Online and semi-online scheduling on two hierarchical machines with a common due date to maximize the total early work
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In this study, we investigated several online and semi-online scheduling problems on two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we designed an optimal online algorithm with a competitive ratio of √(2). For the case when the total processing time is known, we proposed an optimal semi-online algorithm with a competitive ratio of 4/3. Additionally, for the cases when the largest processing time is known, we gave 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, respectively.
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