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Semi-online scheduling with known maximum job size on two uniform machines

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Abstract

In this paper, we investigate the semi-online scheduling problem with known maximum job size on two uniform machines with the speed ratio s≥1. The objective is to minimize the makespan. Two algorithms are presented, where the first is optimal for \(1\leq s\leq\sqrt{2}\) , and the second is optimal for 1.559≤s≤2 and \(s\ge \frac{3+\sqrt{17}}{2}\) . In addition, the improvement on lower bounds is made for \(2<s<\frac{3+\sqrt{17}}{2}\) .

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Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Qian Cao & Zhaohui Liu

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  1. Qian Cao
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  2. Zhaohui Liu
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Correspondence to Zhaohui Liu.

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Cao, Q., Liu, Z. Semi-online scheduling with known maximum job size on two uniform machines. J Comb Optim 20, 369–384 (2010). https://doi.org/10.1007/s10878-009-9214-0

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  • DOI: https://doi.org/10.1007/s10878-009-9214-0

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