Berth Scheduling Problem Research Articles

An Improved Genetic Algorithm for Berth Scheduling at Bulk Terminal

Berth and loading and unloading machinery are not only the main factors that affecting the terminal operation, but also the main starting point of energy saving and emission reduction. In this paper, a genetic Algorithm Framework is designed for the berth allocation with low carbon and high efficiency at bulk terminal. In solving the problem, the scheduler’s experience is transformed into a regular way to obtain the initial solution. The individual is represented as a chromosome, and the sub-chromosomes are encoded as integers, the roulette wheel method is used for selection, the two-point crossing method is used for cross, and the exchange variation method is used for variation in the procedure of designing the Algorithm. Considering the complexity of berth scheduling problem and the diversity of constraints and boundary conditions, the genetic algorithm combines with system simulation to get the final scheme of berth allocation. This model and algorithm are verified to be practical by analyzing multiple sets of examples of shorelines with different lengths. When compared with the traditional algorithms in three aspects which includes berth offset distance, departure delay cost and energy consumption of portal crane, the result indicates that the improved algorithm is more effective and feasible. The study will help to lower energy consumption and resource waste, reduce environmental pollution, and provide a reference for low-carbon, green and sustainable development of the terminal.

Optimal berth scheduling and sequencing under unexpected events

The berth scheduling problem (BSP) at container ports has received significant research attention. Nevertheless, few studies considered the BSP under emergent ship arrivals. Thus, this paper proposes an optimization procedure for scheduling and sequencing of ship arrivals at container port under the occurrence of unexpected events; emergent ship arrivals. Three consecutive models are proposed to maximize the number of served emergent ships at minimal disturbance to service schedule of regular ships. The first model schedules and sequences service of emergent ships at available idle berth(s). The remaining unscheduled emergent ships are then assigned by the second model, which attempts to serve those ships in untapped ranges between the scheduled regular ships. If some emergent ships are still unassigned in the untapped ranges, the third model finally resequences the service schedule of regular ships at the berth of the largest free margin to serve those emergent ships. A case study is employed to illustrate the proposed optimization procedure; where the results showed that the proposed models efficiently solved BSP at acceptable satisfaction levels for both regular and emergent ships. In conclusion, the proposed models may provide valuable support to decision makers in dealing with BSP under emergent ship arrivals.

Berth scheduling at marine container terminals

Purpose Marine transportation has been faced with an increasing demand for containerized cargo during the past decade. Marine container terminals (MCTs), as the facilities for connecting seaborne and inland transportation, are expected to handle the increasing amount of containers, delivered by vessels. Berth scheduling plays an important role for the total throughput of MCTs as well as the overall effectiveness of the MCT operations. This study aims to propose a novel island-based metaheuristic algorithm to solve the berth scheduling problem and minimize the total cost of serving the arriving vessels at the MCT. Design/methodology/approach A universal island-based metaheuristic algorithm (UIMA) was proposed in this study, aiming to solve the spatially constrained berth scheduling problem. The UIMA population was divided into four sub-populations (i.e. islands). Unlike the canonical island-based algorithms that execute the same metaheuristic on each island, four different population-based metaheuristics are adopted within the developed algorithm to search the islands, including the following: evolutionary algorithm (EA), particle swarm optimization (PSO), estimation of distribution algorithm (EDA) and differential evolution (DE). The adopted population-based metaheuristic algorithms rely on different operators, which facilitate the search process for superior solutions on the UIMA islands. Findings The conducted numerical experiments demonstrated that the developed UIMA algorithm returned near-optimal solutions for the small-size problem instances. As for the large-size problem instances, UIMA was found to be superior to the EA, PSO, EDA and DE algorithms, which were executed in isolation, in terms of the obtained objective function values at termination. Furthermore, the developed UIMA algorithm outperformed various single-solution-based metaheuristic algorithms (including variable neighborhood search, tabu search and simulated annealing) in terms of the solution quality. The maximum UIMA computational time did not exceed 306 s. Research limitations/implications Some of the previous berth scheduling studies modeled uncertain vessel arrival times and/or handling times, while this study assumed the vessel arrival and handling times to be deterministic. Practical implications The developed UIMA algorithm can be used by the MCT operators as an efficient decision support tool and assist with a cost-effective design of berth schedules within an acceptable computational time. Originality/value A novel island-based metaheuristic algorithm is designed to solve the spatially constrained berth scheduling problem. The proposed island-based algorithm adopts several types of metaheuristic algorithms to cover different areas of the search space. The considered metaheuristic algorithms rely on different operators. Such feature is expected to facilitate the search process for superior solutions.

An augmented self-adaptive parameter control in evolutionary computation: A case study for the berth scheduling problem

The demand for international seaborne trade has substantially increased over the last three decades and is predicted to continue increasing during the upcoming years. A marine container terminal, as an important node in supply chains, should be able to successfully cope with increasing demand volumes. Berth scheduling can significantly influence the general throughput of marine container terminals. In this study, a mixed-integer linear programming mathematical model is proposed for the berth scheduling problem, aiming to minimize the summation of waiting costs, handling costs, and late departure costs of the vessels that are to be served at a marine container terminal. An innovative Evolutionary Algorithm is designed to solve the developed mathematical model. The proposed solution algorithm relies on the augmented self-adaptive parameter control strategy, which is developed in order to effectively change the algorithmic parameters throughout the search process. Performance of the designed algorithm is evaluated against nine alternative state-of-the-art metaheuristic-based algorithms, which have been frequently used for berth scheduling in the marine container terminal operations literature. The results demonstrate that all the developed algorithms have a high level of stability and return competitive solutions at convergence. The computational experiments also prove superiority of the designed augmented self-adaptive Evolutionary Algorithm over the alternative algorithms in terms of different performance indicators.

An Adaptive Island Evolutionary Algorithm for the berth scheduling problem

Increasing volumes of the seaborne containerized trade put additional pressure on marine container terminal operators. Long congestion periods have been reported at certain marine container terminals due to inability of the infrastructure to serve the growing demand, increasing number of megaships, port disruptions, and other factors. In order to alleviate congestion and avoid potential cargo delivery delays to the end customers, marine container terminal operators have to enhance the efficiency of their operations. This study focuses on improving the seaside operations at marine container terminals. A new Adaptive Island Evolutionary Algorithm is proposed for the berth scheduling problem, aiming to minimize the total weighted service cost of vessels. The developed algorithm simultaneously executes separate Evolutionary Algorithms in parallel on its islands and exchanges individuals between the islands based on an adaptive mechanism, which allows more efficient exploration of the problem search space. A set of extensive computational experiments indicate that the optimality gaps of the Adaptive Island Evolutionary Algorithm do not exceed 1.93% for the considered small-size problem instances. Furthermore, the proposed solution algorithm was compared against the other state-of-the-art metaheuristic algorithms and exhibited statistically significant improvements in terms of the objective function values.

Berth Scheduling Problem Considering Traffic Limitations in the Navigation Channel

In view of the trend of upsizing ships, the physical limitations of natural waterways, huge expenses, and unsustainable environmental impact of channel widening, this paper aims to provide a cost-efficient but applicable solution to improve the operational performance of container terminals that are enduring inefficiency caused by channel traffic limitations. We propose a novel berth scheduling problem considering the traffic limitations in the navigation channel, which appears in many cases including insufficient channel width, bad weather, poor visibility, channel accidents, maintenance dredging of the navigation channel, large vessels passing through the channel, and so on. To optimally utilize the berth and improve the service quality for customers, we propose a mixed-integer linear programming model to formulate the berth scheduling problem under the one-way ship traffic rule in the navigation channel. Furthermore, we develop a more generalized model which can cope with hybrid traffic in the navigation channel including one-way traffic, two-way traffic, and temporary closure of the navigation channel. For large-scale problems, a hybrid simulated annealing algorithm, which employs a problem-specific heuristic, is presented to reduce the computational time. Computational experiments are performed to evaluate the effectiveness and practicability of the proposed method.

A Self-Adaptive Evolutionary Algorithm for the Berth Scheduling Problem: Towards Efficient Parameter Control

Since ancient times, maritime transportation has played a very important role for the global trade and economy of many countries. The volumes of all major types of cargo, which are transported by vessels, has substantially increased in recent years. Considering a rapid growth of waterborne trade, marine container terminal operators should focus on upgrading the existing terminal infrastructure and improving operations planning. This study aims to assist marine container terminal operators with improving the seaside operations and primarily focuses on the berth scheduling problem. The problem is formulated as a mixed integer linear programming model, minimizing the total weighted vessel turnaround time and the total weighted vessel late departures. A self-adaptive Evolutionary Algorithm is proposed to solve the problem, where the crossover and mutation probabilities are encoded in the chromosomes. Numerical experiments are conducted to evaluate performance of the developed solution algorithm against the alternative Evolutionary Algorithms, which rely on the deterministic parameter control, adaptive parameter control, and parameter tuning strategies, respectively. Results indicate that all the considered solution algorithms demonstrate a relatively low variability in terms of the objective function values at termination from one replication to another and can maintain the adequate population diversity. However, application of the self-adaptive parameter control strategy substantially improves the objective function values at termination without a significant impact on the computational time.

Minimizing Carbon Dioxide Emissions Due to Container Handling at Marine Container Terminals via Hybrid Evolutionary Algorithms

Considering a rapidly increasing seaborne trade and drastic climate changes due to emissions, produced by oceangoing vessels and container handling equipment, marine container terminal operators not only have to improve effectiveness of their operations to serve the increasing demand, but also to account for the environmental impact associated with the terminal operations. This paper proposes a novel mixed integer mathematical model for the berth scheduling problem, which minimizes the total service cost of vessels, including the total carbon dioxide emission cost due to container handling. The latter pollutant is a primary greenhouse gas that causes global warming. A Hybrid Evolutionary Algorithm, which deploys a set of local search heuristics, is developed to solve the problem. Computational experiments showcase that the optimality gap of the proposed solution algorithm does not exceed 1.61%. It is further shown that the application of additional local search heuristics allows efficient discovery of promising solutions throughout the search process. Results from numerical experiments also indicate that changes in the carbon dioxide emission cost may significantly affect the design of berth schedules. The developed mathematical model and the proposed solution algorithm can thus be adopted as effective planning tools by the marine container terminal operators and improve the environmental sustainability of the terminal operations.

An Improved Discrete Particle Swarm Optimization for Berth Scheduling Problem

Berth scheduling operation is an important problem in container terminal. The mathematic model of this problem is described in this paper and an improved particle swarm optimization algorithm is introduced to obtain the optimal scheduling solution. A floating-point allocation rule is used to encode the particles in the discrete space. A local search method is combined with PSO to avoid precocity. Finally the experiments are done to prove the improved PSO in this paper can resolve the berth scheduling problem and get better solution and convergence speed than the basic PSO.

Berth scheduling with variable cost functions

This article presents a new mathematical formulation for the berth scheduling problem. The objective is to simultaneously minimize the total costs from vessels’ late departure and waiting time, and maximize the total premiums from vessels’ early departures. It is assumed that different vessels have different variable penalty/premium cost functions (PPCFs) that are based on contractual agreements between the liner shipping company and the terminal operator. A genetic algorithms-based heuristic is proposed to solve the resulting problem. A number of computational examples are presented to: (a) assess four different berth scheduling policies that are based on three different contractual agreements and (b) evaluate the effect of non-linear PPCFs. Computational results show that: (a) penalty/premium cost distribution among vessels display distinctive variations between the four berth scheduling policies, and (b) contractual agreements with constant (within a time window), followed by hourly (outside the time window) penalties/premiums should be favored during contractual agreement negotiations between terminal operators and liner shipping companies.

A Multi-Objective Decision and Analysis Approach for the Berth Scheduling Problem

Berth scheduling can be described as the resource allocation problem of berth space to vessels in a container terminal. When defining the allocation of berths to vessels container terminal operators set several objectives which ideally need to be optimized simultaneously. These multiple objectives are often non-commensurable and gaining an improvement on one objective often causes degrading performance on the other objectives. In this paper, the authors present the application of a multi-objective decision and analysis approach to the berth scheduling problem, a resource allocation problem at container terminals. The proposed approach allows the port operator to efficiently select a subset of solutions over the entire solution space of berth schedules when multiple and conflicting objectives are involved. Results from extensive computational examples using real-world data show that the proposed approach is able to construct and select efficient berth schedules, is consistent, and can be used with confidence.

The Berth-Scheduling Problem

This paper presents a new formulation for the discrete space berth-scheduling problem at marine container terminals. This formulation reflects an environmentally friendly berth-scheduling policy with the objectives of (a) maximizing berth productivity by minimizing the total service time and delayed departures for all vessels and (b) minimizing the total emissions and fuel consumption for all vessels while in transit to their next port of call. A genetic algorithms–based heuristic is presented to solve the resulting problem, and computational examples are presented to evaluate the proposed berth-scheduling policy.

Discrete Berth-Scheduling Problem

The problem of discrete space berth scheduling arises in seaside operations at marine container terminals. This complex problem receives ongoing attention from the research community because operators of marine container terminals deal with it on a daily basis. Despite this interest, most published research does not adequately capture the objectives and restrictions facing terminal operators in the berth-scheduling process. A new mathematical formulation is presented for the discrete space berth-scheduling problem that attempts to capture most of the terminal operators' objectives and move closer to a unified mathematical formulation for the problem. The proposed formulation subsumes the majority of the published berth-scheduling model formulations with a significant reduction in the feasible solution space while retaining linearity of both the objective function and the constraints.

The berth allocation problem: Optimizing vessel arrival time

The berth scheduling problem deals with the assignment of vessels to berths in a marine terminal, with the objective to maximize the ocean carriers’ satisfaction (minimize delays) and/or minimize the terminal operator's costs. In the existing literature, two main assumptions are made regarding the status of a vessel: (a) either all vessels to be served are already in the port before the planning period starts, or (b) they are scheduled to arrive after the planning period starts. The latter case assumes an expected time of arrival for each vessel, which is a function of the departure time of the vessel from the previous port, the average operating speed and the distance between the two ports. Recent increases in fuel prices have forced ocean carriers to reduce current operating speeds, while stressing to terminal operators the need to maintain the integrity of their schedule. In addition, several collaborative efforts between industry and government agencies have been proposed, aiming to reduce emissions from marine vessels and port operations. In light of these issues, this article presents a berth-scheduling policy to minimize vessel delayed departures and indirectly reduce fuel consumption and emissions produced by the vessels while in idle mode. Vessel arrival times are considered as a variable and are optimized to accommodate the objectives of the proposed policy while providing ocean carriers with an optimized vessel speed. Example problems using real data show that the proposed policy reduces the amount of emissions produced by vessels at the port in idle mode, optimizes fuel consumption and waiting time at the port by reducing vessel operating speeds to optimal levels and minimizes the effects of late arrivals to the ocean carriers’ schedule.

A lamda-optimal based heuristic for the berth scheduling problem

Berth scheduling aims to optimally schedule vessels to berthing areas along a quay and is a complex optimization problem. In this paper we propose a lamda-optimal based heuristic as a resolution approach for the discrete space berth scheduling problem. The proposed heuristic can also be applied to validate optimality, in the case where other (meta)heuristics are applied as resolution approaches. A second internal Genetic Algorithms based heuristic is also proposed to reduce the computational time required for medium to large scale instances. Numerical experiments performed show that the proposed heuristic is adequate to produce near-optimal results within acceptable computational times.

An optimization heuristic for the berth scheduling problem

Berths are among the most important resources in a port. In this research we present an optimization-based approach for the berth scheduling problem, which is to determine the berthing time and space for each incoming ship. The neighborhood-search based heuristic treats the quay as a continuous space. In additional to basic physical requirements, this model takes several factors important in practice into consideration, including the first-come-first-served rule, clearance distance between ships, and possibility of ship shifting. Computational experience is provided.

The berth scheduling problem with customer differentiation: a new methodological approach based on hierarchical optimization

The berth scheduling problem deals with the assignment of vessels to berth space in a container terminal. Defining berth schedules in container terminal operations translates in meeting different objectives that are often non-commensurable and gaining an improvement on one objective often causes degrading performance on the others. In this paper the discrete space and dynamic arrival berth scheduling problem is studied and formulated for the first time via a hierarchical optimization framework, using two levels of hierarchy that differentiate between two conflicting objectives terminal operators face when defining vessel to berth assignments. For the resolution of this problem an interactive algorithm is developed based on the k-th best algorithm for the case where multi-objective functions are considered in the upper level. Computational examples showed that the proposed algorithm gives optimal or near optimal solutions that are comparable to the ones obtained by its single level formulation counterpart.

Adaptive Algorithm Based on Time Window Partitioning for Discrete and Dynamic Berth-Scheduling Problem

The berth-scheduling problem is considered with the objective of increasing customer satisfaction by minimizing the late berthing or departure and maximizing the early and timely berthing or departure of vessels. Vessel priority also is considered through the use of weights. An adaptive local search heuristic is developed to solve the resulting problem using a Markovian walk and a time window partitioning approach to improve convergence patterns and the objective function values. Results obtained from the heuristic are shown to be robust, and convergence rates and patterns are promising.

Berth scheduling by simulated annealing

The objective of the berth-scheduling problem is to determine the berthing times and positions of containerships in port container terminals. Every vessel requires a specific amount of space in a wharf for a predetermined length of time to unload and load containers. In this study, a mixed-integer-linear-programming (MIP) model was formulated for the berth-scheduling problem. The simulated annealing algorithm was applied to the berth-scheduling problem to find near-optimal solutions. Experimental results showed that the simulated annealing algorithm obtains solutions that are similar to the optimal solutions found by the MIP model.

Berth scheduling for container terminals by using a sub-gradient optimization technique

A method for establishing a berth schedule consisting of berthing times and berthing positions of containerships in port container terminals is addressed in this paper. Each vessel requires a specific amount of space on the berth during a predetermined length of time for unloading and loading containers. The berth schedule must be constructed in a way to satisfy requests from carriers on berthing times and minimize handling efforts during ship operation. A mixed integer program is formulated for the berth-scheduling problem, which can be solved using a commercial package. In order to overcome the computational load of the mixed integer program, the formulation is converted into another integer linear program in which the solution space of the berth and the time is discretized. A Lagrangean relaxation model of the discretized model is solved using a sub-gradient optimization technique. Results of a numerical experiment are provided and discussed.