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A polynomial algorithm for P | p j =1, r j , outtree | ∑ C j

Author

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  • Peter Brucker
  • Johann Hurink
  • Sigrid Knust

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]. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Peter Brucker & Johann Hurink & Sigrid Knust, 2003. "A polynomial algorithm for P | p j =1, r j , outtree | ∑ C j," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(3), pages 407-412, January.
    • Handle: RePEc:spr:mathme:v:56:y:2003:i:3:p:407-412
    DOI: 10.1007/s001860200228
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    Citations

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    Cited by:

    1. Lushchakova, Irene N., 2006. "Two machine preemptive scheduling problem with release dates, equal processing times and precedence constraints," European Journal of Operational Research, Elsevier, vol. 171(1), pages 107-122, May.
    2. Yumei Huo & Joseph Leung, 2005. "Minimizing total completion time for UET tasks with release time and outtree precedence constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 275-279, November.
    3. Bo Chen & Ed Coffman & Dariusz Dereniowski & Wiesław Kubiak, 2016. "Normal-form preemption sequences for an open problem in scheduling theory," Journal of Scheduling, Springer, vol. 19(6), pages 701-728, December.

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