Multi-machine Scheduling Problem with Optimal Due Interval Assignment Subject to Generalized sum Type Criterion
In this paper, we consider a multi-machine scheduling problem, in which to each job a due interval should be assigned. In the scientific literature of scheduling theory, only an assignment of due date was considered. However in our case, to each job a due interval should be assigned. Due interval is a generalization of classical due date and describes a time interval, in which a job should be finished. For the considered problem, we should find a schedule of jobs and a common due interval such that the sum of: the total tardiness, the total earliness and due interval parameters is minimized. We proved an ordinary NP-completeness of the problem using the well known NP-complete partition problem. A heuristic algorithm solving the problem with its experimental analysis is also presented.
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