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Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one

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  • Evgeny Gafarov
  • Alexander Lazarev
  • Frank Werner

Abstract

We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity status of the problem under consideration which was open. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2012. "Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one," Annals of Operations Research, Springer, vol. 196(1), pages 247-261, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:247-261:10.1007/s10479-011-1055-4
    DOI: 10.1007/s10479-011-1055-4
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    1. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Pascal Babu & Laurent Peridy & Eric Pinson, 2004. "A Branch and Bound Algorithm to Minimize Total Weighted Tardiness on a Single Processor," Annals of Operations Research, Springer, vol. 129(1), pages 33-46, July.
    3. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    4. Mohamed Aloulou & Mikhail Kovalyov & Marie-Claude Portmann, 2004. "Maximization Problems in Single Machine Scheduling," Annals of Operations Research, Springer, vol. 129(1), pages 21-32, July.
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