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Scheduling incompatible tasks on two machines

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  • Lushchakova, Irina N.
  • Strusevich, Vitaly A.

Abstract

The paper studies the problem of scheduling tasks on two machines to minimize the makespan. The tasks are assigned to the machine in advance. An incompatibility relation is defined over the tasks which forbids any two incompatible tasks to be processed at the same time. The problem can serve as a mathematical model for some batching problems in which the jobs are grouped in pairs on two machines. A linear-time algorithm is presented.

Suggested Citation

  • Lushchakova, Irina N. & Strusevich, Vitaly A., 2010. "Scheduling incompatible tasks on two machines," European Journal of Operational Research, Elsevier, vol. 200(2), pages 334-346, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:334-346
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    References listed on IDEAS

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    1. Kellerer, H. & Strusevich, V. A., 2003. "Scheduling parallel dedicated machines under a single non-shared resource," European Journal of Operational Research, Elsevier, vol. 147(2), pages 345-364, June.
    2. C.A. Glass & C.N. Potts & V.A. Strusevich, 2001. "Scheduling Batches with Sequential Job Processing for Two-Machine Flow and Open Shops," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 120-137, May.
    3. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
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    Cited by:

    1. Simon Thevenin & Nicolas Zufferey & Jean-Yves Potvin, 2017. "Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1588-1606, March.
    2. Fang, Kan & Wang, Shijin & Pinedo, Michael L. & Chen, Lin & Chu, Feng, 2021. "A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions," European Journal of Operational Research, Elsevier, vol. 291(1), pages 128-146.

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