IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v62y2014i5p1126-1141.html
   My bibliography  Save this article

An Exact Algorithm for the Two-Dimensional Orthogonal Packing Problem with Unloading Constraints

Author

Listed:
  • Jean-François Côté

    (Département des opérations et systèmes de décision and Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport, Université Laval, Québec G1V 0A6, Canada)

  • Michel Gendreau

    (Département de mathématiques et de génie industriel, École Polytechnique de Montréal, Montréal H3C 3A7, Canada; and Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport, Université de Montréal, Montréal H3C 3J7, Canada)

  • Jean-Yves Potvin

    (Département d'informatique et de recherche opérationnelle and Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport, Université de Montréal, Montréal H3C 3J7, Canada)

Abstract

This paper describes an exact algorithm for solving a two-dimensional orthogonal packing problem with unloading constraints, which occurs as a subproblem of mixed vehicle routing and loading problems. The packing considered in this work is basically a feasibility problem involving a single bin. The problem is addressed through a decomposition approach wherein a branch-and-cut algorithm is designed for solving a one-dimensional relaxation of the original problem. When an integer solution is found in the branching tree, a subsidiary problem is solved to identify a two-dimensional packing that does not lead to any overlap and satisfies the unloading constraints. Cuts are added when the subsidiary problem proves to be infeasible. Several preprocessing techniques aimed at reducing the size of the solution space and uncovering infeasibility are also described. A numerical comparison with the best known exact method is reported at the end based on benchmark instances.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:5:p:1126-1141
    DOI: 10.1287/opre.2014.1307
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2014.1307
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2014.1307?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
    ---><---

    References listed on IDEAS

    as
    1. Sándor P. Fekete & Jörg Schepers, 2004. "A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 353-368, May.
    2. Eitan Zemel, 1989. "Easily Computable Facets of the Knapsack Polytope," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 760-764, November.
    3. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Christos T., 2009. "A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 195(3), pages 729-743, June.
    4. Manuel Iori & Silvano Martello, 2010. "Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 4-27, July.
    5. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    6. Leung, Stephen C.H. & Zhang, Zhenzhen & Zhang, Defu & Hua, Xian & Lim, Ming K., 2013. "A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 225(2), pages 199-210.
    7. Clautiaux, Francois & Carlier, Jacques & Moukrim, Aziz, 2007. "A new exact method for the two-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1196-1211, December.
    8. Manuel Iori & Silvano Martello, 2010. "Rejoinder on: Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 41-42, July.
    9. 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.
    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. Sándor P. Fekete & Jörg Schepers & Jan C. van der Veen, 2007. "An Exact Algorithm for Higher-Dimensional Orthogonal Packing," Operations Research, INFORMS, vol. 55(3), pages 569-587, June.
    12. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.
    13. Manuel Iori & Juan-José Salazar-González & Daniele Vigo, 2007. "An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints," Transportation Science, INFORMS, vol. 41(2), pages 253-264, May.
    14. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    15. 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.
    16. Kenmochi, Mitsutoshi & Imamichi, Takashi & Nonobe, Koji & Yagiura, Mutsunori & Nagamochi, Hiroshi, 2009. "Exact algorithms for the two-dimensional strip packing problem with and without rotations," European Journal of Operational Research, Elsevier, vol. 198(1), pages 73-83, October.
    17. Silvano Martello & Michele Monaci & Daniele Vigo, 2003. "An Exact Approach to the Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 310-319, August.
    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. Alonso, M.T. & Martinez-Sykora, A. & Alvarez-Valdes, R. & Parreño, F., 2022. "The pallet-loading vehicle routing problem with stability constraints," European Journal of Operational Research, Elsevier, vol. 302(3), pages 860-873.
    2. Ali, Ousmane & Côté, Jean-François & Coelho, Leandro C., 2021. "Models and algorithms for the delivery and installation routing problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 162-177.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Emmanouil E. Zachariadis & Christos D. Tarantilis & Chris T. Kiranoudis, 2017. "Vehicle routing strategies for pick-up and delivery service under two dimensional loading constraints," Operational Research, Springer, vol. 17(1), pages 115-143, April.
    8. Wei, Lijun & Hu, Qian & Lim, Andrew & Liu, Qiang, 2018. "A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 270(2), pages 448-474.
    9. 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.
    10. 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.
    11. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).
    12. Manuel Ostermeier & Sara Martins & Pedro Amorim & Alexander Hübner, 2018. "Loading constraints for a multi-compartment vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 997-1027, October.
    13. Zhi-Hua Hu & Yingxue Zhao & Sha Tao & Zhao-Han Sheng, 2015. "Finished-vehicle transporter routing problem solved by loading pattern discovery," Annals of Operations Research, Springer, vol. 234(1), pages 37-56, November.
    14. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.

    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. 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.
    2. 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.
    3. 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.
    4. Alonso, M.T. & Martinez-Sykora, A. & Alvarez-Valdes, R. & Parreño, F., 2022. "The pallet-loading vehicle routing problem with stability constraints," European Journal of Operational Research, Elsevier, vol. 302(3), pages 860-873.
    5. 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.
    6. Bonet Filella, Guillem & Trivella, Alessio & Corman, Francesco, 2023. "Modeling soft unloading constraints in the multi-drop container loading problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 336-352.
    7. Xiang Song & Dylan Jones & Nasrin Asgari & Tim Pigden, 2020. "Multi-objective vehicle routing and loading with time window constraints: a real-life application," Annals of Operations Research, Springer, vol. 291(1), pages 799-825, August.
    8. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    9. Manuel Ostermeier & Sara Martins & Pedro Amorim & Alexander Hübner, 2018. "Loading constraints for a multi-compartment vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 997-1027, October.
    10. Cherkesly, Marilène & Gschwind, Timo, 2022. "The pickup and delivery problem with time windows, multiple stacks, and handling operations," European Journal of Operational Research, Elsevier, vol. 301(2), pages 647-666.
    11. 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.
    12. Wei, Lijun & Zhang, Zhenzhen & Zhang, Defu & Leung, Stephen C.H., 2018. "A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 265(3), pages 843-859.
    13. 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.
    14. Oscar Dominguez & Angel A. Juan & Barry Barrios & Javier Faulin & Alba Agustin, 2016. "Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet," Annals of Operations Research, Springer, vol. 236(2), pages 383-404, January.
    15. 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.
    16. Zhang, Zhenzhen & Wei, Lijun & Lim, Andrew, 2015. "An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 20-35.
    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.
    18. Oscar Dominguez & Angel Juan & Barry Barrios & Javier Faulin & Alba Agustin, 2016. "Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet," Annals of Operations Research, Springer, vol. 236(2), pages 383-404, January.
    19. Mahdi Alinaghian & Komail Zamanlou & Mohammad S. Sabbagh, 2017. "A bi-objective mathematical model for two-dimensional loading time-dependent vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1422-1441, November.
    20. Wei, Lijun & Zhang, Zhenzhen & Zhang, Defu & Lim, Andrew, 2015. "A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 243(3), pages 798-814.

    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:inm:oropre:v:62:y:2014:i:5:p:1126-1141. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.