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Scheduling on a proportionate flowshop to minimise total late work

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  • Enrique Gerstl
  • Baruch Mor
  • Gur Mosheiov

Abstract

We study a scheduling problem to minimise total late work, i.e. each job is penalised according to the duration of its parts scheduled after its due-date. The machine setting is an m-machine proportionate flow shop. Two versions of the problem are studied: (i) the case that total late work refers to the last operation of the job (i.e. the operation performed on the last machine of the flow shop); (ii) the case that total late work refers to all the operations (on all machines). Both versions are known to be NP-hard. We prove a crucial property of an optimal schedule, and consequently introduce efficient pseudo-polynomial dynamic programming algorithms for the two versions. The dynamic programming algorithms are tested numerically and proved to perform well on large size instances.

Suggested Citation

  • Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2019. "Scheduling on a proportionate flowshop to minimise total late work," International Journal of Production Research, Taylor & Francis Journals, vol. 57(2), pages 531-543, January.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:2:p:531-543
    DOI: 10.1080/00207543.2018.1456693
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    Citations

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    Cited by:

    1. Chen, Xin & Miao, Qian & Lin, Bertrand M.T. & Sterna, Malgorzata & Blazewicz, Jacek, 2022. "Two-machine flow shop scheduling with a common due date to maximize total early work," European Journal of Operational Research, Elsevier, vol. 300(2), pages 504-511.
    2. Zhang, Xingong, 2021. "Two competitive agents to minimize the weighted total late work and the total completion time," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    3. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    4. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    5. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    6. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    7. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    8. Koulamas, Christos, 2020. "The proportionate flow shop total tardiness problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 439-444.
    9. Dvir Shabtay, 2023. "A new perspective on single-machine scheduling problems with late work related criteria," Annals of Operations Research, Springer, vol. 322(2), pages 947-966, March.

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