Skip to main content
Log in

A Mathematical Model for the Container Stowage and Ship Routing Problem

  • Published:
Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

The main goal of this paper is to present a mathematical model for a fleet of containerships with no pre-defined routes, considering demands and delivery deadlines and overstowing prevention. The objective is to minimize the total distribution cost in the contest of the short sea shipping. The short sea shipping is a very complex problem that belongs to the class of routing problems, more precisely, to the Capacitated Vehicle Routing Problem with deadlines and loading constraints. In this problem two major decisions must be made: which ports should be visited by each vessel and the related visit sequence, and where to load the containers in vessels in order to prevent overstowing. A mixed integer programming model for the problem is presented and solved. This mathematical formulation intends to contribute to a better management of small fleets of containerships in order to reduce transportation time and delivering costs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Martins, T., Lobo, V., Vairinhos, V.: Container Stowage Problem Solution for Short Sea Shipping. 14° Congresso da Associação Portuguesa de Análise Operacional. Universidade Nova de Lisboa, Monte da Caparica (2009)

  2. Agarwal, R., Ergun, O.: Ship scheduling and network design for cargo routing in liner shipping. J. Transport. Sci. 42, 175–196 (2009)

    Article  Google Scholar 

  3. Avriel, M., Penn, M., Shpirer, N.: Container ship stowage problem: complexity and connection to the coloring of circle graphs. Discrete Appl. Math. 103, 271–279 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Aslidis, A.H.: Combinatorial algorithms for stacking problems. PhD dissertation, MIT (2000)

  5. Avriel, M., Penn, M.: Exact and approximate solutions of the container ship stowage problem. Comput. Ind. Eng. 25, 271–274 (1993)

    Article  Google Scholar 

  6. Avriel, M., Penn, M., Shpirer, N., Witteboon, S.: Stowage planning for container ships to reduce the number of shifts. Ann. Oper. Res. 76, 55–71 (1998)

    Article  MATH  Google Scholar 

  7. Botter, R.C., Brinati, M.A.: Stowage container planning: a model for getting an optimal solution. Computer Applications in the Automation of Shipyard Operation and Ship Design, VII, pp. 217–229. North-Holland (1992)

  8. Ambrosino, D., Sciomachen, A., Tanfani, E.: Stowing a containership: the master bay plan problem. Trans. Res. Part A 38, 81–99 (2004)

    Article  Google Scholar 

  9. Ambrosino, D., Sciomachen, A., Tanfani, E.: A decomposition heuristics for the container ship stowage problem. Journal of Heuristics 12, 211–233 (2006)

    Article  MATH  Google Scholar 

  10. Dubrovsky, O., Levitin, O.G., Penn, M.: A genetic algorithm with a compact solution encoding for the container ship stowage problem. Journal of Heuristics 8, 585–599 (2002)

    Article  Google Scholar 

  11. Martins, T., Moura, A., Campos, A.A., Lobo, V.: Genetic algorithms approach for containerships fleet management dependent on cargo and their deadlines. In: IAME 2010: Annual Conference of the International Association of Maritime Economists, Lisbon, 7–9 July 2010

  12. Wilson, I.D., Roach, P.A.: Container stowage planning: a methodology for generating computerized solutions. J. Oper. Res. Soc. 51, 1248–1255 (2000)

    MATH  Google Scholar 

  13. Wilson, I.D., Roach, P.A.: Principles of combinatorial optimization applied to container-ship stowage planning. Journal of Heuristics 5(4), 403–418(16) (1999)

    Article  MATH  Google Scholar 

  14. Christiansen, M., Nygreen, B.: A method for solving ship routing problems with inventory constraints. Ann. Oper. Res. 81, 357–378 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Agarwal, R., Ergun, O.: Ship scheduling and network design for cargo routing in linear shipping. Transp. Sci. 42(2), 175–196 (2008)

    Article  Google Scholar 

  16. Wei-ying, Z., Yan, L., Zhuo-shang, J.T.: Model and algorithm for container ship stowage planning based on bin-packing problem. J. Mar. Sci. Appl. 4(3), 30–36 (2005)

    Article  Google Scholar 

  17. Gendreau, M., Iori, M., Laporte, G., Martello, S.: A tabu search algorithm for a routing and container loading problem. Transp. Sci. 9(3), 342–350 (2006)

    Article  Google Scholar 

  18. Moura, A., Oliveira, J.F.: An integrated approach to the vehicle routing and container loading problems. Oper. Res. Spectrum. 31, 775–800 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ana Moura.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moura, A., Oliveira, J. & Pimentel, C. A Mathematical Model for the Container Stowage and Ship Routing Problem. J Math Model Algor 12, 217–231 (2013). https://doi.org/10.1007/s10852-012-9207-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-012-9207-3

Keywords

Navigation