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Scheduling UET task systems with concurrency on two parallel identical processors

Author

Listed:
  • Peter Brucker
  • Sigrid Knust
  • Duncan Roper
  • Yakov Zinder

Abstract

Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Peter Brucker & Sigrid Knust & Duncan Roper & Yakov Zinder, 2000. "Scheduling UET task systems with concurrency on two parallel identical processors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 369-387, December.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:3:p:369-387
    DOI: 10.1007/s001860000089
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    Cited by:

    1. Philippe Lacomme & Aziz Moukrim & Alain Quilliot & Marina Vinot, 2019. "Integration of routing into a resource-constrained project scheduling problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 421-464, December.
    2. Alexander Kononov & Yulia Zakharova, 2022. "Speed scaling scheduling of multiprocessor jobs with energy constraint and makespan criterion," Journal of Global Optimization, Springer, vol. 83(3), pages 539-564, July.
    3. Blazewicz, Jacek & Dell'Olmo, Paolo & Drozdowski, Maciej & Maczka, Przemyslaw, 2003. "Scheduling multiprocessor tasks on parallel processors with limited availability," European Journal of Operational Research, Elsevier, vol. 149(2), pages 377-389, September.
    4. Oguz, Ceyda & Zinder, Yakov & Ha Do, Van & Janiak, Adam & Lichtenstein, Maciej, 2004. "Hybrid flow-shop scheduling problems with multiprocessor task systems," European Journal of Operational Research, Elsevier, vol. 152(1), pages 115-131, January.

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