Discrete Berth Allocation Problem Research Articles

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.

Comparison of Planning Models for Dynamic Berth Allocation Problem Using A Sailfish-based Algorithm

Abstract Decide when and where allocate incoming ships at a container terminal is among the main problem confronted by port operators. This problem often called the Berth Allocation Problem (BAP).In this work, we realize an analytical study on the major planning models presented in the literature for the berth allocation problem, namely dynamic and discrete berth allocation problem model (DDBAP), dynamic and continuous berth allocation problem model (DCBAP) and dynamic and hybrid berth allocation problem model (DHBAP). The objective of this study is determine which model among the mentioned above can be used as a standard model for all type of terminal layouts and which of them ensure satisfactory outcome at level of minimization of ships turnaround time in the port. A commercial solver (CPLEX) as well as an efficient sailfish-based algorithm (SFA) are used to solve each model. Finally, computational experiences and comparison have been presented to demonstrate the most suited planning model.

Hybrid GAs for Solving the Simultaneous Discrete Berth Allocation and Dynamic Quay Crane Assignment Problems

This research proposes a hybrid approach, combining a GA with an event-based heuristic, to deal with the discrete berth allocation problem (DBAP) and dynamic quay crane assignment problem (DQCAP) simultaneously. Three hybrid GAs, each using a same crossover operation but different mutation operations, were developed. A two-stage procedure was used to develop solutions for the simultaneous DBAP and DQCAP. Firstly, a berth and an initial number of QCs are assigned to a ship by the GA. Subsequently, the assigned number of QCs to a ship can be adjusted by the event-based heuristic. Experimental results showed that these HGA have a better performance than a traditional GA in terms of fitness value. Especially, the HGA with Thoros mutation operation outperform the others.

A Hybrid GA with Variable Quay Crane Assignment for Solving Berth Allocation Problem and Quay Crane Assignment Problem Simultaneously

Container terminals help countries to sustain their economic development. Improving the operational efficiency in a container terminal is important. In past research, genetic algorithms (GAs) have been widely used to cope with seaside operational problems, including the berth allocation problem (BAP) and quay crane assignment problem (QCAP) individually or simultaneously. However, most GA approaches in past studies were dedicated to generate time-invariant QC assignment that does not adjust QCs assigned to a ship. This may underutilize available QC capacity. In this research, three hybrid GAs (HGAs) have been proposed to deal with the dynamic and discrete BAP (DDBAP) and the dynamic QCAP (DQCAP) simultaneously. The three HGAs supports variable QC assignment in which QCs assigned to a ship can be further adjusted. The three HGAs employ the same crossover operator but a different mutation operator and a two-stage procedure is used. In the first stage, these HGAs can generate a BAP solution and a QCAP solution that is time-invariant. The time-invariant QC assignment solution is then further transformed into a variable one in the second stage. Experiments have been conducted to investigate the effects of the three HGA and the results showed that these HGAs outperformed traditional GAs in terms of fitness value. In particular, the HGA3 with Thoros mutation operator had the best performance.

A Dynamic and Discrete Berth Allocation Problem in Container Terminals Considering Tide Effects

This study aims to minimize vessels’ departure delay time at Shahid Rajaee (SHRA) shallow port of Iran. The problem of SHRA port is its low-depth channel; explaining that when the ebb happens, vessels with high draft are not able to pass through the access channel and thus have to wait for the flow. A mixed integer linear planning model, which is capable of considering tide effects in berth allocation problem, was utilized for the purpose of the study. Loading and unloading data of SHRA port’s current situation were compared with the model outputs to validate the model. The results showed that the proposed model can considerably reduce vessels’ delay time. Next, a sensitivity analysis was performed on the depth of the access channel. The results revealed that channel dredging can significantly reduce vessels’ departure delay time and improve the performance of SHRA container port. Finally, active and active–reactive procedures were suggested to consider parameters’ uncertainty. The findings indicated that active–reactive procedure outperformed active procedure.

The stochastic discrete berth allocation problem

This paper deals with the discrete berth allocation problem with stochastic arrival times of vessels. The problem is to assign incoming vessels to a finite set of berthing points (berths) and to schedule them. The major objective is to minimize the expected total turnaround time of the vessels. We develop several new proactive, reactive and proactive/reactive approaches to this problem. Numerical experiments enable to compare these approaches. They show the impact of using full stochastic information instead of using mean values in a deterministic setting. The proactive/reactive approach, based on iterated tabu search and stochastic dynamic programming, provides good results when uncertainties on arrival times remain limited, while requiring only a few minutes of computing time on average. For larger levels of uncertainty, the proposed pure reactive approach clearly outperforms the others.

Combinatorial approach to exactly solving discrete and hybrid berth allocation problem

This paper presents an exact combinatorial algorithm for solving the Discrete Berth Allocation Problem (DBAP) and the Hybrid Berth Allocation Problem (HBAP) with fixed handling times of vessels based on the original algorithm for solving combinatorial problems called Sedimentation Algorithm. We address the issues of DBAP and HBAP according to the Rashidi and Tsang model. To the best of our knowledge, the proposed algorithm is the first exact combinatorial algorithm for solving the general DBAP and HBAP based on Rashidi and Tsang model. Computational results prove the superiority of the proposed algorithms compared with the exact solvers based on the Mixed Integer Programming (MIP) models. Efficient C implementation enabled us to solve instances with up to 65 vessels. This resolves most of the real life problems, even in large ports.

A HPSO for solving dynamic and discrete berth allocation problem and dynamic quay crane assignment problem simultaneously

Berth allocation problem (BAP) and quay crane assignment problem (QCAP) are two essential seaside operations planning problems faced by operational planners of a container terminal. The two planning problems have been often solved by genetic algorithms (GAs) separately or simultaneously. However, almost all these GAs can only support time-invariant QC assignment in which the number of QCs assigned to a ship is unchanged. In this study a hybrid particle swarm optimization (HPSO), combining an improved PSO with an event-based heuristic, is proposed to deal with two specific seaside operations planning problems, the dynamic and discrete BAP (DDBAP) and the dynamic QCAP (DQCAP). In the HPSO, the improved PSO first generates a DDBAP solution and a DQCAP solution with time-invariant QC assignment. Then, the event-based heuristic transforms the DQCAP solution into one with variable-in-time QC assignment in which the number of QCs assigned to a ship can be further changed. To investigate its effeteness, the HPSO has been compared to a GA (namely GA1) with time-invariant QC assignment and a hybrid GA (HGA) with variable-in-time QC assignment. Experimental results show that the HPSO outperforms the HGA and GA1 in terms of fitness value (FV).

A PSO algorithm for continuous berth allocation problem

Berth allocation problem (BAP) is defined as how to allocate the incoming ships to the berths along the entire quay, so that the total elapsed time of the ships is minimised. The problem is categorised into two types, namely discrete BAP and continuous BAP. In the first type, the ships should be allocated within any of the predefined berths; while in the second, all points of the quay are available as berthing locations. The continuous BAP (BAPC) is formulated as a mixed integer programming model, in which the variables of berthing locations and start times of handling the ships, among others, are integers. The model is difficult to solve on account of its combinatorial nature. This paper considers a relaxed version of the BAPC by treating the variables of berthing locations and start times as real numbers. Recently, a genetic algorithm (GA) was devised for the original BAPC and tested on some test examples. The goal of this paper is applying the particle swarm optimisation (PSO) meta-heuristic to the relaxed problem. An algorithm is implemented and tested by numerical examples, investigating the properties of the model and evaluating the PSO against the GA. The results show that the PSO works better in terms of accuracy and computational time.

The Berth Allocation Problem: A Strong Formulation Solved by a Lagrangean Approach

The berth allocation problem is one of the most relevant logistics problems arising in the management of container ports. Depending on assumptions made on the berthing location policy, two classes of the berth allocation problem have been considered in literature: the discrete case and the continuous case. In this paper, the properties of the discrete berth allocation problem, formulated as a dynamic scheduling problem, are analyzed. A new formulation of the problem is proposed, which is shown to be more compact and stronger than another one from the literature; a Lagrangean heuristic algorithm is developed; and computational results are presented.