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A mixed integer linear programming modelling for the flexible cyclic jobshop problem

Author

Listed:
  • Félix Quinton

    (LAAS-CNRS, Université de Toulouse, CNRS, UPS)

  • Idir Hamaz

    (Université de Montpellier)

  • Laurent Houssin

    (LAAS-CNRS, Université de Toulouse, CNRS, UPS)

Abstract

This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.

Suggested Citation

  • Félix Quinton & Idir Hamaz & Laurent Houssin, 2020. "A mixed integer linear programming modelling for the flexible cyclic jobshop problem," Annals of Operations Research, Springer, vol. 285(1), pages 335-352, February.
    • Handle: RePEc:spr:annopr:v:285:y:2020:i:1:d:10.1007_s10479-019-03387-9
    DOI: 10.1007/s10479-019-03387-9
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    References listed on IDEAS

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    1. Peter Brucker & Thomas Kampmeyer, 2008. "Cyclic job shop scheduling problems with blocking," Annals of Operations Research, Springer, vol. 159(1), pages 161-181, March.
    2. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    3. Thomalla, Christoph S., 2001. "Job shop scheduling with alternative process plans," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 125-134, December.
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    5. Hanen, Claire, 1994. "Study of a NP-hard cyclic scheduling problem: The recurrent job-shop," European Journal of Operational Research, Elsevier, vol. 72(1), pages 82-101, January.
    6. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    7. J.M.J. Schutten, 1998. "Practical job shop scheduling," Annals of Operations Research, Springer, vol. 83(0), pages 161-178, October.
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    Cited by:

    1. Ye Wang & Jiafu Tang, 2022. "Optimized skill configuration for the seru production system under an uncertain demand," Annals of Operations Research, Springer, vol. 316(1), pages 445-465, September.
    2. Sun, Yige & Chung, Sai-Ho & Wen, Xin & Ma, Hoi-Lam, 2021. "Novel robotic job-shop scheduling models with deadlock and robot movement considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    3. Hamaz, Idir & Houssin, Laurent & Cafieri, Sonia, 2024. "The robust cyclic job shop problem," European Journal of Operational Research, Elsevier, vol. 312(3), pages 855-865.
    4. Dauzère-Pérès, Stéphane & Ding, Junwen & Shen, Liji & Tamssaouet, Karim, 2024. "The flexible job shop scheduling problem: A review," European Journal of Operational Research, Elsevier, vol. 314(2), pages 409-432.

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