# SOLVING THE 3D CONTAINER SHIP LOADING PLANNING PROBLEM BY REPRESENTATION BY RULES AND BEAM SEARCH

### Anibal Tavares de Azevedo, Cassilda Maria Ribeiro, Galeno José de Sena, Antônio Augusto Chaves, Luis Leduíno Salles Neto, Antônio Carlos Moretti

#### Abstract

This paper formulates the 3D Container ship Loading Planning Problem (3D CLPP) and also proposes a new and compact representation to efficiently solve it. Containers on board a Container ship are placed in vertical stacks, located in different sections. The only way to access the containers is through the top of the stack. In order to unload a container at a given port j, it is necessary to remove the container whose destination is the port j+1, because it is located above the container we want to download. This operation is called “shifting”. A ship container carrying cargo to several ports may require a large number of shifting operations. These operations spend a lot of time and cost and can be avoided by using efficient stowage planning. The key objective of the stowage planning is to minimize the number of container movements and also the ship instability. The binary formulation of this problem is properly described and also an alternative formulation called representation by rules is proposed. A Beam Search is combined with representation by rules to solve the 3D CLPP in manner that ensures that every solution analyzed in the optimization process is compact and feasible.

#### References

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#### in Harvard Style

Tavares de Azevedo A., Maria Ribeiro C., José de Sena G., Augusto Chaves A., Leduíno Salles Neto L. and Carlos Moretti A. (2012). SOLVING THE 3D CONTAINER SHIP LOADING PLANNING PROBLEM BY REPRESENTATION BY RULES AND BEAM SEARCH . In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 132-141. DOI: 10.5220/0003757801320141

#### in Bibtex Style

@conference{icores12,
author={Anibal Tavares de Azevedo and Cassilda Maria Ribeiro and Galeno José de Sena and Antônio Augusto Chaves and Luis Leduíno Salles Neto and Antônio Carlos Moretti},
title={SOLVING THE 3D CONTAINER SHIP LOADING PLANNING PROBLEM BY REPRESENTATION BY RULES AND BEAM SEARCH},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2012},
pages={132-141},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003757801320141},
isbn={978-989-8425-97-3},
}

#### in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - SOLVING THE 3D CONTAINER SHIP LOADING PLANNING PROBLEM BY REPRESENTATION BY RULES AND BEAM SEARCH
SN - 978-989-8425-97-3
AU - Tavares de Azevedo A.
AU - Maria Ribeiro C.
AU - José de Sena G.
AU - Augusto Chaves A.
AU - Leduíno Salles Neto L.
AU - Carlos Moretti A.
PY - 2012
SP - 132
EP - 141
DO - 10.5220/0003757801320141