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Scheduling with State-Dependent Machine Speed

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Approximation and Online Algorithms (WAOA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9499))

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Abstract

We study a preemptive single machine scheduling problem where the machine speed is externally given and depends on the number unfinished jobs. The objective is to minimize the sum of weighted completion times. We develop a greedy algorithm that solves the problem to optimality when we work with either unit weights or unit processing times. If both weights and processing times are arbitrary, we show the problem is NP-hard by making a reduction from 3-partition.

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Acknowledgements

We thank Urtzi Ayesta for helpful discussion after posing this open question during the Daghstuhl Seminar 13111 “Scheduling” in 2013. Furthermore, we thank the organizers of this seminar and Schloss Daghstuhl for providing the right atmosphere to facilitate research.

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Authors and Affiliations

  1. Maastricht University, Maastricht, The Netherlands

    Veerle Timmermans & Tjark Vredeveld

Authors
  1. Veerle Timmermans
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  2. Tjark Vredeveld
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Corresponding author

Correspondence to Veerle Timmermans .

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Editors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Laura Sanità

  2. Technische Universität Berlin, Berlin, Berlin, Germany

    Martin Skutella

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Timmermans, V., Vredeveld, T. (2015). Scheduling with State-Dependent Machine Speed. In: Sanità, L., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2015. Lecture Notes in Computer Science(), vol 9499. Springer, Cham. https://doi.org/10.1007/978-3-319-28684-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-28684-6_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28683-9

  • Online ISBN: 978-3-319-28684-6

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