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Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem

Author

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  • Alves, Cláudio
  • de Carvalho, José Valério
  • Clautiaux, François
  • Rietz, Jürgen

Abstract

In this paper, we address the 2-dimensional vector packing problem where an optimal layout for a set of items with two independent dimensions has to be found within the boundaries of a rectangle. Many practical applications in areas such as the telecommunications, transportation and production planning lead to this combinatorial problem. Here, we focus on the computation of fast lower bounds using original approaches based on the concept of dual-feasible functions.

Suggested Citation

  • Alves, Cláudio & de Carvalho, José Valério & Clautiaux, François & Rietz, Jürgen, 2014. "Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem," European Journal of Operational Research, Elsevier, vol. 233(1), pages 43-63.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:43-63
    DOI: 10.1016/j.ejor.2013.08.011
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    References listed on IDEAS

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    1. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    2. François Clautiaux & Cláudio Alves & José Valério de Carvalho, 2010. "A survey of dual-feasible and superadditive functions," Annals of Operations Research, Springer, vol. 179(1), pages 317-342, September.
    3. Carlier, Jacques & Neron, Emmanuel, 2007. "Computing redundant resources for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1452-1463, February.
    4. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
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    Citations

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    Cited by:

    1. Roberto Aringhieri & Davide Duma & Andrea Grosso & Pierre Hosteins, 2018. "Simple but effective heuristics for the 2-constraint bin packing problem," Journal of Heuristics, Springer, vol. 24(3), pages 345-357, June.
    2. Yulle G. F. Borges & Vinícius L. Lima & Flávio K. Miyazawa & Lehilton L. C. Pedrosa & Thiago A. Queiroz & Rafael C. S. Schouery, 2024. "Algorithms for the bin packing problem with scenarios," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-28, November.
    3. Hu, Qian & Zhu, Wenbin & Qin, Hu & Lim, Andrew, 2017. "A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function," European Journal of Operational Research, Elsevier, vol. 260(1), pages 70-80.
    4. Timo Gschwind & Stefan Irnich, 2014. "Dual Inequalities for Stabilized Column Generation Revisited," Working Papers 1407, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 23 Jul 2014.
    5. Katrin Heßler & Timo Gschwind & Stefan Irnich, 2017. "Stabilized Branch-and-Price Algorithms for Vector Packing Problems," Working Papers 1713, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    6. Wang, Ting & Hu, Qian & Lim, Andrew, 2022. "An exact algorithm for two-dimensional vector packing problem with volumetric weight and general costs," European Journal of Operational Research, Elsevier, vol. 300(1), pages 20-34.
    7. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    8. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).
    9. Heßler, Katrin & Gschwind, Timo & Irnich, Stefan, 2018. "Stabilized branch-and-price algorithms for vector packing problems," European Journal of Operational Research, Elsevier, vol. 271(2), pages 401-419.
    10. Bentao Su & Naiming Xie, 2020. "Single workgroup scheduling problem with variable processing personnel," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 671-684, June.
    11. Billaut, Jean-Charles & Della Croce, Federico & Grosso, Andrea, 2015. "A single machine scheduling problem with two-dimensional vector packing constraints," European Journal of Operational Research, Elsevier, vol. 243(1), pages 75-81.

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