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Single machine scheduling with non-availability interval and optional job rejection

Author

Listed:
  • Baruch Mor

    (Ariel University)

  • Dana Shapira

    (Ariel University)

Abstract

This paper studies the single machine scheduling problem with availability constraints and optional job rejection. We consider the non-resumable and resumable variants, and show that the problems remain ordinary NP-hard, even with the rejection possibility extension, by presenting pseudo-polynomial dynamic-programming (DP) solutions. We also present an enhanced running time implementation of the algorithm of Kellerer and Strusevich (Algorithmica 57(4):769–795, 2010) for the resumable scenario without job rejection. This solution is adapted to efficiently solve the machine non-availability problem with a floating interval and the problem of two competing agents on a single machine, with and without optional job rejection. Numerical experiments support the efficiency of our DP implementation.

Suggested Citation

  • Baruch Mor & Dana Shapira, 2022. "Single machine scheduling with non-availability interval and optional job rejection," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 480-497, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-022-00845-2
    DOI: 10.1007/s10878-022-00845-2
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    References listed on IDEAS

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    1. Kellerer, Hans & Strusevich, Vitaly, 2013. "Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product," European Journal of Operational Research, Elsevier, vol. 228(1), pages 24-32.
    2. Baruch Mor & Dana Shapira, 2019. "Improved algorithms for scheduling on proportionate flowshop with job-rejection," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(11), pages 1997-2003, November.
    3. Guoqing Wang & Hongyi Sun & Chengbin Chu, 2005. "Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times," Annals of Operations Research, Springer, vol. 133(1), pages 183-192, January.
    4. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    5. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Time-Changing Effects and Rate-Modifying Activities," International Series in Operations Research and Management Science, Springer, number 978-3-319-39574-6, September.
    6. Wang, Dujuan & Yin, Yunqiang & Cheng, T.C.E., 2018. "Parallel-machine rescheduling with job unavailability and rejection," Omega, Elsevier, vol. 81(C), pages 246-260.
    7. Kacem, Imed & Chu, Chengbin, 2008. "Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1080-1089, June.
    8. 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.
    9. Baruch Mor & Gur Mosheiov & Dana Shapira, 2021. "Single machine lot scheduling with optional job-rejection," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 1-11, January.
    10. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
    11. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    12. Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
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    Cited by:

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    2. 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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