A novel mathematical formulation for solving the dynamic and discrete berth allocation problem by using the Bee Colony O
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A novel mathematical formulation for solving the dynamic and discrete berth allocation problem by using the Bee Colony Optimisation algorithm Luigi Pio Prencipe 1
&
Mario Marinelli 2
Accepted: 4 November 2020 # The Author(s) 2020
Abstract 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. Keywords Berth allocation problem . Bee colony optimisation . Container terminal . Berth planning . Combinatorial optimisation
1 Introduction During the last century, global trade and freight growth impose new challenges and requirements for efficient management of transport processes. Therefore, maritime transport is one of the crucial points of intermodal transportation, concerned with the difficulties of developing more efficient port operations. This paper focuses on solving the Berth Allocation Problem (BAP) by optimising port operations using an innovative model. In the literature, this problem has been studied by several researchers using different approaches. Basically, the BAP is a complex operations research problem based on the assignment of ships to berth areas along a quay [41]. Typically, ships arrive at a port in a specific time window,
* Luigi Pio Prencipe [email protected] 1
D.I.C.A.T.E.Ch, Polytechnic University of Bari, Via Orabona 4, Bari, Italy
2
Department of Engineering, University of Sannio, Piazza Roma 21, Benevento, Italy
and port operators indicate their available berths. Models applied to solve the BAP can be divided according to variables related to space and time. Spatial variables are related to the quay. According to Imai et al. [27] and Bierwirth and Maisel [1], there are three different cases of spatial variables: discrete layout (BAPD), continuous layout (BAPC), and hybrid layout (HBAP). The BAPD is the simplest and the most use
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