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Content available Online and semi-online scheduling on two hierarchical machines with a common due date to maximize the total early work
Xiao Man, Liu Xiaoqiao, Li Weidong, Chen Xin, Sterna Malgorzata, Blazewicz Jacek
International Journal of Applied Mathematics and Computer Science
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2024
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Vol. 34, no. 2
253--261
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.
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