Modeling and solution of the joint quay crane and truck scheduling problem

This paper addresses the joint quay crane and truck scheduling problem at a container terminal, considering the coordination of the two types of equipment to reduce their idle time between performing two successive tasks. For the unidirectional flow problem with only inbound containers, in which trucks go back to quayside without carrying outbound containers, a mixed-integer linear programming model is formulated to minimize the makespan. Several valid inequalities and a property of the optimal solutions for the problem are derived, and two lower bounds are obtained. An improved Particle Swarm Optimization (PSO) algorithm is then developed to solve this problem, in which a new velocity updating strategy is incorporated to improve the solution quality. For small sized problems, we have compared the solutions of the proposed PSO with the optimal solutions obtained by solving the model using the CPLEX software. The solutions of the proposed PSO for large sized problems are compared to the two lower bounds because CPLEX could not solve the problem optimally in reasonable time. For the more general situation considering both inbound and outbound containers, trucks may go back to quayside with outbound containers. The model is extended to handle this problem with bidirectional flow. Experiment shows that the improved PSO proposed in this paper is efficient to solve the joint quay crane and truck scheduling problem.     

兼顾成本与时间保证率的泊位及岸桥协同调度优化

针对集装箱班轮根据船期表按计划到离港的运行规律以及港口企业追求低运营成本的需求,本文以集装箱班轮按计划离港保证率最大和码头作业成本最低为目标,构建了泊位及岸桥协同调度多目标优化模型;设计了叠加式局部搜索算法,将其嵌入到带精英策略的非支配排序遗传算法中,经过相互交叉反馈运算,得到Pareto非劣解;采用“性价比”的概念和量化方法,选择出对港口和船公司的利益偏向最小的实施方案,解决了在Pareto解集中寻优的问题。最后,以大连港集装箱码头的生产实际为例,验证了上述优化模型及算法的合理性和有效性。     

集装箱码头桥机调度问题基于完工时间下界的算法

关注单船桥机调度问题,指出了单船桥机的闲置会影响码头整体的运作效率。以单个集装箱为任务单位,考虑桥机移动时间、安全距离等约束,建立了最小化桥机完工时间和闲置时间的多目标规划模型。基于完工时间下界的两种不同情况：以重点贝位工作量确定和以平均工作量确定,分别设计了基于邻域搜索的启发式算法和基于贪心策略的“分割贝位”算法,并且证明了在以平均工作量确定下界的情况中该算法不会导致桥机闲置。不同规模、不同下界类型的算例表明：提出的模型与算法得到的桥机调度计划更适合实际生产作业,能够有效地逼近完工时间下界,算法运行速度较现有的研究有显著的提高。     

考虑潮汐影响的离散型泊位和岸桥集成调度

泊位和岸桥是集装箱港口最紧缺的资源,二者的调度问题存在很强的内在关联。针对大型船需乘潮进出港的离散型泊位,为提高集装箱码头运作效率和客户满意度,将泊位分配、岸桥指派和岸桥调度集成为一体。首先,考虑潮汐的影响以及岸桥作业中可动态调度的现实,以计划期内所有抵港船舶的岸桥作业成本和滞期成本之和最少为目标,建立一个混合整数规划模型,然后设计了一个嵌入启发式规则的遗传算法对其进行求解。最后,算例结果中给出了每艘船舶在确切时刻对应的具体岸桥和每个岸桥的动态作业时间窗,并通过与单独优化的方案对比,验证了集成方案的有效性。     

考虑任务优先约束的同类岸桥作业调度优化

分析了以箱组为任务对象QCSP与以整贝为任务对象QCSP的异同,指出前者更能均衡各岸桥作业负荷,并减少船舶装卸作业时间。考虑到岸桥具有作业效率差异的特点,将其视为同类平行机调度问题,同时结合任务优先约束、岸桥作业不可相互穿越与安全距离等特有约束,建立了更加符合实际的以箱组为任务对象的岸桥作业调度混合整数规划模型,其优化目标是最小化装卸作业的makespan。针对模型求解的复杂度,设计了一种遗传算法,对算法搜索空间进行了讨论,并推导了问题的低界。实验算例表明所建立的模型能够反映岸桥作业调度过程中作业效率差异及任务优先约束现象,其算法能够在允许的运算时间内获得稳定的满意解,并且优化结果要全面优于以整贝为任务对象QCSP的调度方案。     

考虑泊位疏浚的连续型泊位和动态岸桥联合调度

针对集装箱码头泊位需要定期维护的实际特征,研究了泊位疏浚情况下连续型泊位和动态岸桥联合调度问题。首先,建立了一个以船舶周转时间最小为目标的整数线性规划模型;其次,针对问题特性设计了三种启发式算法。为了分析泊位疏浚对码头工作的影响并验证模型正确性和算法有效性,分别对未考虑泊位疏浚和考虑泊位疏浚两种调度情形,进行了小规模与大规模问题输入的多组测试。三种算法在小规模输入上均取得了相同于CPLEX的精确解,从而验证了算法的有效性;进一步通过对比分析这些算法在大规模输入中的运行结果,验证其有效性能。     

A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time

For a container terminal system, efficient berth and quay crane (QC) schedules have great impact on the improvement of both operation efficiency and customer satisfaction. In this paper we address berth and quay crane scheduling problems in a simultaneous way, with uncertainties of vessel arrival time and container handling time. The berths are of discrete type and vessels arrive dynamically with different service priorities. QCs are allowed to move to other berths before finishing processing on currently assigned vessels, adding more flexibility to the terminal system. A mixed integer programming model is proposed, and a simulation based Genetic Algorithm (GA) search procedure is applied to generate robust berth and QC schedule proactively. Computational experiment shows the satisfied performance of our developed algorithm under uncertainty.     

A survey of berth allocation and quay crane scheduling problems in container terminals

Due to the variety of technical equipments and terminal layouts, research has produced a multitude of optimization models for seaside operations planning in container terminals. To provide a support in modeling problem characteristics and in suggesting applicable algorithms this paper reviews the relevant literature. For this purpose new classification schemes for berth allocation problems and quay crane scheduling problems are developed. Particular focus is put on integrated solution approaches which receive increasing importance for the terminal management.     

A local branching-based algorithm for the quay crane scheduling problem under unidirectional schedules

The quay crane scheduling problem (QCSP) is at the basis of a major logistic process in maritime container terminals: the process of discharging/loading containers from/on berthed vessels. Several groups of containers, laying in one or more stowage portions of a containership, have to be assigned to multiple cranes and discharge/loading operations have to be optimally sequenced, under some complicating constraints imposed by the practical working rules of quay cranes. The QCSP has been the object of a great deal of research work since the last decade and it is focused in this paper, with the aim of consolidating a promising solution approach based upon the combination of specialized branch & bound (B&B) and heuristic algorithms. A cost-effective solution technique that incorporates the local branching method within a refined B&B algorithm is proposed and its effectiveness is assessed by numerical comparisons against the latest algorithm available in literature.     

基于两阶段混合动态规划算法的龙门吊路径优化

产业界已出现利用多台轨道式龙门吊同时作业以提升集装箱码头装船效率的情况,由于需要确定每台龙门吊的取箱作业集合以及增加了“避免碰撞”、“顺次移动”等现实约束,故其移动路径规划问题在模型建立与求解上比单台轨道式龙门吊更为复杂。本文针对两台轨道式龙门吊同时作业的情形,建立了龙门吊移动路径网络模型,并开发了基于贪婪算法与动态规划的两阶段混合算法,并通过仿真算例,借助与基于实际调度规则所得到的调度方案的对比,验证了模型及优化算法的有效性与实用性。     

基于泊位偏好与岸桥干扰的泊位和岸桥分配

泊位和岸桥是集装箱港口资源中最紧缺的资源,合理的泊位分配和岸桥调度可以提高集装箱港口的资源利用率和港口的运作效率和效益。针对泊位偏离和岸桥工作损失两个因素,文章建立了集装箱港口泊位和岸桥的混合整数线性规划模型;运用采集自宁波某典型集装箱港口的数据,用Gurobi优化软件和两阶段启发式算法对模型进行了求解;对计算结果进行了经济性分析。计算结果表明:该港口的岸线资源利用率为46%时,1000m~1600m基本没被利用;18台岸桥要比16台岸桥的目标值更优,求解时间更短,而且18台岸桥的平均利用率为80%,为此,建议该港口再增加两台岸桥。同时发现:随着船舶规模的增加,Gurobi优化求解的时间增长较快,而两阶段启发式算法仍能在很短时间内求得准优解。     

DCA for solving the scheduling of lifting vehicle in an automated port container terminal

The container was introduced as a universal carrier for various goods in the 1960s and soon became a standard worldwide transportation. The competitiveness of a container seaport is marked by different success factors, particularly the time in port for ships. Operational problems of container terminals is divided into several problems, such as assignment of vessels, loading/unloading and storage of the containers, quay cranes scheduling cite, planning yard cranes cite and assignment of storage containers cite. In this work, the study will focus on piloting yard trucks. Two different types of vehicles can be used, namely automated guided vehicles (AGVs) and lifting vehicles (LVs). An AGV receives a container from a quay crane and transports containers over fixed path. LVs are capable of lifting a container from the ground by itself. The model that we consider is formulated as a mixed integer programming problem, and the difficulty arises when the number of binary variables increases. There are a lot of algorithms designed for mixed integer programming problem such as Branch and Bound method, cutting plane algorithm, . . . By using an exact penalty technique we treat this problem as a DC program in the context of continuous optimization. Further, we combine the DCA with the classical Branch and Bound method for finding global solutions.     

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.     

MIP approaches for the integrated berth allocation and quay crane assignment and scheduling problem

In this paper we consider an integrated berth allocation and quay crane assignment and scheduling problem motivated by a real case where a heterogeneous set of cranes is considered. A first mathematical model based on the relative position formulation (RPF) for the berth allocation aspects is presented. Then, a new model is introduced to avoid the big-M constraints included in the RPF. This model results from a discretization of the time and space variables. For the new discretized model several enhancements, such as valid inequalities, are introduced. In order to derive good feasible solutions, a rolling horizon heuristic (RHH) is presented. A branch and cut approach that uses the enhanced discretized model and incorporates the upper bounds provided by the RHH solution is proposed. Computational tests are reported to show (i) the quality of the linear relaxation of the enhanced models; (ii) the effectiveness of the exact approach to solve to optimality a set of real instances; and (iii) the scalability of the RHH based on the enhanced mathematical model which is able to provide good feasible solutions for large size instances.     

Optimization of container process at seaport terminals

Seaport container terminals are an important part of the logistics systems in international trades. This paper investigates the relationship between quay cranes, yard machines and container storage locations in a multi-berth and multi-ship environment. The aims are to develop a model for improving the operation efficiency of the seaports and to develop an analytical tool for yard operation planning. Due to the fact that the container transfer times are sequence-dependent and with the large number of variables involved, the proposed model cannot be solved in a reasonable time interval for realistically sized problems. For this reason, List Scheduling and Tabu Search algorithms have been developed to solve this formidable and NP-hard scheduling problem. Numerical implementations have been analysed and promising results have been achieved.     

A Rollout Metaheuristic for Job Shop Scheduling Problems

In this paper we deal with solution algorithms for a general formulation of the job shop problem, called alternative graph. We study in particular the job shop scheduling problem with blocking and/or no-wait constraints. Most of the key properties developed for solving the job shop problem with infinite capacity buffer do not hold in the more general alternative graph model. In this paper we report on an extensive study on the applicability of a metaheuristic approach, called rollout or pilot method. Its basic idea is a look-ahead strategy, guided by one or more subheuristics, called pilot heuristics. Our results indicate that this method is competitive and very promising for solving complex scheduling problems.     

Yard crane scheduling in port container terminals

Yard cranes are the most popular container handling equipment for loading containers onto or unloading containers from trucks in container yards of land scarce port container terminals. However, such equipment is bulky, and very often generates bottlenecks in the container flow in a terminal because of their slow operations. Hence, it is essential to develop good yard crane work schedules to ensure a high terminal throughput. This paper studies the problem of scheduling a yard crane to perform a given set of loading/unloading jobs with different ready times. The objective is to minimize the sum of job waiting times. A branch and bound algorithm is proposed to solve the scheduling problem optimally. Efficient and effective algorithms are proposed to find lower bounds and upper bounds. The performance of the proposed branch and bound algorithm is evaluated by a set of test problems generated based on real life data. The results show that the algorithm can find the optimal sequence for most problems of realistic sizes.     

具有预知信息的集装箱码头泊位与岸桥联合调度在线模型

探讨了预知服务需求信息能力下的集装箱码头泊位与岸桥联合调度 over-list 在线模型. 在每个船舶服务请求释放时, 决策者预知后续 k(k \geq 2)个请求的信息,目标为最小化所有请求的最大完工时间. 针对由3个离散泊位组成的混合型泊位与4个岸桥, 以及只有大小两种服务请求的情形, 给出了预知任意 k \geq 2个请求下的竞争比下界; 同时, 对于k=2的特定情形, 给出了具有最优竞争比7/6 的在线策略. 数值实验进一步表明了所设计策略的良好执行性能.     

排课问题分组优化决策中的CourseRank

时间表(T im etab ling)问题是NP-完全的,因此很难寻求一个有效的整体优化算法.分组作为重要的优化策略,可以将课程按优先等级逐次分组,每组再采用组合优化方法.通常认为课程的规模是优先等级的决定性因素.然而选课的模式允许学生在一定的范围内选择课程,这就使得课程的关联关系更复杂.该文将课程的关联关系描述为一个M arkov链,进而给出了课程优先度(CourseR ank)的概念.通过对清华大学2002年度学生选课数据的分析和计算,结果表明课程的规模仍然是重要的因素,但并不完全是决定性的.     

求解资源受限项目调度问题的人工鱼群算法

提出了将人工鱼群算法应用于求解资源受限项目调度问题中的构想,建立了求解资源受限项目调度问题的人工鱼群算法模型,设计了一种标准随机键编码方式,构建了人工鱼的觅食行为、聚群行为、追尾行为和随机行为四种基本算子,采用了正向逆向局部改进技术和精英保留策略,并给出了算法流程。应用PSPLIB标准问题库对该算法进行了大量的测试,并与其他算法进行了比较,验证了该算法的有效性。