Task Block in a Multistage Flowshop Scheduling Problem Under Uncertainty Reduces the Waiting Time of Tasks
DOI:
https://doi.org/10.26713/cma.v17i1.3554Keywords:
Flowshop scheduling, Uncertain processing periods, Task block, Complete waiting time of tasksAbstract
The current paper investigates the scheduling problem for multiple-stations in a taskblock-based model, particularly under conditions of uncertainty in processing times. We propose a framework for task block scheduling that adaptively schedules tasks across multiple stages with the objective of minimizing the total waiting time of tasks in a fuzzy environment. The algorithm is formulated and analyzed using MATLAB and its performance is supported through a numerical example.
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[1] M. Allahverdi and A. Allahverdi, Minimizing total completion time for flowshop scheduling problem with uncertain processing times, RAIRO-Operations Research 55 (2021), S929 – S946, DOI: 10.1051/ro/2020022.
[2] J. Behnamian and S. M. T. F. Ghomi, Multi-objective multi-factory scheduling, RAIRO-Operations Research 55 (2021), S1447 – S1467, DOI: 10.1051/ro/2020044.
[3] J. Castaneda, X. A. Martin, M. Ammouriova, J. Panadero and A. A. Juan, A fuzzy simheuristic for the permutation flow shop problem under stochastic and fuzzy uncertainty, Mathematics 10(10) (2022), 1760, DOI: 10.3390/math10101760.
[4] Y. Chen and H. Luo, Research on Multi-Factory Production Scheduling Problem with Maritime Transport Plan, in: ICIEAEU’23: Proceedings of the 2023 10th International Conference on Industrial Engineering and Applications, (2023), 162 – 168, DOI: 10.1145/3587889.3587914.
[5] S. Dehnavi, H. Mokhtari and M. T. Rezvan, Energy-efficient scheduling of AGV-assisted robotic flexible flowshops under learning and processing time uncertainty, Scientific Reports 16 (2025), Article number: 2666, DOI: 10.1038/s41598-025-32390-3.
[6] B. Goyal and S. Kaur, Specially structured flow shop scheduling models with processing times as trapezoidal fuzzy numbers to optimize waiting time of jobs, in: Soft Computing for Problem Solving, A. Tiwari, K. Ahuja, A. Yadav, J. C. Bansal, K. Deep and A. K. Nagar (editors), Advances in Intelligent Systems and Computing series, Vol. 1393, Springer, Singapore, pp. 27 – 42 (2021), DOI: 10.1007/978-981-16-2712-5_3.
[7] B. Goyal, D. Gupta, D. Rani and R. Rani, Special structures in flowshop scheduling with separated set-up times and concept of job block: Minimization of waiting time of jobs, Advance in Mathematics: Scientific Journal 9(7) (2020), 4607 – 4619, DOI: 10.37418/amsj.9.7.29.
[8] R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. R. Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics 5 (1979), 287 – 326, DOI: 10.1016/S0167-5060(08)70356-X.
[9] K.I.-J. Ho, J.Y.-T. Leung and W.-D. Wei, Complexity of scheduling tasks with time-dependent execution times, Information Processing Letters 48(6) (1993), 315 – 320, DOI: 10.1016/0020-0190(93)90175-9.
[10] X. Huang and J.-J. Wang, Machine scheduling problems with a position-dependent deterioration, Applied Mathematics Model 39(10-11) (2015), 2897 – 2908, DOI: 10.1016/j.apm.2014.11.002.
[11] S. M. Johnson, Optimal two and three-stage production schedules with setup times included, Naval Research Logistics Quarterly 1 (1954), 61 – 68, DOI: 10.1002/nav.3800010110.
[12] H. Kazemi, M. Nourelfath and M. Gendreau, The multi-factory two-stage assembly scheduling problem, Journal of Industrial Information Integration 38 (2024), 100574, DOI: 10.1016/j.jii.2024.100574.
[13] Y.-D. Kim, A new branch and bound algorithm for minimizing mean tardiness in two-machine flowshops, Computers & Operations Research 20(4) (1993), 391 – 401, DOI: 10.1016/0305-0548(93)90083-U.
[14] J.-H. Lee, T.-S. Yu and K.-S. Park, Scheduling of flow shop with overlapping waiting time constraints using genetic algorithm, Journal of the Korean Institute of Industrial Engineers 47(1) (2021), 34 – 44, DOI: 10.7232/JKIIE.2021.47.1.034. (in Korean)
[15] L. Luo and X. Yan, Scheduling of stochastic distributed hybrid flow-shop by hybrid estimation of distribution algorithm and proximal policy optimization, Expert Systems with Applications 271 (2025), 126523, DOI: 10.1016/j.eswa.2025.126523.
[16] D.-Y. Lv and J.-B. Wang, Research on two-machine flow shop scheduling problem with release dates and truncated learning effects, Engineering Optimization 57(7) (2025), 1828 – 1848, DOI: 10.1080/0305215X.2024.2372633.
[17] C. Miao, Complexity of scheduling with proportional deterioration and release dates, Iranian Journal of Science and Technology, Transactions A: Science 42 (2018), 1337 – 1342, DOI: 10.1007/s40995-017-0466-8.
[18] A. Mokhtari-Moghadam, T. T. Nguyen and M. Mohsendokht, Energy-aware flexible flow-shop scheduling for sustainable manufacturing: A multi-objective approach, Process Integration and Optimization for Sustainability (2026), 16 pages, DOI: 10.1007/s41660-026-00705-0.
[19] M. Nawaz, E. E. Enscore Jr. and I. Ham, A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem, Omega 11(1) (1983), 91 – 95, DOI: 10.1016/0305-0483(83)90088-9.
[20] S. Panwalkar and C. Koulamas, An asymptotically optimal solution for the minimization of the variation of job completion times in two-stage proportionate no-wait flow shops, Journal of the Operational Research Society 76(1) (2023), 131 – 136, DOI: 10.1080/01605682.2024.2330614.
[21] Z. Pei, R. Dou, J. Huang and H. Lu, Distributionally robust scheduling for the two-stage hybrid flowshop with uncertain processing time, European Journal of Operational Research 326(2) (2025), 270 – 285, DOI: 10.1016/j.ejor.2025.04.037.
[22] H. M. Wagner, An integer linear-programming model for machine scheduling, Naval Research Logistics Quarterly 6(2) (1959), 131 – 140, DOI: 10.1002/nav.3800060205.
[23] D.-L. Yang and M.-S. Chern, A two-machine flowshop sequencing problem with limited waiting time constraints, Computers & Industrial Engineering 28(1) (1995), 63 – 70, DOI: 10.1016/0360-8352(94)00026-J.
[24] D.-L. Yang and W.-H. Kuo, Minimizing makespan in a two-machine flowshop problem with processing time linearly dependent on job waiting time, Sustainability 11(24) (2019), 6885, DOI: 10.3390/su11246885.
[25] K.-C. Ying, P. Pourhejazy and C.-E. Sung, Two-agent proportionate flowshop scheduling with deadlines: Polynomial-time optimization algorithms, Annals of Operations Research 343(1) (2024), 543 – 558, DOI: 10.1007/s10479-024-06275-z.
[26] T.-S. Yu, H.-J. Kim and T.-E. Lee, Minimization of waiting time variation in a generalized two-machine flowshop with waiting time constraints and skipping jobs, IEEE Transactions on Semiconductor Manufacturing 30(2) (2017), 155 – 165, DOI: 10.1109/TSM.2017.2662231.
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