Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ambrosino, D., Sciomachen, A., Tanfani, E.: Stowing a containership: the master bay plan problem. Transp. Res. Part A Policy Pract. 38, 81–99 (2004)
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)
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)
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)
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)
Ambrosino, D., Sciomachen, A., Tanfani, E.: A decomposition heuristics for the container ship stowage problem. J. Heuristics 12, 211–233 (2006)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2003)
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)
Acknowledgments
This work was partially financed by CONACYT, DGEST and ITCM. We also thank Gurobi for allowing us to use their optimization engine.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hernández, P.H. et al. (2015). An Efficient Representation Scheme of Candidate Solutions for the Master Bay Planning Problem. In: Melin, P., Castillo, O., Kacprzyk, J. (eds) Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Studies in Computational Intelligence, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-17747-2_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-17747-2_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17746-5
Online ISBN: 978-3-319-17747-2
eBook Packages: EngineeringEngineering (R0)