Parallel processor scheduling problems with optimal due interval

Abstract

In the paper we consider two problems, in which we should find a schedule of jobs on parallel processors and a common due interval determination for all jobs such that the criterion value is minimized. A due interval is a generalization of the classical due date and describes a time interval, in which a job should be finished. In the first problem we minimize the sum of the total tardiness, total earliness and due interval size. In the second problem, we minimize the weighted maximum of the following three parts: maximum tardiness, maximum earliness and due interval size. We proved that the considered problems are equivalent to the strong NP-hard classical scheduling problem with the parallel processors subject to the minimization of the makespan criterion.