Abstract
In this paper, we investigate a single processor scheduling problem where the breakdown interval emerges on the processor in an online way. In particular, in our setting, the relevant data of each job Jk, including the release date rk and the deteriorating rate bk, is known in advance. Furthermore, for each job Jk, its processing time pk is a simple linear function of its starting time Sk, i.e., pk=bkSk. We are interested in scheduling the jobs to minimize the makespan. In addition, we indicate that, there exists no online algorithm such that the competitive ratio is less than 1+bmin, where bmin=min1≤k≤nbk. Moreover, we propose an online algorithm with a competitive ratio of 1+bmax, where bmax=max1≤k≤nbk.
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