Optimization Models for the Three-Dimensional Container Loading Problem with Practical Constraints

  • Leonardo Junqueira
  • Reinaldo Morabito
  • Denise Sato Yamashita
  • Horacio Hideki Yanasse
Part of the Springer Optimization and Its Applications book series (SOIA, volume 73)


The last decades have seen an increasing emergence of solution approaches to three-dimensional container loading problems. Starting from simple constructive algorithms and passing through sophisticated metaheuristics, the container loading literature offers a range of solving options. However, few authors have engaged themselves in proposing optimization models to deal with container loading problems that aim to pack the largest volume (or value) of rectangular boxes orthogonally inside a single container. In this sense, studies are even scarcer when practical constraints are considered. Cargo stability, load bearing strength of the boxes, and multi-drop situations, among others, are constraints that have important practical claim and should be considered in order to model more realistic situations. In this chapter we are concerned with presenting mixed integer linear programming models for container loading problems that consider vertical and horizontal stability of the cargo, load bearing strength of the boxes, and multi-drop situations, besides the non-overlapping of boxes. Computational results achieved with a modeling language and an optimization solver, comparing the performance of the models on instances from the literature, are also presented and discussed. Finally, we discuss some potential directions for future works in this area.


Three-dimensional container loading Mathematical modeling Cargo stability Load bearing Multi-dropping 



This research was partially supported by FAPESP, CAPES, and CNPq.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Leonardo Junqueira
    • 1
  • Reinaldo Morabito
    • 1
  • Denise Sato Yamashita
    • 1
  • Horacio Hideki Yanasse
    • 2
  1. 1.Departamento de Engenharia de ProduçãoUniversidade Federal de São CarlosSão Carlos−São PauloBrazil
  2. 2.Instituto Nacional de Pesquisas Espaciais−INPE/LACSão José dos Campos−São PauloBrazil

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