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Abstract
We consider the problem of scheduling jobs with release times and due dates on a single machine to minimize the maximal job lateness. This problem is NP-hard, and its version when the job processing times are restricted to p, 2 p, 3 p, 4 p, …, for an integer p, is also NP-hard. We consider the case when the maximal job processing time is kp, for any constant k, and propose its polynomial-time solution. We easily establish that the version of this problem with unrestricted k is NP-hard. Moreover, it is strongly NP-hard if p has no exponential-time dependence on the maximal job due date. From a practical point of view, this is a realistic assumption.
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