Abstract
In this paper we consider the maximization of the weighted number of early jobs on a single machine with non-availability constraints. We deal with the resumable and the non-resumable cases. We show that the resumable version of this problem has a fully polynomial time approximation scheme (FPTAS) even if the number of the non-availability intervals is variable and a subset of jobs has deadlines instead of due dates. For the non-resumable version we remark that the problem cannot admit an FPTAS even if all due dates are equal and only one non-availability interval occurs. Nevertheless, we show in this case that it admits a polynomial time approximation scheme (PTAS) for a constant number of non-availability intervals and arbitrary due dates.
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