IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v233y2014i1p43-63.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713006760
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.08.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liao, Chung-Shou & Hsu, Chia-Hong, 2013. "New lower bounds for the three-dimensional orthogonal bin packing problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 244-252.
    2. 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.
    3. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    4. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    5. H. Terashima-Marín & P. Ross & C. Farías-Zárate & E. López-Camacho & M. Valenzuela-Rendón, 2010. "Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems," Annals of Operations Research, Springer, vol. 179(1), pages 369-392, September.
    6. 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.
    7. David Pisinger, 2007. "Denser Packings Obtained in O ( n log log n ) Time," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 395-405, August.
    8. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    9. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    10. Gregory S. Taylor & Yupo Chan & Ghulam Rasool, 2017. "A three-dimensional bin-packing model: exact multicriteria solution and computational complexity," Annals of Operations Research, Springer, vol. 251(1), pages 397-427, April.
    11. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2021. "Queue-constrained packing: A vehicle ferry case study," European Journal of Operational Research, Elsevier, vol. 289(2), pages 727-741.
    12. 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.
    13. Mhand Hifi & Rym M'Hallah, 2005. "An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems," Operations Research, INFORMS, vol. 53(1), pages 140-150, February.
    14. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.
    15. John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie, 2022. "An introduction to stochastic bin packing-based server consolidation with conflicts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 296-331, July.
    16. Sierra-Paradinas, María & Soto-Sánchez, Óscar & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier & Gallego, Micael, 2021. "An exact model for a slitting problem in the steel industry," European Journal of Operational Research, Elsevier, vol. 295(1), pages 336-347.
    17. Gokmen Tayfur, 2017. "Modern Optimization Methods in Water Resources Planning, Engineering and Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(10), pages 3205-3233, August.
    18. Christelle Garrouste & Cyrille Piatecki & Yvan Stroppa, 2021. "Matching dynamics and optima in a multi-agents labor market setting, 2015," Working Papers hal-03245585, HAL.
    19. M. Muntazir Mehdi & Le Wang & Sean P. Willems, 2022. "Developing a Maximum Inscribed Rectangle Heuristic to Satisfy Rush Orders for Heavy Plate Steel," Interfaces, INFORMS, vol. 52(3), pages 283-294, May.
    20. Mateus Martin & Horacio Hideki Yanasse & Luiz Leduíno Salles-Neto, 2022. "Pattern-based ILP models for the one-dimensional cutting stock problem with setup cost," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 557-582, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:43-63. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.