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New efficient algorithms for the two-machine no-wait chain-reentrant shop problem

Author

Listed:
  • Nazim Sami

    (Centre de Recherche sur l’Information Scientifique et Technique (CERIST)
    USTHB University)

  • Karim Amrouche

    (USTHB University
    University of Algiers 3)

  • Mourad Boudhar

    (USTHB University)

Abstract

This paper tackles the two-machine chain-reentrant flow shop scheduling problem with the no-wait constraint; we assume that each job passes from the first machine to the second and returns back to the first machine in order to execute its last operation. The objective is to minimize the makespan. In this work, we prove that the symmetric case of this problem, which is proven to be $$\mathcal NP$$ N P -hard in the strong sense, remains $$\mathcal NP$$ N P -hard. Then we provide two polynomial subproblems. For the main problem’s resolution, we propose two new efficient heuristics as well as two improved lower bounds that consistently outperform the existing methods. Additionally, we provide an effective Branch & Bound algorithm that can solve up to 100 jobs for some types of instances. These contributions not only enhance the theoretical comprehension of the problem but also offer efficient solutions supported by extensive statistical analysis over randomly generated instances.

Suggested Citation

  • Nazim Sami & Karim Amrouche & Mourad Boudhar, 2024. "New efficient algorithms for the two-machine no-wait chain-reentrant shop problem," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-29, July.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:5:d:10.1007_s10878-024-01180-4
    DOI: 10.1007/s10878-024-01180-4
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    References listed on IDEAS

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    1. Karim Amrouche & Mourad Boudhar & Nazim Sami, 2020. "Two-machine chain-reentrant flow shop with the no-wait constraint," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 14(4), pages 573-597.
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    3. Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2020. "Coupled task scheduling with exact delays: Literature review and models," European Journal of Operational Research, Elsevier, vol. 282(1), pages 19-39.
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    8. Hamilton Emmons & George Vairaktarakis, 2013. "Reentrant Flow Shops," International Series in Operations Research & Management Science, in: Flow Shop Scheduling, edition 127, chapter 0, pages 269-289, Springer.
    9. Karim Amrouche & Mourad Boudhar & Mohamed Bendraouche & Farouk Yalaoui, 2017. "Chain-reentrant shop with an exact time lag: new results," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 285-295, January.
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