Abstract
We consider the online scheduling with job rejection to minimize the total weighted completion time of the scheduled jobs plus the total rejection penalty of the rejected jobs. In the problem, a set of independent jobs arriving online over time has to be scheduled with the flexibility of rejecting some of the jobs, where preemption is not allowed and the information of each job, including its processing time, release date, weight, and rejection penalty, is not known in advance. For this problem, using a technique named Greedy-Interval-Rejection, we provide an online algorithm with a competitive ratio of at most \(4+\varepsilon \) on identical machines and an online algorithm with a competitive ratio of at most 8 on unrelated machines, respectively.
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