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Benders decomposition for the mixed no-idle permutation flowshop scheduling problem

Author

Listed:
  • Tolga Bektaş

    (University of Liverpool)

  • Alper Hamzadayı

    (Van Yuzuncu Yil University)

  • Rubén Ruiz

    (Universitat Politècnica de València)

Abstract

The mixed no-idle flowshop scheduling problem arises in modern industries including integrated circuits, ceramic frit and steel production, among others, and where some machines are not allowed to remain idle between jobs. This paper describes an exact algorithm that uses Benders decomposition with a simple yet effective enhancement mechanism that entails the generation of additional cuts by using a referenced local search to help speed up convergence. Using only a single additional optimality cut at each iteration, and combined with combinatorial cuts, the algorithm can optimally solve instances with up to 500 jobs and 15 machines that are otherwise not within the reach of off-the-shelf optimization software, and can easily surpass ad-hoc existing metaheuristics. To the best of the authors’ knowledge, the algorithm described here is the only exact method for solving the mixed no-idle permutation flowshop scheduling problem.

Suggested Citation

  • Tolga Bektaş & Alper Hamzadayı & Rubén Ruiz, 2020. "Benders decomposition for the mixed no-idle permutation flowshop scheduling problem," Journal of Scheduling, Springer, vol. 23(4), pages 513-523, August.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:4:d:10.1007_s10951-020-00637-8
    DOI: 10.1007/s10951-020-00637-8
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    References listed on IDEAS

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    1. Ruiz, Ruben & Maroto, Concepcion, 2005. "A comprehensive review and evaluation of permutation flowshop heuristics," European Journal of Operational Research, Elsevier, vol. 165(2), pages 479-494, September.
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    4. I. Adiri & D. Pohoryles, 1982. "Flowshop/no‐idle or no‐wait scheduling to minimize the sum of completion times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 495-504, September.
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    6. Quan-Ke Pan & Ling Wang, 2008. "A novel differential evolution algorithm for no-idle permutation flow-shop scheduling problems," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 2(3), pages 279-297.
    7. Goncharov, Yaroslav & Sevastyanov, Sergey, 2009. "The flow shop problem with no-idle constraints: A review and approximation," European Journal of Operational Research, Elsevier, vol. 196(2), pages 450-456, July.
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    Cited by:

    1. Chen-Yang Cheng & Shih-Wei Lin & Pourya Pourhejazy & Kuo-Ching Ying & Yu-Zhe Lin, 2021. "No-Idle Flowshop Scheduling for Energy-Efficient Production: An Improved Optimization Framework," Mathematics, MDPI, vol. 9(12), pages 1-18, June.

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