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.     

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.     

Integrated scheduling of handling equipment at automated container terminals

To improve the productivities of an automated container terminal, it is important to schedule different types of handling equipment in an integrated way. A mixed-integer programming model, which considers various constraints related to the integrated operations between different types of handling equipment, is formulated. A heuristic algorithm, called multi-layer genetic algorithm (MLGA) is developed with a view to overcome the computation difficulty for solving the mathematical model. A numerical experimentation is carried out in order to evaluate the performance of the algorithm.     

Discrete time model and algorithms for container yard crane scheduling

Container terminal (CT) operations are often bottlenecked by slow YC (yard crane) movements. PM (prime mover) queues in front of the YCs are common. Hence, efficient YC scheduling to reduce the PM waiting time is critical in increasing a CT’s throughput. We develop an efficient model for YC scheduling by taking into account realistic operational constraints such as inter-crane interference, fixed YC separation distances and simultaneous container storage/retrievals. Among them, only inter-crane interference has ever been considered in the literature. The model requires far fewer integer variables than the literature by using bi-index decision variables. We show how the model can be solved quickly using heuristics and rolling-horizon algorithm, yielding close to optimal solutions in seconds. The solution quality and solution time are both better than the literature even with additional constraints considered. The proposed formulations and algorithms can be extended to other problems with time windows and space constraints.     

An application of cooperative game among container terminals of one port

In this paper a two-stage game that involves three container terminals located in Karachi Port in Pakistan is discussed. In the first stage, the three terminals have to decide on whether to act as a singleton or to enter into a coalition with one or both of the other terminals. The decision at this stage should presumably be based on the predicted outcome for the second stage. The second stage is here modelled as a Bertrand game with one outside competitor, the coalition and the terminal in Karachi Port (if any) that has not joined the coalition. Furthermore, three partial and one grand coalition among the three terminals at Karachi Port are investigated. The concepts of “characteristic function” and “core” are used to analyse the stability of these coalitions and this revealed that one combination does not satisfy the superadditivity property of the characteristic function and can therefore be ruled out. The resulting payoffs (profits) of these coalitions are analysed on the basis of “core”. The best payoff for all players is in the case of a “grand coalition”. However, the real winner is the outsider (the terminal at the second port) which earns a better payoff without joining the coalition, and hence will play the role of the “orthogonal free-rider”.     

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.     

Integrated scheduling of crane handling and truck transportation in a maritime container terminal

This paper studies the interactions between crane handling and truck transportation in a maritime container terminal by addressing them simultaneously. Yard trucks are shared among different ships, which helps to reduce empty truck trips in the terminal area. The problem is formulated as a constraint programming model and a three-stage algorithm is developed. At the first stage, crane schedules are generated by a heuristic method. At the second stage, the multiple-truck routing problem is solved based on the precedence relations of the transportation tasks derived from the first stage. At the last stage a complete solution is constructed by using a disjunctive graph. The three procedures are linked by an iterative structure, which facilitates the search for a good solution. The computational results indicate that the three-stage algorithm is effective for finding high-quality solutions and can efficiently solve large problems.     

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。     

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.     

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.     

Optimising container storage processes at multimodal terminals

Multimodal Container Terminals (MMCT) require comprehensive planning, programming and control in order to operate an efficient storage system. In this paper, a model has been developed for the storage system of the MMCT. It is an extension of the Blocks Relocation Problem, with incoming as well as outgoing containers, or ‘blocks’. The model deals with assigning containers to positions within the storage area, rehandling of containers to be retrieved, and calculation of the processing times in order to perform these actions. A number of constructive heuristics are presented in order to produce good initial solutions for this problem. Meta-heuristics are also used to improve on these solutions. Results from the various heuristics on a few case study problems are compared and discussed. This research will also provide a core piece of technology for the development of autonomous container handling systems for terminals.     

Bi-level programming model of container port game in the container transport supernetwork

In order to analyze the behavior of every participant in decision making, the container transportation business process and the container transportation supernetwork are presented. Furthermore, two kinds of container transport supernetwork equilibrium models are established. Then we established EPEC model, in which the upper layer ports go on non-cooperation competition while the lower layer shippers compete for the path of minimum expense. Finally, a simulation example is employed to show the validity and rationality of bi-level programming model.     

Conservative allocation models for outbound containers in container terminals

This paper examines location assignment for outbound containers in container terminals. It is an extension to the previous modeling work of Kim et al. (2000) and Zhang et al. (2010). The previous model was an “optimistic” handling way and gave a moderate punishment for placing a lighter container onto the top of a stack already loaded with heavier containers. Considering that the original model neglected the stack height and the state-changing magnitude information when interpreting the punishment parameter and hid too much information about the specific configurations for a given stack representation, we propose two new “conservative” allocation models in this paper. One considers the stack height and the state-changing magnitude information by reinterpreting the punishment parameter and the other further considers the specific configurations for a given stack representation. Solution qualities for the “optimistic” and the two “conservative” allocation models are compared on two performance indicators. The numerical experiments indicate that both the first and second “conservative” allocation models outperform the original model in terms of the two performance indicators. In addition, to overcome computational difficulties encountered by the dynamic programming algorithm for large-scale problems, an approximate dynamic programming algorithm is presented as well.     

Increasing the operational efficiency of container terminals in Australia

This paper discusses the major factors influencing the transfer efficiency of rail container terminals, as measured by the throughput time of containers. An analytically based simulation model is designed to describe container progress in the system. Cyclic heuristic rules for equipment assignment are applied and a new heuristic rule is developed to dispatch trains to tracks. The simulation model combined with the heuristic rules is used to address a number of specific objectives of the study. Different performance measures are applied and the impact that the train-to-track despatching and the handling equipment assignment can have on the measures is established. Validation and testing of models make use of data from Acacia Ridge Terminal, Brisbane, Australia.     

Novel constraints satisfaction models for optimization problems in container terminals

The growth of containerization and transporting goods in containers has created many problems for ports. In this paper, we systematically survey a literature over problems in container terminals. The operations that take place in container terminals are described and then the problems are classified into five scheduling decisions. For each of the decisions, an overview of the literature is presented. After that, each of the decisions is formulated as Constraint Satisfaction and Optimization Problems (CSOPs). The literature also includes simulations and performance in container terminals. To evaluate any solution methods to the decisions and to measure its efficiency, several indicators are suggested.     

Crane scheduling in container yards with inter-crane interference

This paper examines the problem of scheduling multiple yard cranes to perform a given set of jobs with different ready times in a yard zone with only one bi-directional travelling lane. Due to sharing of the travelling lane among two or more yard cranes, inter-crane interference, a planned move of a yard crane blocked by the other yard cranes, may happen. The scheduling problem is formulated as an integer program. It is noted that the scheduling problem is NP-complete. This research develops a dynamic programming-based heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. Computational experiments are carried out to evaluate the performance of the heuristic and the results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 7.3% above their lower bounds.     

PORTPLAN,decision support system for port terminals

Models underlying a decision support system (dss) for port terminal planning are described. Among others Markov models, queuing models and simple optimization models are considered. The integration of different models, each describing specific aspects of a decision situation, is one of the major problems in the development of a dss. This paper gives a good insight in this problem field.The paper gives also some theoretical results related to some models that might be interesting in other contexts.     

On double cycling for container port productivity improvement

How quay cranes (QC) are scheduled is vital to the productivity of seaside container port operations. Double cycling concept is an operation strategy of loading the containers into ships as they are unloaded, thus improving the efficiency of a QC as well as the container port. Goodchild and Daganzo (Transp Sci 40(4):473–483, 2006) first described QC double cycling problem and solved the problem after formulating it into a two machine flow shop problem. Song (Port Technol Int 36:50–52, 2007) studied the formula to determine the optimal starting sequence for double cycling while reflecting on the practical issue of QC working direction. The above studies focused on a single QC double cycling and their empirical trials showed the double cycling could improve the productivity of each QC approximately by between 10 and 20 %. In Zhang and Kim (Comput Ind Eng 56(3):979–992, 2009), a multiple QC double cycling model was first suggested by formulating a mixed integer programming model to maximise the number of double cycles between multiple QCs. In the present paper we point out a flaw with the existing multiple QC double cycling model that lets cycles that are not implementable. In addition, the paper discusses the need for imposing constraints arising from real world requirements to the formulations aiming at double cycling.     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

Benchmark optimization and attribute identification for improvement of container terminals

The aim of this paper is to optimize the benchmarks and prioritize the variables of decision-making units (DMUs) in data envelopment analysis (DEA) model. In DEA, there is no scope to differentiate and identify threats for efficient DMUs from the inefficient set. Although benchmarks in DEA allow for identification of targets for improvement, it does not prioritize targets or prescribe level-wise improvement path for inefficient units. This paper presents a decision tree based DEA model to enhance the capability and flexibility of classical DEA. The approach is illustrated through its application to container port industry. The method proceeds by construction of multiple efficient frontiers to identify threats for efficient/inefficient DMUs, provide level-wise reference set for inefficient terminals and diagnose the factors that differentiate the performance of inefficient DMUs. It is followed by identification of significant attributes crucial for improvement in different performance levels. The application of this approach will enable decision makers to identify threats and opportunities facing their business and to improve inefficient units relative to their maximum capacity. In addition, it will help them to make intelligent investment on target factors that can improve their firms’ productivity.