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Dantzig-Wolfe Decomposition for Job Shop Scheduling

In: Column Generation

Author

Listed:
  • Sylvie Gélinas

    (École Polytechnique and GERAD)

  • François Soumis

    (École Polytechnique and GERAD)

Abstract

This chapter presents a formulation for the job shop problem based on Dantzig-Wolfe decomposition with a subproblem for each machine. Each subproblem is a sequencing problem on a single machine with time windows. The formulation is used within an exact algorithm capable of solving problems with objectives C max, T max, as well as an objective consistent with the Just-In-Time principle. This objective involves an irregular cost function of operation completion times. Numerical results are presented for 2 to 10 machine problems involving up to 500 operations.

Suggested Citation

  • Sylvie Gélinas & François Soumis, 2005. "Dantzig-Wolfe Decomposition for Job Shop Scheduling," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 271-302, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25486-9_10
    DOI: 10.1007/0-387-25486-2_10
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    Cited by:

    1. Bürgy, Reinhard & Bülbül, Kerem, 2018. "The job shop scheduling problem with convex costs," European Journal of Operational Research, Elsevier, vol. 268(1), pages 82-100.
    2. Monaci, Marta & Agasucci, Valerio & Grani, Giorgio, 2024. "An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents," European Journal of Operational Research, Elsevier, vol. 312(3), pages 910-926.

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