IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v21y2023i3d10.1007_s10288-022-00522-4.html
   My bibliography  Save this article

Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer

Author

Listed:
  • Manuel V. C. Vieira

    (Universidade NOVA de Lisboa)

  • Margarida Carvalho

    (Université de Montréal)

Abstract

Motivated by a real-world application, we present a multi-container loading problem with 3-open dimensions. We formulate it as a biobjective mixed-integer nonlinear program with lexicographic objectives in order to reflect the decision maker’s optimization priorities. The first objective is to minimize the number of containers, while the second objective is to minimize the volume of those containers. Besides showing the NP-hardness of this sequential optimization problem, we provide bounds for it which are used in the three proposed algorithms, as well as, on their evaluation when a certificate of optimality is not available. The first is an exact parametric-based approach to tackle the lexicographic optimization through the second objective of the problem. Nevertheless, given that the parametric programs correspond to large nonlinear mixed-integer optimizations, we present a heuristic that is entirely mathematical-programming based. The third algorithm enhances the solution quality of the heuristic. These algorithms are specifically tailored for the real-world application. The effectiveness and efficiency of the devised heuristics is demonstrated with numerical experiments.

Suggested Citation

  • Manuel V. C. Vieira & Margarida Carvalho, 2023. "Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer," 4OR, Springer, vol. 21(3), pages 491-512, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00522-4
    DOI: 10.1007/s10288-022-00522-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-022-00522-4
    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/s10288-022-00522-4?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. Manuel V. C. Vieira & Flora Ferreira & José C. M. Duque & Rui M. P. Almeida, 2021. "On the packing process in a shoe manufacturer," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(4), pages 853-864, March.
    2. Toffolo, Túlio A.M. & Esprit, Eline & Wauters, Tony & Vanden Berghe, Greet, 2017. "A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 526-538.
    3. 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.
    4. Kristina Yancey Spencer & Pavel V. Tsvetkov & Joshua J. Jarrell, 2019. "A greedy memetic algorithm for a multiobjective dynamic bin packing problem for storing cooling objects," Journal of Heuristics, Springer, vol. 25(1), pages 1-45, February.
    5. Araya, Ignacio & Moyano, Mauricio & Sanchez, Cristobal, 2020. "A beam search algorithm for the biobjective container loading problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 417-431.
    6. Liu, D.S. & Tan, K.C. & Huang, S.Y. & Goh, C.K. & Ho, W.K., 2008. "On solving multiobjective bin packing problems using evolutionary particle swarm optimization," European Journal of Operational Research, Elsevier, vol. 190(2), pages 357-382, October.
    7. Chen, C. S. & Lee, S. M. & Shen, Q. S., 1995. "An analytical model for the container loading problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 68-76, January.
    8. 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.
    9. Alonso, M.T. & Alvarez-Valdes, R. & Iori, M. & Parreño, F. & Tamarit, J.M., 2017. "Mathematical models for multicontainer loading problems," Omega, Elsevier, vol. 66(PA), pages 106-117.
    10. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, June.
    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. 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.
    2. Kurpel, Deidson Vitorio & Scarpin, Cassius Tadeu & Pécora Junior, José Eduardo & Schenekemberg, Cleder Marcos & Coelho, Leandro C., 2020. "The exact solutions of several types of container loading problems," European Journal of Operational Research, Elsevier, vol. 284(1), pages 87-107.
    3. Novas, Juan M. & Ramello, Juan Ignacio & Rodríguez, María Analía, 2020. "Generalized disjunctive programming models for the truck loading problem: A case study from the non-alcoholic beverages industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    4. Paquay, Célia & Limbourg, Sabine & Schyns, Michaël, 2018. "A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints," European Journal of Operational Research, Elsevier, vol. 267(1), pages 52-64.
    5. Silva, Elsa & Ramos, António G. & Oliveira, José F., 2018. "Load balance recovery for multi-drop distribution problems: A mixed integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 62-75.
    6. Ramos, António G. & Silva, Elsa & Oliveira, José F., 2018. "A new load balance methodology for container loading problem in road transportation," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1140-1152.
    7. I. Gimenez-Palacios & M. T. Alonso & R. Alvarez-Valdes & F. Parreño, 2021. "Logistic constraints in container loading problems: the impact of complete shipment conditions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 177-203, April.
    8. 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.
    9. 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.
    10. Castellucci, Pedro B. & Toledo, Franklina M.B. & Costa, Alysson M., 2019. "Output maximization container loading problem with time availability constraints," Operations Research Perspectives, Elsevier, vol. 6(C).
    11. 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.
    12. Vélez-Gallego, Mario C. & Teran-Somohano, Alejandro & Smith, Alice E., 2020. "Minimizing late deliveries in a truck loading problem," European Journal of Operational Research, Elsevier, vol. 286(3), pages 919-928.
    13. Martin Grunewald & Thomas Volling & Christoph Müller & Thomas S. Spengler, 2018. "Multi-item single-source ordering with detailed consideration of transportation capacities," Journal of Business Economics, Springer, vol. 88(7), pages 971-1007, September.
    14. Gajda, Mikele & Trivella, Alessio & Mansini, Renata & Pisinger, David, 2022. "An optimization approach for a complex real-life container loading problem," Omega, Elsevier, vol. 107(C).
    15. M. T. Alonso & R. Alvarez-Valdes & F. Parreño, 2020. "A GRASP algorithm for multi container loading problems with practical constraints," 4OR, Springer, vol. 18(1), pages 49-72, March.
    16. Coindreau, Marc-Antoine & Gallay, Olivier & Zufferey, Nicolas & Laporte, Gilbert, 2021. "Inbound and outbound flow integration for cross-docking operations," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1153-1163.
    17. Araya, Ignacio & Moyano, Mauricio & Sanchez, Cristobal, 2020. "A beam search algorithm for the biobjective container loading problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 417-431.
    18. McDonald, Conor M., 2016. "Integrating packaging and supply chain decisions: Selection of economic handling unit quantities," International Journal of Production Economics, Elsevier, vol. 180(C), pages 208-221.
    19. Jean-François Côté & Manuel Iori, 2018. "The Meet-in-the-Middle Principle for Cutting and Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 646-661, November.
    20. Yichen Lu & Chao Yang & Jun Yang, 2022. "A multi-objective humanitarian pickup and delivery vehicle routing problem with drones," Annals of Operations Research, Springer, vol. 319(1), pages 291-353, December.

    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:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00522-4. 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.