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An on-line algorithm for the single machine unbounded parallel-batching scheduling with large delivery times. (English) Zbl 1260.68042

Summary: We consider the on-line version of the single machine unbounded parallel-batching scheduling with delivery times of jobs. Each job’s information, such as processing time \(p_j\) and delivery time \(q_j\), is not known in advance and becomes known at its arrival time. Once the processing of a job is completed, we deliver it to the destination. Here, the time is continuous. The objective is to minimize the time by which all jobs have been delivered. In this paper, we consider job system with large delivery times, i.e., \(q_j\geq p_j\), for each job \(J_j\). We provide an on-line algorithm with a competitive ratio \((\sqrt{5}+1)/2\approx 1.618\) and show that any on-line algorithm has a competitive ratio of at least \((\sqrt{3}+1)/2\approx 1.366\).

MSC:

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
68W27 Online algorithms; streaming algorithms
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References:

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