IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v48y2024i4d10.1007_s10878-024-01221-y.html
   My bibliography  Save this article

Algorithms for the bin packing problem with scenarios

Author

Listed:
  • Yulle G. F. Borges

    (University of Campinas)

  • Vinícius L. Lima

    (University of Campinas)

  • Flávio K. Miyazawa

    (University of Campinas)

  • Lehilton L. C. Pedrosa

    (University of Campinas)

  • Thiago A. Queiroz

    (Federal University of Catalão)

  • Rafael C. S. Schouery

    (University of Campinas)

Abstract

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose approximation algorithms whose ratios are bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant, that is, not a part of the input. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential set-cover model and a variable neighborhood search heuristic. Experiments show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:4:d:10.1007_s10878-024-01221-y
    DOI: 10.1007/s10878-024-01221-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-024-01221-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-024-01221-y?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. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    2. Ruslan Sadykov & François Vanderbeck, 2013. "Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 244-255, May.
    3. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    4. Baghalian, Atefeh & Rezapour, Shabnam & Farahani, Reza Zanjirani, 2013. "Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case," European Journal of Operational Research, Elsevier, vol. 227(1), pages 199-215.
    5. Wei, Lijun & Lai, Minghui & Lim, Andrew & Hu, Qian, 2020. "A branch-and-price algorithm for the two-dimensional vector packing problem," European Journal of Operational Research, Elsevier, vol. 281(1), pages 25-35.
    6. Baldi, Mauro Maria & Manerba, Daniele & Perboli, Guido & Tadei, Roberto, 2019. "A Generalized Bin Packing Problem for parcel delivery in last-mile logistics," European Journal of Operational Research, Elsevier, vol. 274(3), pages 990-999.
    7. 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.
    8. Pereira, Jordi, 2016. "Procedures for the bin packing problem with precedence constraints," European Journal of Operational Research, Elsevier, vol. 250(3), pages 794-806.
    9. Attila Bódis & János Balogh, 2019. "Bin packing problem with scenarios," 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. 27(2), pages 377-395, June.
    10. 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.
    11. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    12. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    13. 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.
    14. Saint-Guillain, Michael & Paquay, Célia & Limbourg, Sabine, 2021. "Time-dependent stochastic vehicle routing problem with random requests: Application to online police patrol management in Brussels," European Journal of Operational Research, Elsevier, vol. 292(3), pages 869-885.
    15. 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.
    16. Andrea Bettinelli & Alberto Ceselli & Giovanni Righini, 2010. "A branch-and-price algorithm for the variable size bin packing problem with minimum filling constraint," Annals of Operations Research, Springer, vol. 179(1), pages 221-241, September.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    3. 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.
    4. 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.
    5. Wuttke, David A. & Heese, H. Sebastian, 2018. "Two-dimensional cutting stock problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 265(1), pages 303-315.
    6. Zhu, Wenbin & Huang, Weili & Lim, Andrew, 2012. "A prototype column generation strategy for the multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 223(1), pages 27-39.
    7. Artur Pessoa & Ruslan Sadykov & Eduardo Uchoa, 2021. "Solving Bin Packing Problems Using VRPSolver Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-25, June.
    8. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    9. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
    10. Katrin Heßler & Stefan Irnich & Tobias Kreiter & Ulrich Pferschy, 2020. "Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System," Working Papers 2009, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    11. 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.
    12. 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.
    13. 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.
    14. Herbert Meyr & Mirko Kiel, 2022. "Minimizing setups and waste when printing labels of consumer goods," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 733-761, September.
    15. Becker, Henrique & Buriol, Luciana S., 2019. "An empirical analysis of exact algorithms for the unbounded knapsack problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 84-99.
    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. Dell’Amico, Mauro & Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2019. "Mathematical models and decomposition methods for the multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(3), pages 886-899.
    18. Furini, Fabio & Malaguti, Enrico & Medina Durán, Rosa & Persiani, Alfredo & Toth, Paolo, 2012. "A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size," European Journal of Operational Research, Elsevier, vol. 218(1), pages 251-260.
    19. Lijun Wei & Zhixing Luo, & Roberto Baldacci & Andrew Lim, 2020. "A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 428-443, April.
    20. Adejuyigbe O. Fajemisin & Steven D. Prestwich & Laura Climent, 2023. "Cutting uncertain stock and vehicle routing in a sustainability forestry harvesting problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 139-164, April.

    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:spr:jcomop:v:48:y:2024:i:4:d:10.1007_s10878-024-01221-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.