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An Exact Algorithm for the Two-Dimensional Strip-Packing Problem

Author

Listed:
  • Marco Antonio Boschetti

    (Department of Mathematics, University of Bologna, 47023 Cesena, Italy)

  • Lorenza Montaletti

    (Department of Mathematics, University of Bologna, 47023 Cesena, Italy)

Abstract

This paper considers the two-dimensional strip-packing problem (2SP) in which a set of rectangular items have to be orthogonally packed, without overlapping, into a strip of a given width and infinite height by minimizing the overall height of the packing. The 2SP is NP-hard in the strong sense and finds many practical applications. We propose reduction procedures, lower and upper bounds, and an exact algorithm for the 2SP. The new lower bounds are both combinatorial bounds and bounds derived from different relaxations of mathematical formulations of the 2SP. The new upper bounds are obtained by constructive heuristics based on different strategies to place the items into the strip. The new exact method is based on a branch-and-bound approach. Computational results on different sets of test problems derived from the literature show the effectiveness of the new lower and upper bounds and of the new exact algorithm.

Suggested Citation

  • Marco Antonio Boschetti & Lorenza Montaletti, 2010. "An Exact Algorithm for the Two-Dimensional Strip-Packing Problem," Operations Research, INFORMS, vol. 58(6), pages 1774-1791, December.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:6:p:1774-1791
    DOI: 10.1287/opre.1100.0833
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    References listed on IDEAS

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    Cited by:

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    2. Zhang, Xiangyi & Chen, Lu & Gendreau, Michel & Langevin, André, 2022. "A branch-and-cut algorithm for the vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 302(1), pages 259-269.
    3. Jean-François Côté & Mohamed Haouari & Manuel Iori, 2021. "Combinatorial Benders Decomposition for the Two-Dimensional Bin Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 963-978, July.
    4. 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.
    5. Côté, J.F. & Guastaroba, G. & Speranza, M.G., 2017. "The value of integrating loading and routing," European Journal of Operational Research, Elsevier, vol. 257(1), pages 89-105.
    6. de Queiroz, Thiago A. & Miyazawa, Flávio K., 2013. "Two-dimensional strip packing problem with load balancing, load bearing and multi-drop constraints," International Journal of Production Economics, Elsevier, vol. 145(2), pages 511-530.
    7. Gleb Belov & Heide Rohling, 2013. "LP Bounds in an Interval-Graph Algorithm for Orthogonal-Packing Feasibility," Operations Research, INFORMS, vol. 61(2), pages 483-497, April.
    8. Kaiyuan Liu & Hongyu Zhang & Chong Wang & Hui Li & Yongquan Chen & Qiong Chen, 2023. "Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins," Mathematics, MDPI, vol. 11(23), pages 1-22, November.
    9. Kartak, Vadim M. & Ripatti, Artem V., 2018. "The minimum raster set problem and its application to the d-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 33-39.
    10. Jean-François Côté & Mauro Dell'Amico & Manuel Iori, 2014. "Combinatorial Benders' Cuts for the Strip Packing Problem," Operations Research, INFORMS, vol. 62(3), pages 643-661, June.
    11. Jéssica Gabriela Almeida Cunha & Vinícius Loti de Lima & Thiago Alves Queiroz, 2020. "Grids for cutting and packing problems: a study in the 2D knapsack problem," 4OR, Springer, vol. 18(3), pages 293-339, September.
    12. Krzysztof Fleszar, 2016. "An Exact Algorithm for the Two-Dimensional Stage-Unrestricted Guillotine Cutting/Packing Decision Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 703-720, November.
    13. Jean-François Côté & Michel Gendreau & Jean-Yves Potvin, 2014. "An Exact Algorithm for the Two-Dimensional Orthogonal Packing Problem with Unloading Constraints," Operations Research, INFORMS, vol. 62(5), pages 1126-1141, October.
    14. Jean-François Côté & Michel Gendreau & Jean-Yves Potvin, 2020. "The Vehicle Routing Problem with Stochastic Two-Dimensional Items," Transportation Science, INFORMS, vol. 54(2), pages 453-469, March.
    15. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2011. "A skyline heuristic for the 2D rectangular packing and strip packing problems," European Journal of Operational Research, Elsevier, vol. 215(2), pages 337-346, December.
    16. Maxence Delorme & Manuel Iori, 2020. "Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 101-119, January.
    17. Stéphane Grandcolas & Cyril Pain-Barre, 2022. "A hybrid metaheuristic for the two-dimensional strip packing problem," Annals of Operations Research, Springer, vol. 309(1), pages 79-102, February.

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