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New algorithms and complexity status of the reducibility problem of sequences in open shop scheduling minimizing the makespan

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  • Michael Andresen
  • Tanka Dhamala

Abstract

We consider the problem of minimizing the makespan in open shop scheduling. The decision problem whether a given sequence in open shop scheduling is irreducible has already been considered, however, has not been solved yet. A sequence is an acyclic orientation of the Hamming graph K n ×K m . Irreducible sequences in open shop are the local optimal elements. We present two variants of algorithms based on the specific properties of the H-comparability graph. The first is polynomial whereas the second is exponential. The irreducibility is co-NP. The stated properties argue whether it belongs to P. The complexity status of the considered decision problem is updated. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Michael Andresen & Tanka Dhamala, 2012. "New algorithms and complexity status of the reducibility problem of sequences in open shop scheduling minimizing the makespan," Annals of Operations Research, Springer, vol. 196(1), pages 1-26, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:1-26:10.1007/s10479-012-1075-8
    DOI: 10.1007/s10479-012-1075-8
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    References listed on IDEAS

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    1. H. Bräsel & M. Harborth & T. Tautenhahn & P. Willenius, 1999. "On the set of solutions of the open shop problem," Annals of Operations Research, Springer, vol. 92(0), pages 241-263, January.
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    Cited by:

    1. Tal Grinshpoun & Hagai Ilani & Elad Shufan, 2017. "The representation of partially-concurrent open shop problems," Annals of Operations Research, Springer, vol. 252(2), pages 455-469, May.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

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    2. Tal Grinshpoun & Hagai Ilani & Elad Shufan, 2017. "The representation of partially-concurrent open shop problems," Annals of Operations Research, Springer, vol. 252(2), pages 455-469, May.
    3. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

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