Berth Allocation Problem Research Articles

Berth Allocation in a Bulk Terminal with Overall Quay Length Constraint

Motivated by the operation of bulk terminal in the Pearl River Delta, we study a berth allocation problem (BAP) with 2 berths and overall quay length constraint. The quay length occupied by a vessel depends on its berthing directions. The feasible berthing direction changes in a tide cycle. The objective is to minimize the total service of all vessels. We develop a mixed integer programming (MIP) model for the problem. We also propose an efficient genetic algorithm to tackle the problem. Our computational experiments show that the mixed integral programming model can only be solved by CPLEX for small-size instances, the genetic algorithm obtains good approximation solutions for large-size instances.

Integrated Laycan and Berth Allocation and time-invariant Quay Crane Assignment Problem in tidal ports with multiple quays

Efficient management of port resources plays a crucial role in reducing vessel stay times and avoiding the payment of demurrage charges. In this paper, we focus on the integrated Laycan and Berth Allocation and Quay Crane Assignment Problem, which considers three main decision problems in port management in an integrated way: the Laycan Allocation Problem, the dynamic continuous Berth Allocation Problem and the time-invariant Quay Crane Assignment Problem. In a second part, the integrated problem is extended to the Specific Quay Crane Assignment, which includes the assignment of a set of specific quay cranes to each vessel, considering the productivity of quay cranes and their maximum outreach. The proposed integer programming models are original in several ways. First, the formulation of the models uses predicates which ensure flexibility in the implementation, and significantly improve the computational performance. The numerical study shows that the problems of practical size can be solved to optimality in a reasonable time using commercial software. Second, since the studied problems have different decision levels, a change of decision time-interval is incorporated inside the planning horizon for seamless decision-making. Third, to ensure that this integrated problem is as close as possible to reality, we consider both physical characteristics of the ports rarely studied together (tidal ports with multiple quays and different water depths) and contractual clauses (non-working periods and Charter Party clauses). The output of the models is an efficient schedule for berthing chartered vessels with an efficient quay crane assignment, and laycans to new vessels to charter.

Integrated proactive and reactive strategies for sustainable berth allocation and quay crane assignment under uncertainty

The berth allocation and quay crane assignment problem (BACAP) is a complex port operation planning problem susceptible to uncertainties, such as vessel arrival time fluctuation to its estimated time of arrival and maritime markets. For promoting reliability and sustainability of container terminals, this paper addresses the optimization of BACAP under the uncertain vessels’ arrival times and fluctuation of loading and unloading volumes. We propose a proactive BACAP strategy considering minimum recovery cost under uncertainty using a reactive strategy. A stochastic programming model is formulated to minimize the basic cost in the baseline schedule, and the recovery cost in real uncertain scenarios. A two-stage meta-heuristic framework based on GA is developed for solving this problem. Numerical experiments and scenario analysis are conducted to validate the effectiveness of the proposed model and the proposed solution approaches.

Hybrid Bird Mating Optimizer With Single-Based Algorithms for Combinatorial Optimization Problems

Bird mating optimizer (BMO) is a population-based metaheuristic that has been recently extended to solve combinatorial optimization problems. Even though the algorithm shows promising performance in solving combinatorial optimization problems, it suffers from slow convergence and poor efficiency which leads to poor solution quality for some problem instances. This is due to the limited capability of BMO in exploiting the search space and identifying more promising regions. Therefore, in this work we propose a hybrid BMO with five single-based metaheuristics: hill-climbing, late acceptance hill-climbing, simulated annealing, iterated greedy heuristic and variable iterated greedy heuristic. Each of these algorithms is used inside the BMO to exploit the search space, and improve the quality of solution generated from the BMO population. This work also compares which one of these five is better for hybridizing with BMO. The performance of these algorithms is tested on two combinatorial problems: travelling salesman problem and berth allocation problem. Experimental results demonstrate that the hybrid algorithm is superior to BMO when applied to both problems and it improved the BMO by 1.13% for BAP and by 4.13% for TSP. Furthermore, the hybrid algorithm is able to match the best-known results for most of the instances. In addition, the proposed hybrid approaches perform well over both tested domains and obtain competitive results when compared to the best-known results that have previously been presented in the scientific literature.

Modeling berth allocation and quay crane assignment considering QC driver cost and operating efficiency

Due to high labour costs and difference of QC driver’s handling efficiency existing between day and night, factors concerning QC drivers can significantly impact the schedule of berth allocation and quay crane assignment. This paper tackles the berth allocation and quay crane assignment problem considering QC driver cost, difference of the operating efficiency and performance-related pay between day and night. How QC driver-related factors affect the schedules is analyzed, and the objective composition including QC driver cost is given. A mixed integer programming model with model acceleration algorithms is developed for the proposed problem, and a meta-heuristic framework including a three-stage algorithm is proposed for solving the problem. Numerical experiments are conducted to validate the effectiveness of the proposed model and performance of the meta-heuristic approach, leading to a multitude of managerial insights.

LOW-EMISSION BERTH ALLOCATION BY OPTIMIZING SAILING SPEED AND MOORING TIME

To investigate the relations among delay times (weighted by vessels’ handling times), the emissions during the vessels’ sailing and mooring in a Berth Allocation Problem (BAP) where the berth times and sailing speeds are formulated as decision variables. The vessels’ delay times are computed comparing to the vessels’ Expected Departure Times (EDTs); the sailing emission is determined by the sailing speed and distance; the mooring emission is positive to the mooring time at terminal. Multi-objective mixed-integer programs are established, and the nonlinear functions between emissions and sailing speeds are transferred to linear ones by the Second-Order Cone Programming (SOCP) method. Solution methods are further developed based on e-constraint and stage-based methods by considering the preferences of objectives. Four groups of experiments are conducted to demonstrate the formulations, effects of vessels’ handling times and EDTs on the solutions, and the reduced emissions affected by the number of vessels in the schedules. Experimental results demonstrated that the efficiency purpose is not absolutely conflict with the environment purposes for some instances, and so they can be pursued at the same time; improving the vessels’ handling efficiency help expand the ranges of berth times and sailing speeds, resulting in reducing the delay times and emissions; advancing the EDTs can improve the terminal operators’ service quality to shipping companies, while the weighted delay times and emission may be increased.

Optimal berth allocation under regular and emergent vessel arrivals

This research proposes two optimization models to deal with the berth allocation problem. The first model considers the berth allocation problem under regular vessel arrivals to minimize the flow time of vessels in the marine container terminal, minimize the tardiness penalty costs, and maximize the satisfaction level of vessels’ operators on preferred times of departure. The second model optimizes the berth allocation problem under emergency conditions by maximizing the number of assigned vessels, minimizing the vessel’s waiting time, and maximizing the satisfaction level on the served ships. Two real examples are provided for model illustration under regular and emergent vessel arrivals. Results show that the proposed models effectively provide optimal vessel scheduling in the terminal, reduce costs at an acceptable satisfaction level of vessels’ operators, decrease the waiting time of vessels, and shorten the delay in departures under both regular and emergent vessel arrivals. In conclusion, the proposed models may provide valuable assistance to decision-makers in marine container terminals on determining optimal berth allocation under daily and emergency vessel arrivals. Future research considers quay crane assignment and scheduling problems.

An integrated method for berth allocation and quay crane assignment to allow for reassignment of vessels to other terminals

With globalization increasing countries’ trade volumes, resource management at container terminals has become more complex. To realistically address this problem, this paper proposes a methodology to solve the berth allocation and quay crane assignment problem (BACAP) while allowing the reassignment of vessels to other terminals in a multiuser container terminal. A filtered beam search (FBS)-based heuristic, a greedy randomized adaptive search procedure (GRASP)-based heuristic, and an iterative approach are integrated to provide a solution within a reasonable time frame. Numerical experiments are conducted with realistic instances from a container terminal located in Busan, Republic of Korea. The results show that the proposed approach yields a near-optimal solution with a significantly shorter computational time, compared with a commercial solver.

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.

A reduced VNS based approach for the dynamic continuous berth allocation problem in bulk terminals with tidal constraints

This paper deals with the problem of allocating berth positions for vessels in export bulk port terminals considering tidal constraints and was first formulated by Ernst et al., (2017). This study investigates the dynamic and continuous berth allocation problem (BAP) with respect to tidal constraints (BAP_TC), and seeks to minimize the total service time of berthed vessels. Since the BAP problem is NP-hard the BAP_TC is also NP-hard. A reduced variable neighborhood search (RVNS) based approach is developed to solve the problem. For parameters tuning a machine learning algorithm is developed and used. Problem instances are benchmarked with CPLEX and the numerical experiments proved that the proposed algorithm is capable of generating high-quality solutions in rather short time. Both small and large-scale instances in the literature are tested to evaluate the metaheuristic effectiveness using other solution approaches from the literature. The computational experiment proves that the proposed algorithm provides state of the art results.

New hybrid genetic algorithms to solve dynamic berth allocation problem

Berth allocation problem (BAP) is concerned to assign ships to port terminal positions, seeking to minimize the total service time and maximize the quay occupation. A dynamic model with special features is developed to deal with real scenarios from Port Administration of Paranaguá and Antonina (APPA), located on the Brazilian coast. To solve the problem, this work proposes two metaheuristics comprise by a novel combination of genetic algorithm and an approximated dynamic programming employed as a local search. Two heuristics for solution space reductions, a confinement procedure in a reduced neighborhood, known as Corridor Method, and an elimination process for unpromising solution regions are designed for local search approach. Case studies present a problem complexity discussion and comparative analysis of the metaheuristics regarding two standard genetic algorithms. The computational experiments explore the optimal solutions for small instances and the best results, solutions variability, and probabilistic plots resorting by ten instances based on real data available by APPA. The results show the reliability of the metaheuristics to deal with large instances and tight schedules in busy port systems.

Column generation for low carbon berth allocation under uncertainty

This article investigates a low carbon-oriented berth allocation and quay crane assignment problem considering vessels’ uncertain arrival time and loading/unloading workload for vessels. A two-stage stochastic programming model is formulated based on a set of scenarios. The first stage designs a baseline schedule and the second stage adjusts the schedule in each scenario. A solution method is developed by using column generation techniques. Numerical experiments are conducted to validate the efficiency of our column generation-based solution method and the effectiveness of the proposed decision model. Some sensitivity analysis is also performed to draw some managerial implications.

Optimization of Continuous Berth Scheduling by Taking into Account Double-Line Ship Mooring

“Double-Line Ship Mooring” (DLSM) mode has been applied as an initiative operation mode for solving berth allocation problems (BAP) in certain giant container terminals in China. In this study, a continuous berth scheduling problem with the DLSM model is illustrated and solved with exact and heuristic methods with an objective to minimize the total operation cost, including both the additional transportation cost for vessels not located at their minimum-cost berthing position and the penalties for vessels not being able to leave as planned. First of all, this problem is formulated as a mixed-integer programming model and solved by the CPLEX solver for small-size instances. Afterwards, a particle swarm optimization (PSO) algorithm is developed to obtain good quality solutions within reasonable execution time for large-scale problems. Experimental results show that DLSM mode can not only greatly reduce the total operation cost but also significantly improve the efficiency of berth scheduling in comparison with the widely used single-line ship mooring (SLSM) mode. The comparison made between the results obtained by the proposed PSO algorithm and that obtained by the CPLEX solver for both small-size and large-scale instances are also quite encouraging. To sum up, this study can not only validate the effectiveness of DLSM mode for heavy-loaded ports but also provide a powerful decision support tool for the port operators to make good quality berth schedules with the DLSM mode.

Berth Allocation and Quay Crane Assignment for the Trade-off Between Service Efficiency and Operating Cost Considering Carbon Emission Taxation

To sustain the development of maritime transportation, “green ports,” which operate with a good balance between environmental impact and economic interests, have been the focus of port operators and government agencies and are required to look into energy saving and emission reduction initiatives. One such reduction strategy proposed by the International Maritime Organization suggested imposing a carbon emission tax on ports as a long-term solution to reduce carbon emissions, but this would definitely increase the operating cost of ports. Quay cranes (QCs), as one type of handling equipment, play an important role in the service efficiency and carbon emission of ports. Therefore, this paper makes an effort to explore the study of the integrated berth allocation and QC assignment problem with the consideration of carbon emission taxation. This problem is formulated as a biobjective integer programming model, aimed at minimizing the total completion delay of all tasks and the total operating costs for all QCs. Finally, numerical experiments are performed to assess the applicability of the proposed models and evaluate the efficiency of the developed solution algorithm.

Modelling and solving a berth allocation problem in an automotive transshipment terminal

In this paper, we study a berth allocation problem (BAP) in the automotive transshipment (also called Ro-Ro) terminal of Le Havre seaport. Despite the vast literature on the BAP, very few work deals with automotive transshipment terminals. The main objective of the problem we consider is to define incoming ships berthing positions in the Ro-Ro terminal, for minimising the total handling time while considering several operational constraints. In particular, we introduce the BAP with car flow crossings. We discuss mathematical models for car flow crossings and present integer programming formulations of the problem with and without car flow crossings. Then, we solve the problem using CPLEX 12.5 and discuss some computational issues.

Research on Continuous Berth Allocation Problem based on Genetic-Harmony Search Algorithm

In order to solve the berth allocation problem and improve the efficiency of the dock, a mixed integer nonlinear programming model is built with the length of port stay. The genetic-harmony search algorithm is used to solve it for the first time. Finally, the algorithm and Lingo are used to solve the large-scale berth allocation problem at the same time. Under the same data of arrival ships, several groups of experiments are designed to verify the algorithm. The results show that the genetic-harmony search algorithm can be used to solve the berth allocation problem. On the basis of the consistency between the genetic-harmony search algorithm and Lingo, the genetic-harmony search algorithm is faster and more efficient.

Simulation optimization of the berth allocation in a container terminal with flexible vessel priority management

ABSTRACT Solving the berth allocation problem (BAP) in ports is not trivial where the berth resources are limited and various sizes of vessels arrive with dramatically dissimilar loads. Especially in real scenarios, arriving vessels are accepted for a berth with the first come first served (FCFS) priority rule. This study proposes a decision support system coupled with a simulation optimization module based on the swarm-based Artificial Bee Colony optimization algorithm for solving the BAP. The proposed methodology was implemented for the Izmir port in Turkey. To investigate the influences of the vessel priorities on the BAP, four different experimental scenarios based on the single (SQM) and multiple queue models (MQM) were coupled with FCFS and proposed hybrid queue priority (HQP) rule. The results indicated that SQM scenarios were superior to MQM scenarios in a manner of minimizing the average vessel waiting times and the implementation of a dynamic berth allocation strategy for the MQM significantly decreases the vessel waiting times. Results of the SQM also imply that utilization of the HQP approach further minimizes the average vessel waiting times and increases the berth utilization and port throughput without yielding excessive waiting times for the larger vessels compared with the FCFS priority rule.

Modelling and solving the multi-quays berth allocation and crane assignment problem with availability constraints

In this work, we are interested in the multi-quays berth allocation and crane assignment problem under availability restrictions. Availability restrictions may arise due weather conditions, or when, for example, cranes must undergo planned maintenance in order to stay in good performance. This problem was inspired by a real-case of a bulk port in Morocco. To solve the problem we propose at first a mixed-integer programming model. Then, in view of the limitations of the proposed model, we investigate a set of heuristics based on general variable neighborhood search with three variants of variable neighborhood descent as a local search. To validate the proposed model and the proposed heuristic approach, real-world instances are used. The computational results reveal that CPLEX MIP solver consumes a lot of CPU time to solve this model, even sometimes failing to guarantee the optimality of the provided solution. On the other hand, the proposed GVNS heuristic turns out to be very efficient in solving the considered problem.

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.

Bird Mating Optimizer for Combinatorial Optimization Problems

The bird mating optimizer is a new metaheuristic algorithm that was originally proposed to solve continuous optimization problems with a very promising performance. However, the algorithm has not yet been applied for solving combinatorial optimization problems. Thus, the formulation may not be able to generate a discrete feasible solution. Many continuous algorithms used random-key representation to represent the discrete solution using real numbers or a discrete variant of the algorithm is used to deal with the discrete solution of the problem. However, there is no evidence which methodology is better for solving combinatorial optimization problems. Therefore, this work proposes two variants of bird mating optimizer (random-key bird mating optimizer and the discrete bird mating optimizer), to identify which one is more efficient in solving combinatorial optimization problems. In the first one, we use a random-key encoding scheme, whilst, in the later one, we use crossover (multi-parent) and mutation operators to combine the components of the selected parents to generate new broods. The performance of these algorithms is tested on the travelling salesman problem and berth allocation problem, and are compared with the results of two well-known optimization algorithms: Genetic Algorithm and Particle Swarm Optimization. Experimental results show that the discrete bird mating optimizer is more efficient than the others on all tested benchmark instances. Indeed, it is able to attain the best-known results in some of the BAP benchmark instances. These indicate the applicability and the effectiveness of the proposed discrete bird mating optimizer in solving combinatorial optimization problems.