Abstract
It is well-known that the classical Johnson’s Rule leads to optimal schedules on a two-stage flowshop. However, it is still unclear how Johnson’s Rule would help in approximation algorithms for scheduling an arbitrary number of parallel two-stage flowshops with the objective of minimizing the makespan. Thus within the paper, we study the problem and propose a new efficient algorithm that incorporates Johnson’s Rule applied on each individual flowshop with a carefully designed job assignment process to flowshops. The algorithm is successfully shown to have a runtime \(O(n \log n)\) and an approximation ratio 7/3, where n is the number of jobs. Compared with the recent PTAS result for the problem (Dong et al. in Eur J Oper Res 218(1):16–24, 2020), our algorithm has a larger approximation ratio, but it is more efficient in practice from the perspective of runtime.
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Funding
This work is supported by the National Natural Science Foundation of China under Grants 62072476; Natural Science Foundation of Hunan Province under Grant 2020JJ4949 and 2021JJ40791; Excellent Youth Project of Scientific Research of Hunan Provincial Education Department under Grant 19B604; the Open Project of Xiangjiang Laboratory (No. 22XJ03005).
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A preliminary version of this paper has appeared in Proceedings of the International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW), 2023, pp. 212–224.
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Wu, G., Zuo, F., Shi, F. et al. On scheduling multiple parallel two-stage flowshops with Johnson’s Rule. J Comb Optim 47, 12 (2024). https://doi.org/10.1007/s10878-024-01107-z
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DOI: https://doi.org/10.1007/s10878-024-01107-z