Advertisement

Fuzziness in the Berth Allocation Problem

  • Flabio GutierrezEmail author
  • Edwar Lujan
  • Rafael Asmat
  • Edmundo Vergara
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 795)

Abstract

The berth allocation problem (BAP) in a marine terminal container is defined as the feasible berth allocation to the incoming vessels. In this work, we present two models of fuzzy optimization for the continuous and dynamic BAP. The arrival time of vessels are assumed to be imprecise, meaning that the vessel can be late or early up to a threshold allowed. Triangular fuzzy numbers represent the imprecision of the arrivals. The first model is a fuzzy MILP (Mixed Integer Lineal Programming) and allow us to obtain berthing plans with different degrees of precision; the second one is a model of Fully Fuzzy Linear Programming (FFLP) and allow us to obtain a fuzzy berthing plan adaptable to possible incidences in the vessel arrivals. The models proposed has been implemented in CPLEX and evaluated in a benchmark developed to this end. For both models, with a timeout of 60 min, CPLEX find the optimum solution to instances up to 10 vessels; for instances between 10 and 45 vessels it find a non-optimum solution and for bigger instants no solution is founded.

Keywords

Berth Allocation Problem (BAP) Mixed Integer Liner Programming (MILP) Berth Planning Vessel Arrivals Incoming Vessels 
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.

Notes

Acknowledgements

This work was supported by INNOVATE-PERU, Project N PIBA-2-P-069-14.

References

  1. 1.
    Bierwirth, C., Meisel, F.: A survey of berth allocation and quay crane scheduling problems in container terminals. Eur. J. Oper. Res. 202(3), 615–627 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bruggeling, M., Verbraeck, A., Honig, H.: Decision support for container terminal berth planning: integration and visualization of terminal information. In: Proceedings of the Van de Vervoers logistieke Werkdagen (VLW2011), University Press, Zelzate, pp. 263–283 (2011)Google Scholar
  3. 3.
    Das, S.K., Mandal, T., Edalatpanah, S.A.: A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Appl. Intell. 46(3), 509–519 (2017)CrossRefGoogle Scholar
  4. 4.
    Exposito-Izquiero, C., Lalla-Ruiz, E., Lamata, T., Melian-Batista, B., Moreno-Vega, J.: Fuzzy optimization models for seaside port logistics: berthing and quay crane scheduling. In: Computational Intelligence, pp. 323–343. Springer International Publishing (2016)Google Scholar
  5. 5.
    Gutierrez, F., Vergara, E., Rodrguez, M., Barber, F.: Un modelo de optimizacin difuso para el problema de atraque de barcos. Investigacin Operacional 38(2), 160–169 (2017)Google Scholar
  6. 6.
    Jimenez, M., Arenas, M., Bilbao, A., Rodrı, M.V.: Linear programming with fuzzy parameters: an interactive method resolution. Eur. J. Oper. Res. 177(3), 1599–1609 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kim, K.H., Moon, K.C.: Berth scheduling by simulated annealing. Transp. Res. Part B Methodol. 37(6), 541–560 (2003)CrossRefGoogle Scholar
  8. 8.
    Laumanns, M., et al.: Robust adaptive resource allocation in container terminals. In: Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making, Coimbra, Portugal, pp. 501–517 (2010)Google Scholar
  9. 9.
    Lim, A.: The berth planning problem. Oper. Res. Lett. 22(2), 105–110 (1998)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Luhandjula, M.K.: Fuzzy mathematical programming: theory, applications and extension. J. Uncertain Syst. 1(2), 124–136 (2007)Google Scholar
  11. 11.
    Nasseri, S.H., Behmanesh, E., Taleshian, F., Abdolalipoor, M., Taghi-Nezhad, N.A.: Fullyfuzzy linear programming with inequality constraints. Int. J. Ind. Math. 5(4), 309–316 (2013)Google Scholar
  12. 12.
    Rodriguez-Molins, M., Ingolotti, L., Barber, F., Salido, M.A., Sierra, M.R., Puente, J.: A genetic algorithm for robust berth allocation and quay crane assignment. Prog. Artif. Intell. 2(4), 177–192 (2014)CrossRefGoogle Scholar
  13. 13.
    Rodriguez-Molins, M., Salido, M.A., Barber, F.: A GRASP-based metaheuristic for the Berth Allocation Problem and the Quay Crane Assignment Problem by managing vessel cargo holds. Appl. Intell. 40(2), 273–290 (2014)CrossRefGoogle Scholar
  14. 14.
    Steenken, D., Vo, S., Stahlbock, R.: Container terminal operation and operations research—a classification and literature review. OR Spectr. 26(1), 3–49 (2004)CrossRefGoogle Scholar
  15. 15.
    Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst. 118(3), 375–385 (2001)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(2), 143–161 (1981)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Young-Jou, L., Hwang, C.: Fuzzy Mathematical Programming: Methods and Applications, vol. 394. Springer Science & Business Media (2012)Google Scholar
  18. 18.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)CrossRefGoogle Scholar
  19. 19.
    Zimmermann, H.: Fuzzy Set Theory and Its Applications, Fourth Revised Edition. Springer, Berlin (2001)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Flabio Gutierrez
    • 1
    Email author
  • Edwar Lujan
    • 2
  • Rafael Asmat
    • 3
  • Edmundo Vergara
    • 3
  1. 1.Department of MathematicsNational University of PiuraPiuraPeru
  2. 2.Department of InformaticsNational University of TrujilloTrujilloPeru
  3. 3.Department of MathematicsNational University of TrujilloTrujilloPeru

Personalised recommendations