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A polynomial algorithm for P | pj=1, rj, outtree | ∑ Cj

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Abstract.

A polynomial algorithm is proposed for two scheduling problems for which the complexity status was open. A set of jobs with unit processing times, release dates and outtree precedence relations has to be processed on parallel identical machines such that the total completion time ∑ C j is minimized. It is shown that the problem can be solved in O(n 2) time if no preemption is allowed. Furthermore, it is proved that allowing preemption does not reduce the optimal objective value, which verifies a conjecture of Baptiste & Timkovsky [1].

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Authors and Affiliations

  1. Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany (e-mail: peter@mathematik.uni-osnabrueck.de), , , , , , DE

    Peter Brucker

  2. University of Twente, Faculty of Mathematical Sciences, P.O. Box 217, 7500 AE Enschede, The Netherlands (e-mail: J.L.Hurink@math.utwente.nl), , , , , , NL

    Johann Hurink

  3. Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany (e-mail: sigrid@mathematik.uni-osnabrueck.de), , , , , , DE

    Sigrid Knust

Authors
  1. Peter Brucker
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  2. Johann Hurink
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  3. Sigrid Knust
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Additional information

Manuscript received: March 2001/Final version received: April 2002

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ID="*"  Supported by the DFG, Project `Komplexe Maschinen-Schedulingprobleme'.

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Brucker, P., Hurink, J. & Knust, S. A polynomial algorithm for P | pj=1, rj, outtree | ∑ Cj . Mathematical Methods of OR 56, 407–412 (2003). https://doi.org/10.1007/s001860200228

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  • DOI: https://doi.org/10.1007/s001860200228

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