A novel mathematical formulation for solving the dynamic and discrete berth allocation problem by using the Bee Colony Optimisation algorithm

Berth allocation is one of the crucial points for efficient management of ports. This problem is complex due to all possible combinations for assigning ships to available compatible berths. This paper focuses on solving the Berth Allocation Problem (BAP) by optimising port operations using an innovative model. The problem analysed in this work deals with the Discrete and Dynamic Berth Allocation Problem (DDBAP). We propose a novel mathematical formulation expressed as a Mixed Integer Linear Programming (MILP) for solving the DDBAP. Furthermore, we adapted a metaheuristic solution approach based on the Bee Colony Optimisation (BCO) for solving large-sized combinatorial BAPs. In order to assess the solution performance and efficiency of the proposed model, we introduce a new set of instances based on real data of the Livorno port (Italy), and a comparison between the BCO algorithm and CPLEX in solving the DDBAP is performed. Additionally, the application of the proposed model to a real berth scheduling (Livorno port data) and a comparison with the Ant Colony Optimisation (ACO) metaheuristic are carried out. Results highlight the feasibility of the proposed model and the effectiveness of BCO when compared to both CPLEX and ACO, achieving computation times that ensure a real-time application of the method.