Abstract
In this paper, a single machine preemptive scheduling problem to minimize the weighted number of late jobs is considered under the assumption that release and due date intervals are nested and certain specified jobs have to be completed on time, that is, some of the due dates are in fact deadlines. Sidney [8] was the first who considered the problem to minimize the number of late jobs in the situation when certain specified jobs have to be on time. Unlike [8], we consider this situation in the case of given release dates and weights of jobs subject to nested release and due date intervals.
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