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Exact solution techniques for two-dimensional cutting and packing

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  • Iori, Manuel
  • de Lima, Vinícius L.
  • Martello, Silvano
  • Miyazawa, Flávio K.
  • Monaci, Michele

Abstract

We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the literature: finding a packing with minimum height, packing the items into the minimum number of bins, finding a packing of maximum value, and determining the existence of a feasible packing.

Suggested Citation

  • Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:2:p:399-415
    DOI: 10.1016/j.ejor.2020.06.050
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    4. Braam, Florian & van den Berg, Daan, 2022. "Which rectangle sets have perfect packings?," Operations Research Perspectives, Elsevier, vol. 9(C).
    5. Xiangyi Zhang & Lu Chen & Michel Gendreau & André Langevin, 2022. "Learning-Based Branch-and-Price Algorithms for the Vehicle Routing Problem with Time Windows and Two-Dimensional Loading Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1419-1436, May.
    6. Çalık, Hatice & Juwet, Marc & Yaman, Hande & Vanden Berghe, Greet, 2023. "Cargo securing under multi-drop and axle weight constraints," European Journal of Operational Research, Elsevier, vol. 307(1), pages 157-176.
    7. Silva, Elsa & Oliveira, José Fernando & Silveira, Tiago & Mundim, Leandro & Carravilla, Maria Antónia, 2023. "The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems," Omega, Elsevier, vol. 114(C).
    8. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.
    9. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam & Renaud, Jacques, 2022. "A cutting plane method and a parallel algorithm for packing rectangles in a circular container," European Journal of Operational Research, Elsevier, vol. 303(1), pages 114-128.
    10. Rapine, Christophe & Pedroso, Joao Pedro & Akbalik, Ayse, 2022. "The two-dimensional knapsack problem with splittable items in stacks," Omega, Elsevier, vol. 112(C).
    11. 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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