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Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval

Author

Listed:
  • Imed Kacem

    (Université de Lorraine)

  • Hans Kellerer

    (ISOR, University of Graz)

  • Maryam Seifaddini

    (Université de Lorraine)

Abstract

In this paper we deal with the single machine scheduling problem with one non-availability interval to minimize the maximum lateness where jobs have positive tails. Two cases are considered. In the first one, the non-availability interval is due to the machine maintenance. In the second case, the non-availability interval is related to the operator who is organizing the execution of jobs on the machine. The contribution of this paper consists in an improved fully polynomial time approximation scheme (FPTAS) for the maintenance non-availability interval case and the elaboration of the first FPTAS for the operator non-availability interval case. The two FPTASs are strongly polynomial.

Suggested Citation

  • Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9924-4
    DOI: 10.1007/s10878-015-9924-4
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    References listed on IDEAS

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    Cited by:

    1. Yunqiang Yin & Jianyou Xu & T. C. E. Cheng & Chin‐Chia Wu & Du‐Juan Wang, 2016. "Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 172-183, March.
    2. Imed Kacem & Hans Kellerer, 2024. "Minimizing the maximum lateness for scheduling with release times and job rejection," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-22, October.
    3. Lili Zuo & Zhenxia Sun & Lingfa Lu & Liqi Zhang, 2019. "Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval," Mathematics, MDPI, vol. 7(8), pages 1-8, July.
    4. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.
    5. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.
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    7. Lin, Ran & Wang, Jun-Qiang & Liu, Zhixin & Xu, Jun, 2023. "Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions," European Journal of Operational Research, Elsevier, vol. 309(1), pages 53-64.

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