Annals of Operations Research

, Volume 199, Issue 1, pp 51–75 | Cite as

MIP-based approaches for the container loading problem with multi-drop constraints

  • Leonardo Junqueira
  • Reinaldo Morabito
  • Denise Sato Yamashita


In this paper, we present approaches based on a mixed integer linear programming model (MIP) for the problem of packing rectangular boxes into a container or truck, considering multi-drop constraints. We assume that the delivery route of the container is already known in advance and that the volume of the cargo is less than or equal to the container volume. Considering the sequence that the boxes should be unloaded, the aim is to avoid additional handling when each drop-off point of the route is reached, as well as ensuring that the boxes do not overlap each other and the cargo loading is stable. Computational tests with the proposed model and the approaches were performed with randomly generated instances and instances from the literature using an optimization solver embedded into a modeling language. The results validate the model and the approaches, but indicate that they are able to handle only problems of a moderate size. However, the model and the approaches can be useful to motivate future research to solve larger problems, as well as to solve more general problems considering integrated vehicle routing and container loading problems.


Three-dimensional container loading Multi-drop constraints Cutting and packing problems Combinatorial optimization Mathematical modeling 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Leonardo Junqueira
    • 1
  • Reinaldo Morabito
    • 1
  • Denise Sato Yamashita
    • 1
  1. 1.Departamento de Engenharia de ProduçãoUniversidade Federal de São CarlosSão CarlosBrazil

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