Skip to main content
Log in

A dynamic programming-based matheuristic for the dynamic berth allocation problem

  • S.I.: CLAIO 2016
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The increasing maritime traffic forces terminal operators to efficiently reduce the container ships’ service time in order to maintain or increase their market share. This situation gives rise to the well-known berth allocation problem. Its goal is to determine the allocation and the berthing time of container ships arriving to the port with the aim of minimizing the total service time. For tackling this problem, we propose a dynamic programming-based matheuristic that allows to derive lower and upper bounds, and therefore, evaluate the optimality of the provided solutions. Its behavior is assessed on realistic problem instances from the related literature as well as on a new set of larger instances with 150 ships and 15 berths. The results indicate that our proposed approach shows a competitive performance.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Bae, H., & Moon, I. (2016). Multi-depot vehicle routing problem with time windows considering delivery and installation vehicles. Applied Mathematical Modeling, 40, 6536–6549.

    Article  Google Scholar 

  • Buhrkal, K., Zuglian, S., Ropke, S., Larsen, J., & Lusby, R. (2011). Models for the discrete berth allocation problem: A computational comparison. Transportation Research Part E, 47, 461–473.

    Article  Google Scholar 

  • Caserta, M., & Voß, S. (2013). A math-heuristic Dantzig–Wolfe algorithm for capacitated lot sizing. Annals of Mathematics and Artificial Intelligence, 69(2), 207–224.

    Article  Google Scholar 

  • Congram, R. K., Potts, C. N., & van de Velde, S. L. (2002). An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS Journal on Computing, 14, 52–67.

    Article  Google Scholar 

  • Cordeau, J. F., Laporte, G., Legato, P., & Moccia, L. (2005). Models and tabu search heuristics for the berth allocation problem. Transportation Science, 39(4), 526–538.

    Article  Google Scholar 

  • Cordeau, J. F., Laporte, G., & Mercier, A. (2001). A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society, 52(8), 928–936.

    Article  Google Scholar 

  • de Oliveira, R. M., Mauri, G. R., & Lorena, L. A. N. (2012). Clustering search for the berth allocation problem. Expert Systems with Applications, 39(5), 5499–5505.

    Article  Google Scholar 

  • Grosso, A., Croce, F. D., & Tadei, R. (2004). An enhanced dynasearch neighborhood for the single-machine total weighted tardiness scheduling problem. Operations Research Letters, 32, 68–72.

    Article  Google Scholar 

  • Imai, A., Nishimura, E., & Papadimitriou, S. (2001). The dynamic berth allocation problem for a container port. Transportation Research Part B, 35, 401–417.

    Article  Google Scholar 

  • Lalla-Ruiz, E., González-Velarde, J. L., Melían-Batista, B., & Moreno-Vega, J. M. (2014). Biased random key genetic algorithm for the tactical berth allocation problem. Applied Soft Computing, 22, 60–76.

    Article  Google Scholar 

  • Lalla-Ruiz, E., Melián-Batista, B., & Moreno-Vega, M. (2012). Artificial intelligence hybrid heuristic based on tabu search for the dynamic berth allocation problem. Engineering Applications of Artificial Intelligence, 25, 1132–1141.

    Article  Google Scholar 

  • Lalla-Ruiz, E., & Voß, S. (2016). POPMUSIC as a matheuristic for the berth allocation problem. Annals of Mathematics and Artificial Intelligence, 76, 173–189.

    Article  Google Scholar 

  • Mauri, G. R., Ribeiro, G. M., Lorena, L. A. N., & Laporte, G. (2016). An adaptive large neighborhood search for the discrete and continuous berth allocation problem. Computers and Operations Research, 70, 140–154.

    Article  Google Scholar 

  • Nishi, T., & Hiranaka, Y. (2013). Lagrangian relaxation and cut generation for sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness. International Journal of Production Research, 51, 4778–4796.

    Article  Google Scholar 

  • Nishi, T., Hiranaka, Y., & Inuiguchi, M. (2010). Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness. Computers and Operations Research, 37, 189–198.

    Article  Google Scholar 

  • Potts, C. N., & Van de Velde, S. L. (1995). Dynasearch—Iterative local improvement by dynamic programming: Part I, traveling salesman problem. Technical Report, University of Twente.

  • Saadaoui, Y., Umang, N., & Frejinger, E. (2016). A column generation framework for berth scheduling at port terminals. CIRRELT-2015-15. https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2015-15.pdf. (Available on 2016).

  • Sniedovich, M., & Voß, S. (2006). The corridor method: A dynamic programming inspired metaheuristic. Control and Cybernetics, 35–3, 551–578.

    Google Scholar 

  • Sourd, F. (2006). Dynasearch for the earliness-tardiness scheduling problem with release dates and setup constraints. Operations Research Letters, 34, 591–598.

    Article  Google Scholar 

  • Steenken, D., Voß, S., & Stahlbook, R. (2004). Container terminal operations and operations research—A classification and literature review. OR Spectum, 26, 3–49.

    Article  Google Scholar 

  • Taillard, E., & Voß, S. (2002). POPMUSIC—Partial optimization metaheuristic under special intensification conditions. In C. Ribeiro & P. Hansen (Eds.), Essays and Surveys in Metaheuristics (pp. 613–629). Boston, MA: Kluwer.

    Chapter  Google Scholar 

  • Ting, C. J., Wu, K. C., & Chou, H. (2014). Particle swarm optimization algorithm for the berth allocation problem. Expert Systems with Applications, 41(4), 1543–1550.

    Article  Google Scholar 

  • UNCTAD. (2016). Review of maritime transport. http://unctad.org/en/PublicationsLibrary/rmt2016_en.pdf. (Available on 2016).

Download references

Acknowledgements

This work was partially supported by Japan Society for the Promotion of Science (Grant No. 15H02971). Also, this work was partially funded by the Spanish Ministry of Economy and Competitiveness with FEDER funds (Project TIN2015- 70226-R).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tatsushi Nishi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nishi, T., Okura, T., Lalla-Ruiz, E. et al. A dynamic programming-based matheuristic for the dynamic berth allocation problem. Ann Oper Res 286, 391–410 (2020). https://doi.org/10.1007/s10479-017-2715-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-017-2715-9

Keywords

Navigation