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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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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.

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Acknowledgements

We thank the anonymous referees for their comments and suggestions which improved the quality of the paper. The second author would like to thank DAAD for the support of his research visit at University of Magdeburg, Germany, May-June 2010.

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Authors and Affiliations

  1. Department of Mathematics, Otto-von-Guericke-University Magdeburg, P.O. Box 4120, 39016, Magdeburg, Germany

    Michael Andresen

  2. Central Department of Mathematics, TU, P.O. Box 13143, Kathmandu, Nepal

    Tanka Nath Dhamala

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  1. Michael Andresen
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  2. Tanka Nath Dhamala
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Correspondence to Tanka Nath Dhamala.

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Andresen, M., Dhamala, T.N. New algorithms and complexity status of the reducibility problem of sequences in open shop scheduling minimizing the makespan. Ann Oper Res 196, 1–26 (2012). https://doi.org/10.1007/s10479-012-1075-8

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