Online and semi-online scheduling on two hierarchical machines with a common due date to maximize the total early work

• Autorzy: Xiao, Man , Liu, Xiaoqiao , Li, Weidong , Chen, Xin , Sterna, Malgorzata , Blazewicz, Jacek
• Języki publikacji: EN

Abstrakty

EN

In this study, we investigate several online and semi-online scheduling problems related to two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we design an optimal online algorithm with a competitive ratio of √2. Additionally, for the cases when the largest processing time is known, we give optimal algorithms with a competitive ratio of 6/5 if the largest job is a lower-hierarchy one, and of √5 − 1 if the largest job is a higher-hierarchy one.

Słowa kluczowe

EN

online scheduling; semi online scheduling; early work; hierarchical scheduling; competitive ratio

• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2024
• Tom: Vol. 34, no. 2
• Strony: 253--261
• Opis fizyczny: Bibliogr. 24 poz., tab.

Twórcy

autor

Xiao, Man

• School of Mathematics and Statistics, Yunnan University, Wujiaying, Kunming 650504, China,

autor

Liu, Xiaoqiao

• School of Mathematics and Statistics, Yunnan University, Wujiaying, Kunming 650504, China,

autor

Li, Weidong

• School of Mathematics and Statistics, Yunnan University, Wujiaying, Kunming 650504, China,

autor

Chen, Xin

• School of Electronics and Information Engineering, Liaoning University of Technology, Shiying 169, Jinzhou 121001, China,

autor

Sterna, Malgorzata

• Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznań, Poland,

autor

Blazewicz, Jacek

• Institute of Computing Science, Poznan University of Technology, ul. Piotrowo 2, 60-965 Poznań, Poland,
• European Centre for Bioinformatics and Genomics, Polish Academy of Sciences, ul. Piotrowo 2, 60-965 Poznań, Poland

Bibliografia

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• [3] Chen, X., Kovalev, S., Liu, Y., Sterna, M., Chalamon, I. and Błażewicz, J. (2021). Semi-online scheduling on two identical machines with a common due date to maximize total early work, Discrete Applied Mathematics 290: 71-78.
• [4] Chen, X., Liang, Y., Sterna, M., Wang, W. and Błażewicz, J. (2020a). Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date, European Journal of Operational Research 284(1): 67-74.
• [5] Chen, X., Shen, X., Kovalyov, M.Y., Sterna, M. and Błażewicz, J. (2022). Alternative algorithms for identical machines scheduling to maximize total early work with a common due date, Computers & Industrial Engineering 171: 108386.
• [6] Chen, X., Sterna, M., Han, X. and Błażewicz, J. (2016). Scheduling on parallel identical machines with late work criterion: Offline and online cases, Journal of Scheduling 19: 729-736.
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• [16] Liu, X., Wang, W., Chen, X., Sterna, M. and Blazewicz, J. (2023). Exact approaches to late work scheduling on unrelated machines, International Journal of Applied Mathematics and Computer Science 33(2): 285-295, DOI: 10.34768/amcs-2023-0021.
• [17] Luo, T. and Xu, Y. (2015). Semi-online hierarchical load balancing problem with bounded processing times, Theoretical Computer Science 607: 75-82.
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• [22] Wang, W., Chen, X., Musial, J. and Blazewicz, J. (2020). Two meta-heuristic algorithms for scheduling on unrelated machines with the late work criterion, International Journal of Applied Mathematics and Computer Science 30(3): 573-584, DOI: 10.34768/amcs-2020-0042.
• [23] Xiao, M., Liu, X. and Li, W. (2021). Semi-online early work maximization problem on two hierarchical machines with partial information of processing time, in W.Wu and H. Du (Eds), Algorithmic Applications in Management, Lecture Notes in Computer Science, Vol. 13153, Springer, Cham, pp. 146-156.
• [24] Xiao, M., Liu, X. and Li, W. (2023). Semi-online early work maximization problems on two hierarchical uniform machines with partial information of processing time, Journal of Combinatorial Optimization 46(3): 21.

Identyfikatory

DOI

10.61822/amcs-2024-0018