Fully fuzzy linear programming model for the berth allocation problem with two quays

Abstract

In this work, we study the berth allocation problem (BAP), considering the cases continuous and dynamic for two quays; also, we assume that the arrival time of vessels is imprecise, meaning that vessels can be late or early up to a allowed threshold. Triangular fuzzy numbers represent the imprecision of the arrivals. We present two models for this problem: The first model is a fuzzy MILP (Mixed Integer Lineal Programming) and allows us to obtain berthing plans with different degrees of precision; the second one is a model of Fully Fuzzy Linear Programming (FFLP) and allows us to obtain a fuzzy berthing plan adaptable to possible incidences in the vessel arrivals. The models proposed have 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 for instances up to 10 vessels; for instances between 10 and 65 vessels it finds a non-optimum solution and for bigger instants no solution is founded. Finally we suggest the steps to be taken to implement the model for the FFLP BAP in a maritime terminal of containers.