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An exact algorithm for scheduling identical coupled tasks

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Abstract.

The coupled task problem is to schedule n jobs on one machine where each job consists of two subtasks with required delay time between them. The objective is to minimize the makespan. This problem was analyzed in depth by Orman and Potts [3]. They investigated the complexity of different cases depending on the lengths a i and b i of the two subtasks and the delay time L i . -hardness proofs or polynomial algorithms were given for all cases except for the one where a i =a, b i =b and L i =L. In this paper we present an exact algorithm for this problem with time complexity O(nr 2L) where holds. Therefore the algorithm is linear in the number of jobs for fixed L.

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Authors and Affiliations

  1. Institute of Computer Science, University of Heidelberg, Im Neuenheimer Feld 368, D-69120, Heidelberg, Germany

    Dino Ahr, Marcus Oswald & Gerhard Reinelt

  2. Department of Informatics, Juhász Gyula Teacher’s Training College, University of Szeged, Pf. 396, H-6720, Szeged, Hungary

    József Békési & Gábor Galambos

Authors
  1. Dino Ahr
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  2. József Békési
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  3. Gábor Galambos
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  4. Marcus Oswald
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  5. Gerhard Reinelt
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Additional information

Acknowledgements. The authors are grateful to Hans Kellerer who called their attention to this problem.

Research was supported by DAAD exchange program 324 PPP-Ungarn.

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Ahr, D., Békési, J., Galambos, G. et al. An exact algorithm for scheduling identical coupled tasks. Math Meth Oper Res 59, 193–203 (2004). https://doi.org/10.1007/s001860300328

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  • DOI: https://doi.org/10.1007/s001860300328

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