Algorithms for some maximization scheduling problems on a single machine

Authors:
E. R. Gafarov;A. A. Lazarev;F. Werner
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
Venue:
Automation and Remote Control
Year:
2010

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Abstract

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1驴max-ΣT j and for the problem of maximizing the number of tardy jobs 1驴maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1驴max-ΣT j is polynomially solvable. For several special cases of problem 1驴maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.