An Efficient Representation Scheme of Candidate Solutions for the Master Bay Planning Problem

  • Paula Hernández HernándezEmail author
  • Laura Cruz-Reyes
  • Patricia Melin
  • Julio Mar-Ortiz
  • Héctor Joaquín Fraire Huacuja
  • Héctor José Puga Soberanes
  • Juan Javier González Barbosa
Part of the Studies in Computational Intelligence book series (SCI, volume 601)


The master bay planning problem (MBPP) arises in the context of maritime transportation. In particular, MBPP consists of determining an efficient plan to stowage the containers into the containership such that the total loading time is minimized. This problem is classified as NP-hard due to the large number of possible solutions generated by the combination of assigning containers to locations in the containership. These solutions are both feasible and infeasible, which increases even more the hardness of MBPP. To deal with this problem, there are several exact and heuristic approaches that are well documented in the literature. One of the most important exact methods is in the form of an integer linear programming (ILP) formulation. However, the number of variables and constraints generated by this ILP model is very large. In this chapter, we propose a new exact algorithm based on a branch and bound (B&B) approach. The main feature is the usage of an efficient representation structure of candidate solutions. We test the proposed B&B on a set of small-sized instances. Experimental results demonstrate that, within this set of instances, our B&B is competitive with respect to the ILP model from the literature.


Candidate Solution Quay Crane Integer Linear Programming Model Weight Constraint Binary Scheme 
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.



This work was partially financed by CONACYT, DGEST and ITCM. We also thank Gurobi for allowing us to use their optimization engine.


  1. 1.
    Ambrosino, D., Sciomachen, A., Tanfani, E.: Stowing a containership: the master bay plan problem. Transp. Res. Part A Policy Pract. 38, 81–99 (2004)CrossRefGoogle Scholar
  2. 2.
    Avriel, M., Penn, M., Shpirer, N.: Container ship stowage problem: complexity and connection to the coloring of circle graphs. Discrete Appl. Math. 103(1), 271–279 (2000)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Cruz-Reyes, L., Hernández, P.H., Melin, P., Huacuja, H.J.F., Mar-Ortiz, J., Soberanes, H.J.P., Barbosa, J.J.G.: A loading procedure for the containership stowage problem. In: Recent Advances on Hybrid Approaches for Designing Intelligent Systems, pp. 543–554. Springer, Berlin (2014)Google Scholar
  4. 4.
    Hernández, P.H., Cruz-Reyes, L., Melin, P., Mar-Ortiz, J., Huacuja, H.J.F., Soberanes, H.J.P., Barbosa, J.J.G.: An ant colony algorithm for improving ship stability in the containership stowage problem. Advances in Soft Computing and Its Applications. Lecture Notes in Computer Science, vol. 8266, pp. 93–104 (2013)Google Scholar
  5. 5.
    Ambrosino, D., Anghinolfi, D., Paolucci, M., Sciomachen, A.: A new three-stepheuristic for the master bay plan problem. Marit. Econ. Logistics 11, 98–120 (2009)CrossRefGoogle Scholar
  6. 6.
    Ambrosino, D., Sciomachen, A., Tanfani, E.: A decomposition heuristics for the container ship stowage problem. J. Heuristics 12, 211–233 (2006)zbMATHCrossRefGoogle Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2003)Google Scholar
  8. 8.
    Cruz-Reyes, L., Hernández, P., Melin, P., Huacuja, H.J.F., Mar-Ortiz, J.: Constructive algorithm for a benchmark in ship stowage planning. In: Recent Advances on Hybrid Intelligent Systems, pp. 393–408. Springer, Berlin (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Paula Hernández Hernández
    • 1
    Email author
  • Laura Cruz-Reyes
    • 1
  • Patricia Melin
    • 2
  • Julio Mar-Ortiz
    • 3
  • Héctor Joaquín Fraire Huacuja
    • 1
  • Héctor José Puga Soberanes
    • 4
  • Juan Javier González Barbosa
    • 1
  1. 1.Tecnológico Nacional de MéxicoInstituto Tecnológico de Ciudad MaderoCiudad MaderoMexico
  2. 2.Tecnológico Nacional de MéxicoInstituto Tecnológico de TijuanaTijuanaMexico
  3. 3.Universidad Autónoma de TamaulipasTampicoMexico
  4. 4.Tecnológico Nacional de MéxicoInstituto Tecnológico de LeónLeonMexico

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