Abstract
In this paper, we consider two single-processor online scheduling problems with an unexpected breakdown. Speaking specifically, there is a group of nonresumable jobs being processed on the single processor. Note that the breakdown will emerge on the processor suddenly, which signifies that its beginning time and its length are unknown in advance. In this study, we are interested in scheduling the jobs so as to minimize the maximum weighted completion time. Most noticeably, when all jobs respect an agreeable condition, i.e., for each two jobs [Formula: see text] and [Formula: see text], [Formula: see text] means that [Formula: see text], we design an optimal online algorithm. In addition, for the general version, we propose an online algorithm with a competitive ratio of at most 2.
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