considering an assembly stage and lot streaming. J. Ind. Manag. Perspect. 61(86), 61–86 (2019).
Shakeri, Z., Benfriha, K., Varmazyar, M., Talhi, E. & Quenehen, A. Production scheduling with multirobot task allocation in a real industry 4.0 setting. Sci. Rep. 15, 1795 (2025).
Bogner, K., Pferschy, U., Unterberger, R. & Zeiner, H. Optimised scheduling in human–robot collaboration—A use case in the assembly of printed circuit boards. Int. J. Prod. Res. 56(16), 5522–5540 (2018).
Vital-Soto, A., Baki, M. F. & Azab, A. A multi-objective mathematical model and evolutionary algorithm for the dual-resource flexible job-shop scheduling problem with sequencing flexibility. Flex. Serv. Manuf. J. 35(3), 626–668 (2023).
Vahedi-Nouri, B., Tavakkoli-Moghaddam, R., Hanzálek, Z. & Dolgui, A. Production scheduling in a reconfigurable manufacturing system benefiting from human-robot collaboration. Int. J. Prod. Res. 62(3), 767–783 (2024).
Khadivi, M., Abbasi, M., Charter, T., & Najjaran, H. A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling. arXiv, vol. 15670, pp. 1–24 (2024).
Alimian, M., Ghezavati, V. & Tavakkoli-Moghaddam, R. New integration of preventive maintenance and production planning with cell formation and group scheduling for dynamic cellular manufacturing systems. J. Manuf. Syst. 56, 341–358 (2020).
Liu, Q., Li, X. & Gao, L. Mathematical modeling and a hybrid evolutionary algorithm for process planning. J. Intell. Manuf. 32, 781–797 (2021).
Ghaleb, M., Taghipour, S. & Zolfagharinia, H. Real-time integrated production-scheduling and maintenance-planning in a flexible job shop with machine deterioration and condition-based maintenance. J. Manuf. Syst. 61, 423–449 (2021).
Gharoun, H., Hamid, M. & Torabi, S. A. An integrated approach to joint production planning and reliability-based multi-level preventive maintenance scheduling optimisation for a deteriorating system considering due-date satisfaction. Int. J. Syst. Sci. Oper. Logist. 9(4), 489–511 (2022).
Goli, A., Ala, A. & Hajiaghaei-Keshteli, M. Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem. Expert Syst. Appl. 213, 119077 (2023).
Zhang, B., Wang, Z. X., Meng, L. L., Sang, H. Y., & Jiang, X. C. Multi-objective scheduling for surface mount technology workshop: automatic design of two-layer decomposition-based approach. Int. J. Prod. Res. 63(20), 7570–7590 (2025).
Zhang, B., Sang, H., Meng, L., Jiang, X., & Lu, C. Knowledge- and data-driven hybrid method for lot streaming scheduling in hybrid flowshop with dynamic order arrivals. Comput. Oper. Res. 184, 107244. https://doi.org/10.1016/j.cor.2025.107244 (2025).
Xu, W. et al. Blockchain-Based Verifiable Decentralized Identity for Intelligent Flexible Manufacturing. IEEE Internet Things J. 12(16), 32366–32378. https://doi.org/10.1109/JIOT.2025.3576735 (2025).
Hari, S. K. K., Nayak, A. & Rathinam, S. An approximation algorithm for a task allocation, sequencing and scheduling problem involving a human-robot team. IEEE Robot. Autom. Lett. 5(2), 2146–2153 (2020).
Yu, T., Huang, J. & Chang, Q. Optimizing task scheduling in human-robot collaboration with deep multi-agent reinforcement learning. J. Manuf. Syst. 60, 487–499 (2021).
Maderna, R., Pozzi, M., Zanchettin, A. M., Rocco, P. & Prattichizzo, D. Flexible scheduling and tactile communication for human–robot collaboration. Robot. Comput. Integr. Manuf. 73, 102233 (2022).
Xie, W., Song, D., Tang, W., Ma, J., & Li, J. Auxiliary support path planning for robot-assisted machining of thin-walled parts with non-uniform thickness and closed cross-section based on a neutral surface. J. Manuf. Process. 147, 16–28. https://doi.org/10.1016/j.jmapro.2025.05.002 (2025).
Wang, D. & Zhang, J. Flow shop scheduling with human–robot collaboration: A joint chance-constrained programming approach. Int. J. Prod. Res. 62(4), 1297–1317 (2024).
Aerts, D., et al. The origin of quantum mechanical statistics: Some insights from the research on human language. arXiv preprint arXiv, vol. 2407, p. 14924 (2024).
Bazargan-Lari, M. R., Taghipour, S., Zaretalab, A. & Sharifi, M. Production scheduling optimization for parallel machines subject to physical distancing due to COVID-19 pandemic. Oper. Manag. Res. 15(1), 503–527 (2022).
Baroud, M. M. et al. A new method for solving the flow shop scheduling problem on symmetric networks using a hybrid nature-inspired algorithm. Symmetry 15(7), 1409 (2023).
Yu, F., Lu, C., Zhou, J. & Yin, L. Mathematical model and knowledge-based iterated greedy algorithm for distributed assembly hybrid flow shop scheduling problem with dual-resource constraints. Expert Syst. Appl. 239, 122434 (2024).
Zacharia, P. T., Xidias, E. K. & Nearchou, A. C. The fuzzy human–robot collaboration assembly line balancing problem. Comput. Ind. Eng. 187, 109774 (2024).
Hashemi-Petroodi, S. E., Mezghani, Y., Thevenin, S. & Dolgui, A. An adversarial approach for the mixed-model assembly line design with new product variants in production generations. IFAC-PapersOnLine 58(19), 97–102 (2024).
Shao, S., Tian, Y., Zhang, Y., & Zhang, X. Knowledge Learning-Based Dimensionality Reduction for Solving Large-Scale Sparse Multiobjective Optimization Problems. IEEE Trans. Cybern. 55(7), 3471–3484. https://doi.org/10.1109/TCYB.2025.3558354 (2025).
Jia, Z., Xie, S. & Zhang, W. Flexible task assignment and assembly scheduling for human–robot collaboration cell considering uncertainty. Int. J. Prod. Res. 63(16), 6134–6154 (2025).
Sadik, A. R. & Urban, B. Flow shop scheduling problem and solution in cooperative robotics case-study: One cobot in cooperation with one worker. Future Internet 9(3), 48 (2017).
Qin, W., Zhang, J. & Song, D. An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time. J. Intell. Manuf. 29, 891–904 (2018).
Lu, C., Gao, L., Pan, Q., Li, X. & Zheng, J. A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution. Appl. Soft Comput. 75, 728–749 (2019).
Shao, W., Shao, Z. & Pi, D. Modeling and multi-neighborhood iterated greedy algorithm for distributed hybrid flow shop scheduling problem. Knowl. Based Syst. 194, 105527 (2020).
Ham, A. & Park, M. J. Human–robot task allocation and scheduling: Boeing 777 case study. IEEE Robot. Autom. Lett. 6(2), 1256–1263 (2021).
Vieira, M. et al. A two-level optimisation-simulation method for production planning and scheduling: The industrial case of a human–robot collaborative assembly line. Int. J. Prod. Res. 60(9), 2942–2962 (2022).
Guo, X. et al. Human–robot collaborative disassembly line balancing problem with stochastic operation time and a solution via multi-objective shuffled frog leaping algorithm. IEEE Trans. Autom. Sci. Eng. 21(3), 4448–4459 (2023).
Amirnia, A. & Keivanpour, S. A context-aware real-time human-robot collaborating reinforcement learning-based disassembly planning model under uncertainty. Int. J. Prod. Res. 62(11), 3972–3993 (2024).
Guo, D. Fast scheduling of human-robot teams collaboration on synchronised production-logistics tasks in aircraft assembly. Robot. Comput.-Integr. Manuf. 85, 102620 (2024).
Nourmohammadi, A., Fathi, M. & Ng, A. H. Balancing and scheduling human-robot collaborated assembly lines with layout and objective consideration. Comput. Ind. Eng. 187, 109775 (2024).
Liu, B. & Liu, Y. K. Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10(4), 445–450 (2002).
Roshanaei, V., Azab, A. & ElMaraghy, H. Mathematical modelling and a meta-heuristic for flexible job shop scheduling. Int. J. Prod. Res. 51(20), 6247–6274 (2013).
Rastgar, I., Rezaeian, J., Mahdavi, I. & Fattahi, P. A novel mathematical model for integration of production planning and maintenance scheduling. Int. J. Ind. Eng. Manag. 14(2), 122–137 (2023).
Yao, M., Zhao, T., Cao, J., & Li, J. Hierarchical Fuzzy Topological System for High-Dimensional Data Regression Problems. IEEE Trans. Fuzzy Syst. 33(7), 2084–2095. https://doi.org/10.1109/TFUZZ.2025.3549791 (2025).
Tasgetiren, M. F., Kizilay, D. & Pan, Q. K. A new iterated greedy algorithm for the no-idle permutation flowshop scheduling problem with makespan criterion. Int. J. Prod. Res. 55(16), 4509–4526 (2017).
Deb, k, Pratap, A., Agarwal, S. & Meyarivan, T. A. M. T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
Yang, Z. et al. Observer-Based Fuzzy Adaptive Dynamic Surface Force Control for Pneumatic Polishing System End-Effector With Uncertain Contact Environment Model. IEEE Trans. Autom. Sci. Eng. 22, 17898–17913. https://doi.org/10.1109/TASE.2025.3585136 (2025).
Contributed Indexing:
Keywords: Fuzzy programming; Human–robot interaction; Multi-objective optimization; Production planning; Scheduling
Entry Date(s):
Date Created: 20260227 Latest Revision: 20260227
Update Code:
20260228
DOI:
10.1038/s41598-026-40004-9
PMID:
41760726
Database:
MEDLINE
*Further Information*
*This study addresses the optimization of production planning and scheduling for human-robot interaction in a fuzzy environment, a critical challenge in modern manufacturing, especially under fluctuating market demand. The proposed model simultaneously determines production quantities, inventory/shortage levels, human-robot task allocation, and job sequencing. All decisions are optimized in a multi-period, multi-product setting. Three objective functions are considered: maximizing net present value, minimizing maximum completion time, and minimizing total early and tardy times. To handle uncertainties in demand and processing times, a pessimistic (credibility-constrained) fuzzy programming approach is employed. The model is solved using the epsilon-constraint method for small-scale problems and metaheuristic algorithms (NSGA-II, MOPSO, and MOWOA) for larger instances. Sensitivity analyses reveal that reducing completion times increases costs, lowering net present value, while higher uncertainty rates increase production times and shortages, reducing net present value. A 4% increase in bank interest rate reduces net present value by 15.68%, with no impact on completion or early/tardy times. The MOWOA algorithm demonstrates superior performance in generating efficient solutions for large-scale problems, offering practical insights for optimizing human-robot collaboration in manufacturing.
(© 2026. The Author(s).)*
*Declarations. Competing interests: The authors have no competing interests, or other interests that might be perceived to influence the results and/or discussion reported in this paper. Ethical approval: Not applicable.*