Abstract
The Berth Allocation (BA) problem is an important problem in port logistics. It aims at finding optimal berthing times and positions of arriving vessels in a wharf subject to physical constraints. The optimisation criteria in the BA problem are diverse and respond to specific interests of vessels and wharves operators. Furthermore, although the BA problem has been dealt with mostly under complete certainty, it is a highly uncertain problem due to many factors that can affect vessels arrival and handling times. This paper takes fuzzy uncertainty into account and presents a fully fuzzy two-objective BA problem, by considering the minimisation of the total waiting time of vessels and the makespan of the wharf operation from the perspectives of vessels and wharves operators, respectively. A fuzzy epsilon-constraint method and a lexicographic method for fully fuzzy linear programming with inequality constraints are used jointly to solve the problem. A numerical example is given as illustration. Results demonstrate the usefulness of the proposed approach in handling fuzziness and conflicting objectives simultaneously in a BA problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bellman, R.E., Zadeh, L.A.: Decision-making in fuzzy environment. Manag. Sci. 17(4), 141–164 (1970). https://doi.org/10.1287/mnsc.17.4.B141
Bojadziev, G., Bojadziev, M.: Fuzzy sets, fuzzy Logic, applications. In: Advances in Fuzzy Systems – Applications and Theory, vol. 5. World Scientific Publishing (1995)
Cheong, C., Tan, K., Liu, D.: Solving the berth allocation problem with service priority via multi-objective optimization. In: 2009 IEEE Symposium on Computational Intelligence in Scheduling, vol. 117576, pp. 95–102. IEEE (2009). https://doi.org/10.1109/SCIS.2009.4927021
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). https://doi.org/10.1007/s10489-016-0779-x
Expósito-Izquiero, C., Lalla-Ruiz, E., Lamata, T., Melián-Batista, B., Moreno-Vega, J.M.: Fuzzy optimization models for seaside port logistics: berthing and quay crane scheduling. In: Madani, K., Dourado, A., Rosa, A., Filipe, J., Kacprzyk, J. (eds.) Computational Intelligence. SCI, vol. 613, pp. 323–343. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-23392-5_18
Farhadinia, B.: Ranking fuzzy numbers based on lexicographical ordering. Int. J. Appl. Math. Comput. Sci. 5(4), 248–251 (2009)
Greco, S., Ehrgott, M., Figueira, J.R.: Multiple Criteria Decision Analysis. ISOR, vol. 233. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-3094-4
Gupta, A., Kumar, A., Kaur, A.: Mehar’s method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems. Optim. Lett. 6(8), 1737–1751 (2012). https://doi.org/10.1007/s11590-011-0367-2
Gutierrez, F., Lujan, E., Asmat, R., Vergara, E.: Fully fuzzy linear programming model for the berth allocation problem with two quays. In: Bello, R., Falcon, R., Verdegay, J.L. (eds.) Uncertainty Management with Fuzzy and Rough Sets. SFSC, vol. 377, pp. 87–113. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10463-4_5
Gutierrez, F., Lujan, E., Asmat, R., Vergara, E.: Fuzziness in the berth allocation problem. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. SCI, vol. 795, pp. 149–174. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-99648-6_9
Hanss, M.: Applied Fuzzy Arithmetic. Springer, Heidelberg (2005). https://doi.org/10.1007/b138914
Hashemi, S.M., Modarres, M., Nasrabadi, E., Nasrabadi, M.M.: Fully fuzzified linear programming, solution and duality. J. Intell. Fuzzy Syst. 17(1), 253–261 (2006)
Hosseinzadeh Lotfi, F., Allahviranloo, T., Alimardani Jondabeh, M., Alizadeh, L.: Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl. Math. Model. 33, 3151–3156 (2009). https://doi.org/10.1016/j.apm.2008.10.020
Kim, K.H., Moon, K.C.: Berth scheduling by simulated annealing. Transp. Res. Part B: Methodol. 37(6), 541–560 (2003). https://doi.org/10.1016/S0191-2615(02)00027-9
López Plata, I.: Improvement of the logistics processes in maritime container terminals through intelligent optimization techniques. Ph.D. dissertation, University of La Laguna, Spain (2020)
Maher, S.J., et al.: The SCIP Optimization Suite 4.0. Technical report, Optimization Online, March 2017. http://www.optimization-online.org/DB_HTML/2017/03/5895.html
Mitchell, S., O’Sullivan, M., Dunning, I.: PuLP: a linear programming toolkit for python (2011). http://www.optimization-online.org/DB_FILE/2011/09/3178.pdf. The University of Auckland, Auckland, New Zealand
Pérez-Cañedo, B., Concepción-Morales, E.R.: A method to find the unique optimal fuzzy value of fully fuzzy linear programming problems with inequality constraints having unrestricted L-R fuzzy parameters and decision variables. Expert Syst. Appl. 123, 256–269 (2019). https://doi.org/10.1016/j.eswa.2019.01.041
Pérez-Cañedo, B., Verdegay, J.L., Miranda Pérez, R.: An epsilon-constraint method for fully fuzzy multiobjective linear programming. Int. J. Intell. Syst. 35(4), 600–624 (2020). https://doi.org/10.1002/int.22219
Wang, M.L., Wang, H.F., Chih-Lung, L.: Ranking fuzzy number based on lexicographic screening procedure. Int. J. Inf. Technol. Decis. Making 4(4), 663–678 (2005). https://doi.org/10.1142/S0219622005001696
Wang, W., Wang, Z.: Total orderings defined on the set of all fuzzy numbers. Fuzzy Sets Syst. 243, 131–141 (2014). https://doi.org/10.1016/j.fss.2013.09.005
Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X
Acknowledgements
The research of José Luis Verdegay is supported in part by project TIN2017-86647-P (Spanish Ministry of Economy and Competitiveness and FEDER funds from the European Union).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Pérez-Cañedo, B., Verdegay, J.L., Rosete, A., Concepción-Morales, E.R. (2020). Fully Fuzzy Multi-objective Berth Allocation Problem. In: de la Cal, E.A., Villar Flecha, J.R., Quintián, H., Corchado, E. (eds) Hybrid Artificial Intelligent Systems. HAIS 2020. Lecture Notes in Computer Science(), vol 12344. Springer, Cham. https://doi.org/10.1007/978-3-030-61705-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-61705-9_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61704-2
Online ISBN: 978-3-030-61705-9
eBook Packages: Computer ScienceComputer Science (R0)