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Two-dimensional cutting stock problem with sequence dependent setup times

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  • Wuttke, David A.
  • Heese, H. Sebastian

Abstract

Motivated by a firm in the technical textile industry, we study a two-dimensional cutting stock problem with sequence dependent setup times and permissible tolerances. We provide a sequential heuristic with feedback loop based on the approach of Gilmore and Gomory and formulate the sequencing problem as a mixed integer program. We derive a lower bound algorithm and demonstrate the near-optimal performance of our heuristic. Finally, we use real data to test our heuristic and illustrate its applicability to a problem of realistic size.

Suggested Citation

  • Wuttke, David A. & Heese, H. Sebastian, 2018. "Two-dimensional cutting stock problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 265(1), pages 303-315.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:303-315
    DOI: 10.1016/j.ejor.2017.07.036
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    References listed on IDEAS

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    Cited by:

    1. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
    2. Douglas Nogueira Nascimento & Adriana Cristina Cherri & José Fernando Oliveira, 2022. "The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches," Operational Research, Springer, vol. 22(5), pages 5363-5403, November.
    3. Heiner Ackermann & Erik Diessel, 2020. "A hierarchical approach for solving an integrated packing and sequence-optimization problem in production of glued laminated timber," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 263-288, October.
    4. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    5. Gislaine Mara Melega & Silvio Alexandre de Araujo & Reinaldo Morabito, 2020. "Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems," Annals of Operations Research, Springer, vol. 295(2), pages 695-736, December.
    6. Silva, Eduardo M. & Melega, Gislaine M. & Akartunalı, Kerem & de Araujo, Silvio A., 2023. "Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 304(2), pages 443-460.
    7. Hadj Salem, Khadija & Silva, Elsa & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "Mathematical models for the two-dimensional variable-sized cutting stock problem in the home textile industry," European Journal of Operational Research, Elsevier, vol. 306(2), pages 549-566.

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