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Annals of Computer Science and Information Systems, Volume 11

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

A Fully Fuzzy Linear Programming Model to the Berth Allocation Problem

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DOI: http://dx.doi.org/10.15439/2017F339

Citation: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 11, pages 453458 ()

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Abstract. The berth allocation problem (BAP) in marine container terminals is defined as the feasible berth allocation to the incoming vessels. In this work, we develop a model of fully fuzzy linear programming (FFLP) for the continuous and dynamic BAP. The vessel arrival times are assumed to be imprecise, meaning that the vessel can be late or early up to a threshold permitted. Triangular fuzzy numbers represent the uncertainty of the arrivals. The model proposed has been implemented in CPLEX and evaluated for different instances. The results obtained show that the model proposed is helpful to the administrators of a marine container terminal, since a plan supporting imprecision in the arrival time of vessels, optimized with respect to the waiting time and easily adaptable to possible incidents and delays, is available to them.


  1. A. Lim, “The berth planning problem”,  Operations Research letters, vol. 22, no 2, p. 105-110, 1998. http://dx.doi.org/10.1016/S0167-6377(98)00010-8
  2. M. Bruggeling, A. verbraeck, and H. Honig: “Decision support for container terminal berth planning: Integration and visualization of terminal information”. In Proc. Van de Vervoers logistieke Werkdagen (VLW2011), University Press, Zelzate, p. 263 – 283, 2011.
  3. M. Laumanns, et al., “Robust adaptive resource allocation in container terminals”. In Proc. 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making, Coimbra, Portugal, p. 501-517. 2010.
  4. H. Zimmermann, “Fuzzy set theory and its applications”, Fourth Revised Edition. Springer, 2001.
  5. C. Bierwirth, F. Meisel, “A survey of berth allocation and quay crane scheduling problems in container terminals”, European Journal of Operational Research, vol. 202, no 3, pp. 615-627, 2010. http://dx.doi.org/10.1007/978-0-387-75240-2_4
  6. B. Melián-Batista, J. Moreno-Vega, and J. Verdegay, “Una primera aproximación al problema de asignación de atraques con tiempos de llegada difusos”. In. Proc. XV Congreso Español Sobre Tecnologías y Lógica Fuzzy. p. 37-42, 2010.
  7. F. Gutiérrez, E. Vergara, M. Rodríguez and F. Barber, “Un modelo de optimización difuso para el problema de atraque de barcos”. Investigación operacional, vol. 38, no. 2, pp. 160-169, 2017.
  8. L. Young-Jou, C. Hwang, “Fuzzy mathematical programming: methods and applications”, vol. 394, Springer Science& Business Media, 2012. http://dx.doi.org/10.1007/978-3-642-48753-8
  9. R. Yager, “A procedure for ordering fuzzy subsets of the unit interval. Information sciences”, vol. 24, no.2, pp.143-161, 1981. http://dx.doi.org/10.1016/0020-0255(81)90017-7
  10. L. Zadeh, “Fuzzy sets as a basisfor a theory of possibility”. Fuzzy sets and systems, vol. 1. no. 1, pp. 3-28.1978. http://dx.doi.org/10.1016/0165-0114(78)90029-5
  11. M. Luhandjula, “Mathematical programming: theory, applications and extension”. Journal of Uncertain Systems, vol. 1, no. 2, 124-136. 2007.
  12. S. Das, T. Mandal, and S. Edalatpanah. “A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers”. Applied Intelligence, pp.1-11, 2016. http://dx.doi.org/10.1007/s10489-016-0779-x
  13. S. Nasseri, E. Behmanesh, F. Taleshian, M. Abdolalipoor, and N. Taghi-Nezhad. “Fullyfuzzy linear programming with inequality constraints”. International Journal of Industrial Mathematics, vol. 5, no. 4, pp. 309-316, 2013.
  14. K. Kim, K. Moon. “Berth scheduling by simulated annealing,” Transportation Research Part B: Methodological, vol. 37, no. 6, pp. 541-560. 2003. http://dx.doi.org/10.1016/S0191-2615(02)00027-9