Generating Optimal Stowage Plans for Container Vessel Bays

  • Alberto Delgado
  • Rune Møller Jensen
  • Christian Schulte
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5732)


Millions of containers are stowed every week with goods worth billions of dollars, but container vessel stowage is an all but neglected combinatorial optimization problem. In this paper, we introduce a model for stowing containers in a vessel bay which is the result of probably the longest collaboration to date with a liner shipping company on automated stowage planning. We then show how to solve this model efficiently in - to our knowledge - the first application of CP to stowage planning using state-of-the-art techniques such as extensive use of global constraints, viewpoints, static and dynamic symmetry breaking, decomposed branching strategies, and early failure detection. Our CP approach outperforms an integer programming and column generation approach in a preliminary study. Since a complete model of this problem includes even more logical constraints, we believe that stowage planning is a new application area for CP with a high impact potential.


Column Generation Constraint Programming Master Problem Global Constraint Empty Container 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Botter, R., Brinati, M.: Stowage container planning: A model for getting an optimal solution. In: Proceedings of the Seventh International Conference on Computer Applications in the Automation of Shipyard Operation and Ship Design (1992)Google Scholar
  2. 2.
    Giemesh, P., Jellinhaus, A.: Optimization models for the containership stowage problem. In: Proceedings of the International Conference of the German Operations Research Society (2003)Google Scholar
  3. 3.
    Ambrosino, D., Sciomachen, A., Tanfani, E.: Stowing a conteinership: the master bay plan problem. Transportation Research 38 (2004)Google Scholar
  4. 4.
    Avriel, M., Penn, M., Shpirer, N., Witteboon, S.: Stowage planning for container ships to reduce the number of shifts. Annals of Operations Research 76(55-71) (1998)Google Scholar
  5. 5.
    Dubrovsky, O., Penn, M.: A genetic algorithm with a compact solution encoding for the container ship stowage problem. Journal of Heuristics 8(585-599) (2002)Google Scholar
  6. 6.
    Ambrosino, D., Sciomachen, A., Tanfani, E.: A decomposition heuristics for the container ship stowage problem. Journal of Heuristics 12(3) (2006)Google Scholar
  7. 7.
    Kang, J., Kim, Y.: Stowage planning in maritime container transportation. Journal of the Operations Research society 53(4) (2002)Google Scholar
  8. 8.
    Wilson, I., Roach, P.: Principles of combinatorial optimisation applied to container-ship stowage planning. Journal Heuristics 1(5) (1999)Google Scholar
  9. 9.
    Gumus, M., Kaminsky, P., Tiemroth, E., Ayik, M.: A multi-stage decomposition heuristic for the container stowage problem. In: Proceedings of 2008 MSOM Conference (2008)Google Scholar
  10. 10.
    Pacino, D., Jensen, R.: A local search extended placement heuristic for stowing under deck bays of container vessels. In: Proceedings of ODYSSEUS 2009 (2009)Google Scholar
  11. 11.
    Gecode Team: Gecode: Generic constraint development environment (2006),
  12. 12.
    Rose, H.T., Janstrup, K., Andersen, K.H.: The Container Stowage Problem. Technical report, IT University of Copenhagen (2008)Google Scholar
  13. 13.
    Smith, B.: Modelling. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. Elsevier, Amsterdam (2006)Google Scholar
  14. 14.
    Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Paul, S.: A constraint for bin packing. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 648–662. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alberto Delgado
    • 1
  • Rune Møller Jensen
    • 1
  • Christian Schulte
    • 2
  1. 1.IT University of CopenhagenDenmark
  2. 2.KTH - Royal Institute of TechnologySweden

Personalised recommendations