We consider a semi-online scheduling problem on a single machine with an unexpected breakdown period. In the problem, each job has a processing time and a subsequent delivery time. All these data are known in the beginning. The scheduler has to determine a sequence S of these jobs for processing. After S is given, a machine unavailability period may occur where its starting time and length are not known in advance. The objective is to minimize the time by which all jobs are delivered. We present an online algorithm with a competitive ratio of \(\frac{\sqrt{5}+1}{2}\approx 1.618\), which improves the previously known algorithm with \(\frac{2+\sqrt{2}}{2}\approx 1.707\)-competitive.

中文翻译：

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改进的半在线算法，可在单机上进行意外故障调度

我们考虑一台机器上有意外故障期的半在线调度问题。在问题中，每个作业都有一个处理时间和一个后续的交付时间。所有这些数据在一开始都是已知的。调度程序必须确定这些作业的顺序S以进行处理。给定S后，可能会出现机器不可用时间段，在此期间机器的启动时间和长度事先未知。目的是最大程度地减少交付所有作业的时间。我们提出了一种具有竞争比\（\ frac {\ sqrt {5} +1} {2} \约1.618 \）的在线算法，该算法改进了先前已知的\（\ frac {2+ \ sqrt {2 }} {2} \约1.707 \）-竞争性。