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Complexity and Approximation Results for Setup-Minimal Batch Scheduling with Deadlines on a Single Processor

In: Operations Research Proceedings 2018

Author

Listed:
  • Dominik Kress

    (University of Siegen)

  • Maksim Barketau

    (NAS of Belarus)

  • Erwin Pesch

    (University of Siegen
    HHL Leipzig)

  • David Müller

    (University of Siegen)

Abstract

We address the problem of sequencing n jobs that are partitioned into F families on a single processor. A setup operation is needed at the beginning of the schedule and whenever a job of one family is succeeded by a job of another family. These setup operations are assumed to not require time but are associated with a fixed setup cost which is identical for all setup operations. Jobs must be completed no later than by a given deadline. The objective is to schedule all jobs such that the total setup cost is minimized. This objective is identical to minimizing the number of setup operations. We provide a sketch of the proof of the problem’s strong NP-hardness as well as some properties of optimal solutions and an O ( n log n + n F ) $$O(n \log n + nF)$$ algorithm that approximates the cost of an optimal schedule by a factor of F. For details, we refer to our full paper.

Suggested Citation

  • Dominik Kress & Maksim Barketau & Erwin Pesch & David Müller, 2019. "Complexity and Approximation Results for Setup-Minimal Batch Scheduling with Deadlines on a Single Processor," Operations Research Proceedings, in: Bernard Fortz & Martine Labbé (ed.), Operations Research Proceedings 2018, pages 475-480, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-18500-8_59
    DOI: 10.1007/978-3-030-18500-8_59
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