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Automation and Remote Control

, Volume 71, Issue 10, pp 2070–2084 | Cite as

Algorithms for some maximization scheduling problems on a single machine

  • E. R. Gafarov
  • A. A. Lazarev
  • F. Werner
Scheduling Problems on a Single Machine

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‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖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‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖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.

Keywords

Remote Control Optimal Schedule Idle Time Single Machine Total Tardiness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • E. R. Gafarov
    • 1
  • A. A. Lazarev
    • 1
  • F. Werner
    • 2
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.Otto-von-Guericke-Universität MagdeburgMagdeburgGermany

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