An enriched model for the integrated berth allocation and quay crane assignment problem

Given the increasing pressure to improve the efficiency of container terminals, a lot of research efforts have been devoted to optimizing container terminal operations. Most papers deal with either the berth allocation problem (BAP) or the (quay) crane assignment problem (CAP). In the literature on the BAP, handling times are often simplified to be berth dependent or proportional to vessel size, so the CAP can be ignored when scheduling vessels. This is unsatisfactory for real-life applications because the handling time primarily depends on the number of containers to be handled and the number of cranes deployed. Only a limited number of papers deals with the combination of berth allocation and crane assignment. In these papers however, authors often have resorted to algorithmic simplifications that limit the practical use of the models. This paper presents a MILP model for the integrated BAP–CAP taking into account vessel priorities, preferred berthing locations and handling time considerations. The model is used in a hybrid heuristic solution procedure that is validated on real-life data illustrating the potential to support operational and tactical decision-making.     

多目标约束处理方法求解泊位岸桥联合分配问题

为了制定合理高效的泊位岸桥联合分配方案,加快船舶周转,本文针对船舶动态到港的连续泊位建立了以船舶总在港时间最短为目标的泊位岸桥联合分配混合整数非线性模型.通过多目标约束处理策略将复杂约束的违反程度转化为另一个目标,从而将原单目标优化模型转化为双目标优化模型,并用基于快速非支配排序的多目标遗传算法(NSGA-II)对其进行求解.同时,针对问题特点,分别设计了基于调整、惩罚函数、可行解优先和综合约束处理策略的单目标遗传算法对原模型进行求解.通过多组不同规模的标准算例对本文的方法进行测试,验证了基于多目标约束处理策略的方法求解效果相较于单目标约束处理策略的方法更加高效和稳定.     

A biased random-key genetic algorithm for the time-invariant berth allocation and quay crane assignment problem

Maritime transportation plays a crucial role in the international economy. Port container terminals around the world compete to attract more traffic and are forced to offer better quality of service. This entails reducing operating costs and vessel service times. In doing so, one of the most important problems they face is the Berth Allocation and quay Crane Assignment Problem (BACAP). This problem consists of assigning a number of cranes and a berthing time and position to each calling vessel, aiming to minimize the total cost. An extension of this problem, known as the BACAP Specific (BACASP), also involves determining which specific cranes are to serve each vessel. In this paper, we address the variant of both BACAP and BACASP consisting of a continuous quay, with dynamic arrivals and time-invariant crane-to-vessel assignments. We propose a metaheuristic approach based on a Biased Random-key Genetic Algorithm with memetic characteristics and several Local Search procedures. The performance of this method, in terms of both time and quality of the solutions obtained, was tested in several computational experiments. The results show that our approach is able to find optimal solutions for some instances of up to 40 vessels and good solutions for instances of up to 100 vessels.     

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.     

基于滚动规划的泊位和岸桥分配集成模型研究

泊位分配（BA）,岸桥配置（QCA）及岸桥调度（QCS）是三个基本的岸边决策问题。提出了一个基于混合整数线性规划的BA和QCA的集成模型,模型综合考虑了货轮优先权,理想泊位及处理时间三个方面的因素。在实际生产数据上的运行结果表明该模型具有决策支持的潜在能力。     

An optimization approach for coupling problem of berth allocation and quay crane assignment in container terminal

This paper addresses an effective approach to solve the issue of berth allocation and quay crane assignment in a multi-user container terminal. First of all, the studied coupling problem is formulated with the interactions between berth allocation and quay crane assignment considered. Then, an evolutionary algorithm with nested loops was developed to obtain optimal solutions. The algorithm is well structured, where two inner loops are used to solve sub-problems of berth allocation and quay crane assignment respectively; an outer loop is then utilized to find an approximate solution based on the results of the two inner loops. The results of numerical experiments show that the proposed approach can improve the essential operations in container terminals.     

Hybrid rolling-horizon optimization for berth allocation and quay crane assignment with unscheduled vessels

Port operations usually suffer from uncertainties, such as vessels’ arrival time and handling time and unscheduled vessels. To address this, this study presents a dynamic berth allocation and crane assignment specific problem (BACASP) when unscheduled vessels arrive at the port, which is branded the berth allocation and quay crane assignment specific problem with unscheduled vessels (UBACASP). A rolling-horizon based method is proposed to decompose the UBACASP into a multi-stage static decision BACASP, wherein a rescheduling margin-based hybrid rolling-horizon optimization method is developed by incorporating the event-driven and periodical rolling-horizon strategies as the urgency of dynamic events is evaluated. In each rolling horizon, a mixed integer linear programming model (MILP) is presented for the BACASP to minimize the total port stay time of vessels and the penalties of delays associated with the spatial and temporal constraints, such as the length of continuous berth, number of quay cranes (QCs) and non-crossing of QCs. A discretization strategy is designed to divide the continuous berth into discrete segments, and convert the BACASP to a discrete combinatorial optimization problem, which is efficiently solved by the proposed adaptive large neighborhood search algorithm (ALNS). Case studies with different problem characteristics are conducted to prove the effectiveness of the solution methods proposed in this study. Moreover, the performances of the ALNS and the existing methods for solving the BACASP are compared, and the advantages and disadvantages of different rolling strategies under different degrees of uncertainties are deeply analyzed.     

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.     

A berth allocation planning problem with direct transshipment consideration

With the rapid development of container transport industry, container terminal systems have become more and more busy. Some measures and facilities are taken to improve the container throughput, such as Mega Ship, Mega Crane, Deep water Port, Automatic Container Terminal, Mobile Port, Dock Type Berth and Floating Berth. This paper deals with the transshipment transport problem in a container terminal arising from the usage of Mega Ship. We introduce the Berth Allocation Planning problem considering transshipment of ship to ship and formulate a mathematical model with different number of Quay Cranes in berth. A hybrid multistage operation-based Genetic Algorithm (h-moGA) with a priority-based encoding method is proposed. To demonstrate the effectiveness of the proposed h-moGA approach, numerical experiments are carried out and the best solution to the problem is obtained.     

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.     

改进Memetic算法求解集装箱码头泊位岸桥调度问题

针对集装箱码头泊位岸桥调度这一NP难题,提出了一种改进的Memetic算法。算法中采用三层染色体结构表示个体,通过改进顺序交叉算子和基于领域搜索的变异算子以避免个体超出可行域,在交叉和变异后采用改进的模拟退火策略进行局部搜索。试验算例表明该算法收敛速度较快,且能获得较好的满意解。     

The discrete time/cost trade-off problem: extensions and heuristic procedures

Time/cost trade-offs in project networks have been the subject of extensive research since the development of the critical path method (CPM) in the late 50s. Time/cost behaviour in a project activity basically describes the trade-off between the duration of the activity and its amount of non-renewable resources (e.g., money) committed to it. In the discrete version of the problem (the discrete time/cost trade-off problem), it is generally accepted that the trade-off follows a discrete non-increasing pattern, i.e., expediting an activity is possible by allocating more resources (i.e., at a larger cost) to it. However, due to its complexity, the problem has been solved for relatively small instances. In this paper we elaborate on three extensions of the well-known discrete time/cost trade-off problem in order to cope with more realistic settings: time/switch constraints, work continuity constraints, and net present value maximization. We give an extensive literature overview of existing procedures for these problem types and discuss a new meta-heuristic approach in order to provide near-optimal heuristic solutions for the different problems. We present computational results for the problems under study by comparing the results for both exact and heuristic procedures. We demonstrate that the heuristic algorithms produce consistently good results for two versions of the discrete time/cost trade-off problem.     

A network flow model for the dynamic and flexible berth allocation problem

This paper presents a new model for the dynamic berth allocation problem (BAP). The model is developed using a berth-flow network modeling approach and is formulated as an integer multi-commodity network flow problem. In addition, an innovative flexible berth-space utilization scheme, based on blocking plans, is incorporated into the proposed model. This is referred to as the dynamic (vessel arrivals) and flexible (berth space) BAP model (or DFBAP), and is designed to better utilize wharf space in a container port. Computational experiments conducted on an instance generated using actual data show that the DFBAP model is more effective and efficient than the method currently used by port authorities. A set of scenario analyses is also performed to obtain insights into important model parameters.     

基于滚动策略的集装箱码头连续泊位与桥吊集成调度

针对连续泊位与桥吊集成调度大规模求解困难的问题,提出一种基于滚动策略的优化方法。首先,建立了最小化船舶偏离偏好泊位的成本以及延迟靠泊、延迟离港的惩罚成本的基本的多目标优化模型;然后,采用滚动调度方法根据动态抵泊的船舶抵达顺序将调度过程分成连续的调度窗口,并设计窗口的平移策略、当前窗口对下一窗口的参数更新方式;对每个窗口内船舶进行调度优化,根据每个窗口内的优化结果,更新下一个窗口中数学模型的输入参数;通过选取以船舶数量表示的滚动计划窗口和冻结船舶的数量,持续滚动获得每个窗口的最优解,叠加后获得对所有船舶的靠泊计划。通过算例分析表明,滚动调度能够解决较大规模的调度问题,其效率受滚动窗口大小、冻结船舶数量及滚动次数影响     

A multi-vessel quay crane assignment and scheduling problem: Formulation and heuristic solution approach

This paper presents a new approach to analyze the integrated quay crane assignment and scheduling problem (QCASP). The problem determines the assignment of quay cranes to vessels and the sequence of tasks to be processed by each quay crane simultaneously, and accounts for important considerations such as safety margins between quay cranes (QCs), ordering conditions and vessel priority. Furthermore, QCs can travel from one vessel to another vessel whenever tasks are complete. The integrated problem is difficult to solve with exact methods due to its complexity. Therefore, a genetic algorithm (GA) is proposed to solve the integrated QCASP. Computational results validate the performance of the proposed GA.     

Real-time management of berth allocation with stochastic arrival and handling times

In this research we study the berth allocation problem (BAP) in real time as disruptions occur. In practice, the actual arrival times and handling times of the vessels deviate from their expected or estimated values, which can disrupt the original berthing plan and possibly make it infeasible. We consider a given baseline berthing schedule, and solve the BAP on a rolling planning horizon with the objective to minimize the total realized cost of the updated berthing schedule, as the actual arrival and handling time data is revealed in real time. The uncertainty in the data is modeled by making appropriate assumptions about the probability distributions of the uncertain parameters based on past data. We present an optimization-based recovery algorithm based on set partitioning and a smart greedy algorithm to reassign vessels in the event of disruption. Our research problem derives from the real-world issues faced by the Saqr port, Ras Al Khaimah, UAE, where the berthing plans are regularly disrupted owing to a high degree of uncertainty in information. A simulation study is carried out to assess the solution performance and efficiency of the proposed algorithms, in which the baseline schedule is the solution of the deterministic BAP without accounting for any uncertainty. Results indicate that the proposed reactive approaches can significantly reduce the total realized cost of berthing the vessels as compared to the ongoing practice at the port.     

A problem of task allocation with fuzzy information and two-stage solution algorithm

The problem of high-performance allocation of tasks between executives, where the competence of each for implementation of tasks is specified in the form of fuzzy relations, is considered. Maximization of the aggregated degree of competence of the entire allocation and maximization of the degree of the overall level of employment of standard executives are the optimization criteria. Aggregation is performed by means of the Hurwicz operator and the Ordered Weighted Average (OWA) operator. A two-stage heuristic algorithm is proposed for the solution of the problem. An analysis of different algorithms and assessment of the results of computational experiments is conducted.     

Maximum dynamic network flow interdiction problem: New formulation and solution procedures

We consider the dynamic version of the maximum flow network interdiction problem; that is, we assume a positive number is assigned to each arc which indicates the traversal time of the flow through that arc. We also assume that an intruder uses a single resource with limited budget to interrupt the flow of a single commodity through the network within a given time limit of T. A new formulation based on the concept of Temporally Repeated Flow (TRF) is presented. The problem is then solved using Benders’ decomposition. Another solution method, based on the most vital arcs in a network is also discussed. Finally, some computational results are reported.     

The problem of definition expansion and contraction

This article is the fourth of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research focuses on finding criteria that would enable an automated reasoning program to expand or contract definitions wisely. For evaluating a proposed solution to this research problem, we include suggestions concerning possible test problems.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.