This study has formulated a mixed integer linear programming (MILP) mathematical model for continuous and dynamic multiple-quay berth allocation problems (MQ-BAP) to minimize the total cost of activities. Some parameters of the problem are considered indeterministic to approach the optimum solution in reality assuming the indeterministic nature of ship activities and operations.

Uncertainty of parameters has been assessed using a credibility-based fuzzy approach considering them triangular fuzzy parameters. Uncertainty and ambiguity of parameters may depend on some conditions, such as delayed arrival and berthing of ships and vessels in container terminals due to bad weather conditions, operator schedule errors, equipment failure, etc. An improved metaheuristic genetic algorithm (IMGA) optimization algorithm has been used to solve this real problem with large dimensions and complex solution time. The efficiency of the proposed algorithm has been compared and ensured by solving the model based on the metaheuristic Simulated Annealing (SA) algorithm. The proposed algorithm has a perfect performance in obtaining fast and good solutions in MQ-BAP in real dimensions. These computations show that the proposed indeterministic problem-solving based on the algorithms mentioned above can be one of the underlying factors in increasing the efficiency of container terminals, which is the main purpose and advantage of this study compared to the base model presented by Pablo Frojan et al. (2015) that is analyzed based on the deterministic data.