A heuristic for the quay crane scheduling problem based on contiguous bay crane operations

Quay cranes (QC) are key resources at container terminals, and the efficiency of QC operations is vital for terminal productivity. The Quay Crane Scheduling Problem (QCSP) is to schedule the work activities for a set of cranes assigned to a single berthed vessel with the objective of minimizing the completion time of all container handling tasks. The problem is complicated by special characteristics of QC operations. Considering QC moving time and interference constraints, the concept of contiguous bay operations is proposed and a heuristic is developed to generate QC schedules with this feature. The heuristic is efficient and effective: it has polynomial computational complexity, and it produces schedules with a completion time objective bounded above by a small increment over the optimal completion time. Importantly, the heuristic guarantees that no quay cranes are idle due to interference. Numerical experiments demonstrate that the optimality gap is small for practical instances.     

Dynamic rolling strategy for multi-vessel quay crane scheduling

This paper focuses on the container loading and unloading problem with dynamic ship arrival times. Using a determined berth plan, in combination with the reality of a container terminal production scheduling environment, this paper proposes a scheduling method for quay cranes that can be used for multiple vessels in a container terminal, based on a dynamic rolling-horizon strategy. The goal of this method is to minimize the operation time of all ships at port and obtain operation equilibrium of quay cranes by establishing a mathematical model and using a genetic algorithm to solve the model. Numerical simulations are applied to calculate the optimal loading and unloading order and the completion time of container tasks on a ship. By comparing this result with the traditional method of quay crane loading and unloading, the paper verifies that the quay crane scheduling method for multiple vessels based on a dynamic rolling-horizon strategy can provide a positive contribution to improve the efficiency of container terminal quay crane loading and unloading and reduce resource wastage.     

干扰约束下考虑分组作业面的岸桥AGV联合调度

为解决自动化码头海侧多阶段设备作业的协调问题,加快集装箱在码头内部的周转过程。考虑干扰约束下分组作业面的的岸桥自动导引小车（AGV）联合调度问题。以岸桥、AGV完工时间和AGV等待时间加权总和最小为目标,考虑岸桥实际操作中的干扰约束与AGV堵塞等待等情况,建立岸桥与AGV联合调度优化模型。提出岸桥动态调度与AGV分组作业面调度模式,设计不同规模的算例,并采用遗传算法（GA）进行求解,将计算结果与传统调度模式进行对比。结果表明,该算法能有效提高岸桥与AGV作业效率,降低AGV的等待时间与堵塞次数,为码头实际作业提供依据。     

A tabu search heuristic for the quay crane scheduling problem

This paper proposes a tabu search heuristic for the Quay Crane Scheduling Problem (QCSP), the problem of scheduling a fixed number of quay cranes in order to load and unload containers into and from a ship. The optimality criterion considered is the minimum completion time. Precedence and non-simultaneity constraints between tasks are taken into account. The former originate from the different kind of operations that each crane has to perform; the latter are needed in order to avoid interferences between the cranes. The QCSP is decomposed into a routing problem and a scheduling problem. The routing problem is solved by a tabu search heuristic, while a local search technique is used to generate the solution of the scheduling problem. This is done by minimizing the longest path length in a disjunctive graph. The effectiveness of our algorithm is assessed by comparing it to a branch-and-cut algorithm and to a Greedy Randomized Adaptive Search Procedure (GRASP).     

全岸线集装箱装卸桥调度模型研究

集装箱装卸桥是集装箱物流多式联运的关键设备,处于整个集装箱物流的重要节点。集装箱装卸桥的调度计划直接影响集装箱码头的运作效率。通过对集装箱码头装卸桥生产过程的研究,建立全岸线集装箱装卸桥调度与分配的混合整数动态规划模型,并采用基于段编码技术的遗传算法,进行模型优化求解;优化后的集装箱装卸桥调度方案的生产效率和生产作业均衡有明显改善。     

A quay crane dynamic scheduling problem by hybrid evolutionary algorithm for berth allocation planning

A considerable growth in worldwide container transportation needs essential optimization of terminal operations. An operation schedule for berth and quay cranes can significantly affect turnaround time of ships, which is an important objective of all schedules in a port. This paper addresses the problem of determining the berthing position and time of each ship as well as the number of quay cranes assigned to each ship. The objective of the problem is to minimize the sum of the handling time, waiting time and the delay time for every ship. We introduce a formulation for the simultaneous berth and quay crane scheduling problem. Next, we combine genetic algorithm with heuristic to find an approximate solution for the problem. Computational experiments show that the proposed approaches are applicable to solve this difficult but essential terminal operation problem.     

A new continuous berth allocation and quay crane assignment model in container terminal

Over the past decades, Chinese ports throughput grew rapidly, and more and more concerns were shown on the operational efficiency and effectiveness. Many studies have been made for scheduling berth and quay cranes, which are the critical resources in container terminals. In this paper, a two-phase model for berth allocation and quay crane assignment is proposed. In the first phase, according to the relationships of time and space between vessels, a new continuous berth allocation model is established, in which not only the common restricts but the coverage area of quay crane are considered. Then in the quay crane assignment phase, a multi-objective programming model is proposed, in which the first objective is to minimize the range of maximum and minimum quay cranes used for resources saving, and the second one is to minimize the movements of quay cranes so as to improve the efficiency. A particle swarm optimization algorithm for BAP was developed. The results of numerical experiments show that the proposed approach can improve the essential operations in container terminal.     

Heuristics for solving continuous berth allocation problem considering periodic balancing utilization of cranes

This study investigates a berth allocation problem considering the periodic balancing utilization of quay cranes in container terminals. The proposed model considers that the quay cranes allocated to a work shift should be fully used and other real-world considerations, such as the continuous quay line, the penalties for early arrivals and departure delays. To solve the model, several heuristics are developed: the model for large problems is decomposed into sub-models that are solved by rolling-horizon heuristics; neighborhood search heuristics are used for optimizing a berthing order of vessels; parallel computing is used to improve the algorithmic performance. The method performs well when applied to real-world large-scale instances with promising computation time that is linearly related to the number of vessels.     

A simulation-based Genetic Algorithm approach for the quay crane scheduling under uncertainty

The fast-paced growth in containerized trade market sparks the need for efficient operations at seaport container terminals. One major determinant of terminal efficiency is the productivity of Quay Cranes (QC) resulting from QC scheduling. This paper focuses on the QC Scheduling Problem (QCSP). The objective is to minimize vessel handling time while considering the entire container handling process involving both seaside operations and container transfer operations, taking place between the quay and the stacking yard. A stochastic mixed integer programming model is proposed, and a simulation-based Genetic Algorithm (GA) is applied to construct QC schedules that account for the dynamics and the uncertainty inherent to container handling process. Computational experiment shows satisfactory results of the proposed algorithm and stresses the importance of simulation to obtain more reliable estimates of QC schedule performance.     

Multi-objective bacterial colony optimization algorithm for integrated container terminal scheduling problem

Natural Computing - This paper proposes a multi-objective integrated container terminal scheduling problem considering three key components: berth allocation, quay cranes assignment and containers...     

The berth allocation problem with mobile quay walls: problem definition,solution procedures,and extensions

The berth allocation problem (BAP), which defines a processing interval and a berth at the quay wall for each ship to be (un-)loaded, is an essential decision problem for efficiently operating a container port. In this paper, we integrate mobile quay walls into the BAP. Mobile quay walls are huge propelled floating platforms, which encase ships moored at the immobile quay and provide additional quay cranes for accelerating container processing. Furthermore, additional ships can be processed at the seaside of the platform, so that scarce berthing space at a terminal is enlarged. We formalize the BAP with mobile quay walls and provide suitable solution procedures.     

A fast heuristic for quay crane scheduling with interference constraints

This paper considers the problem of scheduling quay cranes which are used at sea port container terminals to load and unload containers. This problem is studied intensively in a recent stream of research but still lacks a correct treatment of crane interference constraints. We present a revised optimization model for the scheduling of quay cranes and propose a heuristic solution procedure. At its core a Branch-and-Bound algorithm is applied for searching a subset of above average quality schedules. The heuristic takes advantage from efficient criteria for branching and bounding the search with respect to the impact of crane interference. Although the used techniques are quite standard, the new heuristic produces much better solutions in considerably shorter run times than all algorithms known from the literature.     

An Integrated Quay Crane Assignment and Scheduling Problem

As maritime container transport is developing rapidly, the need arises for efficient operations at container terminals. One of the most important determinants of container handling efficiency is the productivity of quay cranes, which are responsible for unloading and loading operations for container vessels. For this reason, the Quay Crane Assignment Problem (QCAP) and the Quay Crane Scheduling Problem (QCSP) have received increasing attention in the literature and the present paper deals with the integration of these interrelated problems. A formulation is developed for the Quay Crane Assignment and Scheduling Problem (QCASP), which accounts for crane positioning conditions and a Genetic Algorithm (GA) is developed to solve the QCASP. Both the model formulation and the solution methodology are presented in detail and computational analysis is conducted in order to evaluate the performance of the proposed GA. The results obtained from the GA are compared with the results from an exact technique, thus providing complete information about the performance of the heuristic in terms of solution quality.     

Modeling and solving rich quay crane scheduling problems

The quay crane scheduling problem is a core task of managing maritime container terminals. In this planning problem, discharge and load operations of containers of a ship are scheduled on a set of deployed quay cranes. In this paper, we provide a rich model for quay crane scheduling that covers important issues of practical relevance like crane-individual service rates, ready times and due dates for cranes, safety requirements, and precedence relations among container groups. Focus is put on the incorporation of so-called unidirectional schedules into the model, by which cranes move along the same direction, either from bow to stern or from stern to bow, when serving the vessel. For solving the problem, we employ a branch-and-bound scheme that is known to be the best available solution method for a class of less rich quay crane scheduling problems. This scheme is extended by revising and extending the contained lower bounds and branching criteria. Moreover, a novel Timed Petri Net approach is developed and incorporated into the scheme for determining the starting times of the discharge and load operations in a schedule. Numerical experiments are carried out on both, sets of benchmark instances taken from the literature and real instances from the port of Gioia Tauro, Italy. The experiments confirm that the new method provides high quality solutions within short runtimes. It delivers new best solutions for some of the benchmark problems from the literature. It also shows capable of coping with rich real world problem instances where it outperforms the planning approach applied by practitioners.     

The Quay Crane Scheduling Problem

The recent growth in worldwide container terminals’ traffic resulted in a crucial need for optimization models to manage the seaside operations and resources. Along with the recent increase in ship size and the container volume, the advancements in the field of Quay Crane Scheduling introduced the need for new modeling approaches. This is the motivation behind the current paper, which focuses on developing a novel yet simple formulation to address the Quay Crane Scheduling Problem (QCSP). The objective of the problem is to determine the sequence of discharge operations of a vessel that a set number of quay cranes will perform so that the completion time of the operations is minimized. The major contribution is attributed to the way that minimization is performed, which is by minimizing the differences between the container loads stacked over a number of bays and by maintaining a balanced load across the bays. Furthermore, important considerations are taken into account, such as the bidirectional movement of cranes and the ability to travel between bays even before completion of all container tasks. These realistic assumptions usually increase model complexity; however, in the current work this is offset by the novel simple objective. This paper presents a mixed-integer programming (MIP) formulation for the problem, which has been validated through multiple test runs with different parameters. Results demonstrate that the problem is solved extremely efficiently, especially for small problem sizes.     

双循环策略下岸桥与跨运车的联合调度

集装箱码头采用跨运车能够减少作业环节和码头机械设备的种类与数量,同时缓存区容量的设置至关重要。首先,为降低码头总完工时间、提高码头作业效率,并解决采用跨运车作为水平运输设备与岸桥进行联合装卸作业时产生的时空协调问题,引入了双循环操作策略,对岸桥与跨运车的联合作业序列优化问题进行研究。其次,建立以总完工时间最小化为目标,考虑岸桥与跨运车双循环操作的实际约束、岸桥缓存区容量限制、安全时间等约束的混合整数规划模型。然后,针对传统禁忌搜索（TS）算法的局限性,加入贪婪算法、多种邻域搜索方式、响应性策略,设计了基于贪婪算法的响应性TS算法,并进行了数值实验。实验结果验证了所提模型与算法的有效性。最后,通过对缓存区容量与跨运车数量、岸桥与跨运车配比的实验分析,得出了最优的跨运车数量和缓存区容量、岸桥与跨运车配比。结果表明：与传统码头设备配置相比,双循环策略可减少跨运车使用数量,提高岸桥与跨运车使用率。     

基于时间窗的双小车岸桥与AGV协调调度研究

针对自动化集装箱码头（automated container terminals,ACT）的自动导引车 ( automatic guided vehicle,AGVs) 与自动化双小车岸桥（double-trolley quay cranes,QCs）协调调度优化问题,以上海洋山港四期工程的实际布局和装卸工艺为基础,考虑装卸同时进行条件下以最小化任务总完工时间为目标,建立带有时间窗约束的双小车岸桥和AGV的协调调度模型,并采用遗传算法对实际算例进行求解。通过灵敏度分析,验证了该模型及算法的有效性,并对遗传算法参数设置的有效性进行检验。结果分析表明,该调度方法有助于提高自动化集装箱码头的作业效率,减少集装箱船的在港时间,提高码头竞争力。     

Biased random key genetic algorithm for the Tactical Berth Allocation Problem

The Tactical Berth Allocation Problem (TBAP) aims to allocate incoming ships to berthing positions and assign quay crane profiles to them (i.e. number of quay cranes per time step). The goals of the TBAP are both the minimization of the housekeeping costs derived from the transshipment container flows between ships, and the maximization of the total value of the quay crane profiles assigned to the ships. In order to obtain good quality solutions with considerably short computational effort, this paper proposes a biased random key genetic algorithm for solving this problem. The computational experiments and the comparison with other solutions approaches presented in the related literature for tackling the TBAP show that the proposed algorithm is applicable to efficiently solve this difficult and essential container terminal problem. The problem instances used in this paper are composed of both, those reported in the literature and a new benchmark suite proposed in this work for taking into consideration other realistic scenarios.     

An optimization methodology for intermodal terminal management

A solution to the problems of resource allocation and scheduling of loading and unloading operations in a container terminal is presented. The two problems are formulated and solved hierarchically. First, the solution of the resource allocation problem returns, over a number of work shifts, a set of quay cranes used to load and unload containers from the moored ships and the set of yard cranes to store those containers on the yard. Then, a scheduling problem is formulated to compute the loading and unloading lists of containers for each allocated crane. The feasibility of the solution is verified against a detailed, discrete-event based, simulation model of the terminal. The simulation results show that the optimized resource allocation, which reduces the costs by [frac13], can be effectively adopted in combination with the optimized loading and unloading list. Moreover, the simulation shows that the optimized lists reduce the number of crane conflicts on the yard and the average length of the truck queues in the terminal.     

基于仿真模型的集装箱码头排队系统分析

基于Witness仿真软件建立了集装箱码头桥吊服务系统的排队系统仿真模型,通过对M/M/m排队系统参数分析,发现随着服务台数量的增大,排队系统的性能逐渐变好。各指标的变化曲线存在拐点,拐点之后变化幅度不再明显,此拐点对应的x坐标值就是桥吊配置数量的最佳值。通过对比不同排队模型进行仿真分析,认为集装箱码头桥吊服务系统的M/M/m排队系统的工作能力和效率都更高,且性能更容易改善。研究结果对码头其它节点的排队系统的分析也有参考价值。