Quay Crane Scheduling Research Articles

Berth Allocation and Quay Crane Assignment Considering the Uncertain Maintenance Requirements

The strategic optimization of a container terminal’s quayside assets, including the berth and quay cranes, is crucial for maximizing their deployment and utilization. The interrelated and complex challenges of Berth Allocation (BAP) and Quay Crane Scheduling (QCSP) are fundamental to enhancing the resilience of container ports, as berths and quay cranes constitute essential infrastructure. Efficient berth allocation and quay crane scheduling can mitigate operational disruptions, even in the face of maintenance or failures, thereby improving both operational reliability and resilience. However, previous studies have often overlooked the uncertainty associated with quay crane maintenance when planning these operations. This paper aims to minimize vessel turnaround time by accounting for the uncertain in quay crane maintenance activities. To address this novel problem, we propose a proactive-reactive method that incorporates a reliability-based model into the Swarm Optimization with Differential Evolution (SWO-DE) algorithm. Computational results confirm the practical relevance and effectiveness of our proposed solution methods for container terminals.

Two-stage robust optimization for the integrated dynamic berth allocation and quay crane scheduling problem under uncertainty

A container port is an important cargo transit node that links the land and maritime regions, with berth allocation and quay crane scheduling tasks. Often, bad weather and delays in loading information make vessels’ navigation uncertain. Therefore, in contrast to the classical berth allocation and quay crane assignment and scheduling problem, which minimizes the makespan, this study proposes a novel two-stage robust mixed-integer linear programming model for the integrated dynamic berth allocation and time-variant quay crane scheduling problem to minimize the total departure time, under uncertainties of vessel arrival time and container demand. An extended column constraint generation algorithm with a variable reduction strategy is designed to solve the model. Extensive computational experiments are performed to verify the effectiveness of the proposed model and algorithm. The conclusions drawn from this study could provide operational guidance for container operators to deal with uncertainties.

Integrated berth allocation and quay crane assignment and scheduling problem under the influence of various factors

AbstractAs the important resources and equipment of container terminals, berths and quay cranes (QCs) face various challenges in actual operations and their operation efficiency in turn affects the performance of the whole terminal. The authors investigate an integrated berth allocation and QC assignment and scheduling problem under the influence of various factors, including the two main factors of vessel arrival time uncertainty and tide, and the two secondary factors of berth deviation and interference between cranes. To formulate the problem, the authors develop a multi‐factor robust scheduling model. A Genetic Algorithm (GA) with Brain Storm Optimisation based on the Contract Net Protocol (CNP) is designed to optimise the berth and QC scheduling scheme. Specifically, the authors use the GA for individual coding and population initialisation, use the brainstorming algorithm for clustering, and introduce the CNP for individual updating. The experimental results show that the designed algorithm can adapt the scheduling plan to complex environments and can improve the service level of terminals.

Decomposition algorithms for the robust unidirectional quay crane scheduling problems

Our study focuses on a two-stage robust optimization model for the unidirectional quay crane scheduling problem with uncertain handling times at container terminals. We first implement two classical algorithms adopted in Li and Zhang (2021), the Benders decomposition algorithm and the column-and-constraint generation algorithm, to solve the robust model. Based on analytical and numerical comparisons of them, we design an exact hybrid algorithm to leverage capabilities of both algorithms by alternatively adding cuts of both kinds. Extensive experiments validate the effectiveness of this mechanism. Numerical experiments also reveal that the benefit and the cost of robustness fade away as the uncertainty budget increases and highlight the advantage of our robust approach to deal with uncertainty over a two-stage stochastic program under extreme situations.

A Simulated Annealing Algorithm for Quay Crane Scheduling and Assignment Problem Under Uncertain Conditions

In this paper, a mixed integer programming (MIP) mathematical model was formulated for the quay crane scheduling and assignment problem (QCSAP) in container terminals with the aim of minimizing the total cost of activities. With the assumption that due to the uncertain nature of the ship’s activities and operations, we have considered most of the parameters of the problem to be indeterminate in order to bring the optimal solution closer to the real world. In this paper, the uncertain nature of the parameters was investigated by using uncertainty theory and in the form of indeterminate quantities. These uncertainties might be subject to the conditions, such as the failure of cranes, container terminal transportation means, congestion in the dockyard, adverse weather conditions, etc. Further, considering the large dimensions of such real problems and the complexity of solving them in terms of processing time, the simulated annealing (SA) meta-heuristic optimization algorithm was utilized to solve the above model. The proposed algorithm has been coded by MATLAB software and its efficiency was put on test by comparing its results for a low-dimensional problem with the accurate solution from GAMS software is compared in terms of computational times for small sizes. The proposed algorithm exhibited promising potentials for quick approximation of usable solutions to high-dimensional QCSAPs. The calculations show that, nondeterministic model with the help of the above proposed algorithm can be one of the basic factors in increasing the productivity of container terminals and the main purpose and advantage of this research is compared to the basic model presented by Tavakkoli-Moghaddam et al. in 2009 which has been analyzed and investigated with definitive data and optimized with the help of genetic algorithm. In addition, some restrictions were added to the basic model in order to make the above crane assignment scheduling problem more practical.

Robust multi-equipment scheduling for U-shaped container terminals concerning double-cycling mode and uncertain operation time with cascade effects

The integrated scheduling of quay cranes, internal vehicles, and yard cranes in container terminals aims to improve port operations and often requires scheduling robustness under uncertainty with cascade effects. In container terminal operations, uncertainty in equipment operating time poses challenges to effective scheduling, as even small fluctuations can create cascade effects throughout the operations, rendering the original schedule ineffective. This research aims to develop a new method that enables a balance between optimization and robustness in container terminal scheduling. Additionally, the double-cycling operation mode and U-shaped port layout, known for their improved efficiency in container terminals, are gaining increasing attention and hence are incorporated into this study. It creates a three-stage hybrid flow shop scheduling problem with bi-directional flows, waiting time, and uncertain operation time. To address the complex problem, a mixed integer programming model is proposed to characterize the integrated scheduling problem, and an index based on complex network structure entropy is designed to evaluate the anti-cascade effect as well as the robustness of the schedule. The index and makespan serve as the bi-objectives, transforming the original problem into a bi-objective optimization one. The non-dominated sorting genetic algorithm-Ⅱ with appropriate coding and decoding rules is utilized to solve the model and obtain a set of Pareto frontier solutions. The feasibility of the new method is verified through a real case analysis. Specifically, comparative analysis with basic stochastic programming, basic robust optimization, triangular fuzzy programming, and maximum gap method are used to demonstrate the effectiveness of the new method. The paper also provides insightful practical implications for port managers, and the genericity of the method could also contribute to its practical values spreading to a wider scope of beneficiaries, such as manufacturing warehousing and distribution management.

A Decomposition Method for the Group-Based Quay Crane Scheduling Problem

This study addresses the quay crane scheduling problem (QCSP), which involves scheduling a fixed number of quay cranes to load and unload containers from ships in a maritime container terminal. The objective is to minimize the completion time while adhering to precedence, safety margin, and noncrossing constraints. Efficient scheduling of quay cranes plays a crucial role in reducing the time vessels spend at terminals. To solve the QCSP, we explore different schedule directions for the quay cranes. Specifically, we consider three directions: unidirectional, where the quay cranes maintain a consistent movement direction from upper to lower bays or vice versa after initial repositioning; bidirectional, allowing the cranes to change direction once during operations; and multidirectional, permitting freely changing movement direction during operations. For the bidirectional QCSP, we propose a new compact mathematical formulation. To obtain valid lower bounds on the optimal completion time, we derive various relaxations of this new formulation based on the different schedule directions. Our solution framework employs logic-based Benders decomposition, decomposing the problem into an assignment master problem and operation-sequence slave subproblems. Extensive computational experiments using benchmark instances from existing literature and newly generated instances validate the efficiency and effectiveness of the lower bounds and the exact solution approach. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Major Program of the National Natural Science Foundation of China [Grants 72192830 and 72192831], the National Natural Science Foundation of China [Grant 72102034], and the 111 Project [Grant B16009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0298

Optimization for Green Container Shipping: A Review and Future Research Directions

Maritime freight transportation is one of the least emissions-producing transportation alternatives in terms of transported tonnage per distance. However, it produces a high amount of emissions as around 80% of international freight transportation is conducted through seas and 20% of maritime transportation is conducted through container shipping. This makes it crucial to reduce emissions in container shipping. In this regard, this study reviewed previous studies on the environmental optimization of container shipping and identified various future research directions. The results showed that in the sea segment of environmental optimization of container shipping, decisions which require further attention include resource allocation, emission reduction technology choice, disruption recovery, freight rate optimization, and shipment scheduling. The decisions that require future research in the port segment are related to internal transportation and handing operations in container terminals (i.e., yard crane deployment, yard truck deployment, yard truck scheduling, yard container stack allocation, yard container retrieval), renewable energy source installation, and emission reduction technology choice. Vessel scheduling and speed optimization decisions are the most frequently studied decisions in the sea segment, but they are rarely considered for inland shipping of containers. In the sea-port combined segment of container shipping, future studies are required in quay crane scheduling, vessel scheduling, container route allocation, ship route allocation vessel deployment, and emission reduction technology choice. The least studied decision in the door-to-door segment of container shipping includes hub location-allocation, empty container relocation, ship route allocation, vessel deployment, environmental taxation and subsidy scheme, emissions reduction technology choice, and speed optimization. It was also demonstrated that modeling of future studies should more frequently consider uncertainties and social sustainability parameters.

Enhanced Multi-Objective Evolutionary Algorithm for Green Scheduling of Heterogeneous Quay Cranes Considering Cooperative Movement and Safety

Heterogeneous quay cranes (HQCs) are the main energy-consuming equipment of automated container terminals, and they need to move from one bay to another along the rail and maintain a safe distance from one another. Improving the operational efficiency of HQCs and reducing the ineffective walking distance of HQCs are key to reducing the energy consumption of QCs. In this paper, an energy-efficient HQC cooperative scheduling problem is studied, and the HQCs are required to ensure safe and efficient operation. A multi-objective scheduling model is formulated to minimize the maximum completion time of containers, the average completion time of HQCs, and the total energy consumption of HQCs simultaneously. An Enhanced Multi-Objective Evolutionary Algorithm (EMOEA) is designed to solve this problem using a problem-feature-based encoding method to encode and initialize the population, a cooperative strategy to ensure the safe operating distance of HQCs, and a novel multi-objective evaluation mechanism with effective evolutionary operators. The results indicate that the different operational capacities of HQCs had a significant impact on the three studied objectives, especially for some large-scale problems, and that our algorithm outperforms three other well-known multi-objective algorithms in solving the EHQCCSP.

Bi-Objective Integrated Scheduling of Quay Cranes and Automated Guided Vehicles

Operational efficiency is one of the key performance indicators of a port’s service level. In the process of making scheduling plans for container terminals, different types of equipment are usually scheduled separately. The interaction between quay cranes (QCs) and automated guided vehicles (AGVs) is neglected, which results in low operational efficiency. This research explores the integrated scheduling problem of QCs and AGVs. Firstly, a multi-objective mixed integer programming model (MOMIP) is conducted, with the aim of minimizing the makespan of vessels and the unladen time of AGVs. Then, embedded with a new heuristic method, the non-dominated sorting genetic algorithm-II (NSGA-II) is designed for the scheduling problem. The heuristic method includes two parts: a bay-based QC allocation strategy and a container-based QC-AGV scheduling strategy. Finally, in order to test the performance of the proposed algorithm, differently sized benchmark tests are performed, and the results are compared to the multi-objective particle swarm optimization algorithm (MOPSO) and the weighted-sum method. The computational results indicate that the proposed algorithm can effectively solve the multi-objective integrated scheduling problem of QCs and AGVs. For large-scale problems, the NSGA-II algorithm has better performance and more obvious advantages compared to others. The proposed method has the capability of providing a theoretical reference for the QC and AGV scheduling of container terminals.

Port integrated scheduling under uncertain operation time and cascade effects: A complex network structure entropy solution

The integrated scheduling of quay cranes, yard cranes, and internal vehicles in a port allows for further optimization of resource allocation on a global scale. Since the scheduling objects are all mobile equipment and their mutual waiting time needs to be reduced as much as possible, new requirements are brought for integrated scheduling. Uncertain operation time is a common phenomenon in ports. How to ensure the effectiveness and robustness of integrated schedules under uncertainties is worth studying. Moreover, although the cascading effects of operation time fluctuation is an important factor affecting the robustness of schedules, less attention has been paid to it. To solve this problem, firstly, a mixed integer nonlinear programming model for integrated scheduling in a port that allows internal vehicles to travel deep into the yard is formulated. A genetic algorithm for solving the model is designed. Then, “gaps” between adjacent operations in schedules are focused on, and the complex network structural entropy theory is used to construct an anti-cascade effect and robustness evaluation index of schedules. In addition, a scheduling plan generation framework that gives a way to use the evaluation index is proposed. Specifically, the anti-cascade effect and robustness evaluation indices of scheduling plans whose objective function values are within a given threshold are calculated, and the final scheduling plan with the largest index is selected. Finally, the feasibility and effectiveness of the proposed method are verified by extensive experiments.

A Novel Proactive–Reactive Scheduling Approach for the Quay Crane Scheduling Problem: A VUCA Perspective

As the port operations are becoming volatile and uncertain, container handling in the port terminals is becoming more complex due to the rising customer demands. Further, scheduling interruptions create ambiguity in real-time operations. Therefore, the present study focused on the container terminal’s ability to schedule and mitigate real-time probabilistic fluctuations. This article proposes a novel proactive–reactive scheduling approach to solve the quay crane (QC) scheduling problem in the volatility, uncertainty, complexity, and ambiguity world, using equipment reliability functions. The proposed approach is based on a novel reliability assessment formula based on practical facts, including the reliability probabilistic distribution of QC and the container workload variability. Moreover, a proactive iterated local search algorithm is proposed and incorporated with the reliability formula to solve the QC scheduling under fluctuations. The efficiency of the algorithm is illustrated through comparison to an exact method. Real-time reactive simulations that compare the schedules before and after the Go-Live phase show the noteworthy improvement derived from generating plans using the proposed proactive approach compared to an alternative nonproactive one.

Blocks allocation and handling equipment scheduling in automatic container terminals

The blocks allocation and integrated scheduling of quay cranes (QCs), yard cranes(YCs), and automated guided vehicles(AGVs) between the apron, side-loading blocks and end-loading blocks for multiple berthing ships is investigated, where the inbound, outbound and transship containers from several ships berthing at the same time is considered. A multi-ship blocks-sharing strategy is proposed to increase the efficiency in double cycling operations of YCs and AGVs through centrally storing containers from different ships. A two-stage mixed integer programming model is formulated in which the first stage is to optimize the problem of blocks allocation and QCs scheduling, and the second stage is to optimize the problem of YCs and AGVs scheduling. To solve the model, adaptive variable neighbourhood immune algorithm (AVNIA) and rule-based heuristic algorithm are proposed. Compared with the lower bound compiled with Gurobi, ANVIN is highly effective based on case study layout data of the automated container terminal of Yangshan port, Shanghai. Experiments demonstrate that the proposed blocks-sharing strategy can significantly improve the utilization rate of YCs and AGVs, and effectively reduce the operation cost of automatic container terminals.

Multi-Terminal Berth and Quay Crane Joint Scheduling in Container Ports Considering Carbon Cost

As container ports become increasingly important to the global supply chain, a growing number of ports are improving their competencies by consolidating multiple terminal resources internally. In addition, in the context of energy conservation and emission reduction, ports measure competitiveness not only in terms of terminal size, throughput and service level, but also in terms of low energy consumption and low pollution. Therefore, a nonlinear mixed-integer programming model considering the cost of carbon is developed for the multi-terminal berth and quay crane joint robust scheduling problem under uncertain environments to minimize the sum of expectation and variance of total cost under all randomly generated samples. The model considers the water depth and interference of quay cranes, etc. The expected vessel arrival time and the average operational efficiency plus relaxation are used as their actual values when scheduling. Finally, an improved adaptive genetic algorithm is developed by combining the simulated annealing mechanism, and numerical experiments are designed. The results show that the joint berth and quay crane scheduling with uncertainties and a multi-terminal coordination mechanism can effectively reduce the operating cost, including carbon costs and the vessel departure delay rate, and can improve resource utilization. Meanwhile, the scheduling with the multi-terminal coordination mechanism can obtain more significant improvement effects than the scheduling with uncertainties.

A comprehensive review and directions for future research on the integrated scheduling of quay cranes and automated guided vehicles and yard cranes in automated container terminals

Automated Container Terminals (ACTs) have attracted an increasing number of researchers over the last decade, compared to conventional terminals, because of their ability to increase terminal productivity and performance and cope with the increasing containerized trade volumes. Also, there ae several developments in the handling equipment used in ACTs to expand the terminal efficiency and serve large-size vessels efficiently and with lower costs. Due to the fact that in ACTs, all equipment is automatically controlled, interference avoidance between each pair of equipment is important to avoid any disruption or backlog of cargo. Therefore, integrated scheduling of ACT’s handling equipment has been one of the most effective ways to increase the terminal’s performance and equipment utilization and minimize costs. This paper presents a comprehensive review and analysis of the literature addressing the integrated handling equipment scheduling problem in ACTs. Based on the provided gap analysis, the paper discussed the possible directions for future research. After explaining the problem and its importance, the reviewed literature is classified based on four main categories: the type of the integrated problem, the solution techniques, the objectives, and the equipment type used in each study. The main outcome is that most papers that addressed the integrated scheduling problem of handling equipment in automated container terminals generally focused on scheduling only a single type of equipment, mostly the AVs, and assumed that the scheduling of other equipment is known in advance. This opens the arena for addressing the integrated problem as it is illustrated in this paper.

Integrated proactive-reactive approach and a hybrid adaptive large neighborhood search algorithm for berth and quay crane scheduling under uncertain combination

<p style='text-indent:20px;'>The integrated berth and quay crane scheduling problem is frequently encountered in port management issue, and the dynamic random data obtained by the container terminals under uncertain combination usually makes it unworkable to execute the scheduling. To promote sustainability and adaptivity of container terminals, this paper focuses on developing an integrated proactive-reactive approach for berth and quay crane scheduling under the fluctuation of vessels' arrival time and breakdown of quay crane. The problem is modelled as a two-stage mixed integer program where the baseline schedule with robustness is established in the first stage, and the recovery schedule is established in the second stage. This study aims to minimize the total management cost deviation and total time deviation of the terminal scheduling, so as to implement minimal changes compared with the baseline schedule. Therefore, the scheduling performance such as robustness, recoverability and adaptability is considered. To solve this model, a hybrid adaptive large neighborhood search (HALNS) algorithm framework combined with variable neighborhood search is developed, and the greedy algorithm is developed to construct the initial feasible solution. The performance evaluation tests of the proposed algorithm are performed on the three scales of benchmark. Computational results indicate the strength of solution methods and effectiveness of the proposed model.</p>

A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy

Motivated by the call of the International Maritime Organization to meet the emission targets of 2030, this study considers two important practical aspects of quay crane scheduling: efficiency and energy consumption. More precisely, we introduce the bi-objective quay crane scheduling problem where the objective is to minimize the vessel’s completion time and the crane’s energy consumption. This is done by formulating a bi-objective mixed-integer programming model. A branch-and-bound algorithm was developed as the exact solution approach to find the full set of Pareto-optimal solutions. We consider (i) various lower bounds for both objectives, (ii) specific upper bounds, (iii) additional branching criteria, and (iv) fathoming criteria to detect Pareto-optimal solutions. Numerical experiments on benchmark instances show that the branch-and-bound algorithm can efficiently solve small- and medium-sized problems.

Scheduling quay cranes and shuttle vehicles simultaneously with limited apron buffer capacity

How to schedule quay cranes (QCs) and shuttle vehicles (SVs) simultaneously or model them in an integrated scheduling problem is one of the most important problems in operations and management of a container terminal. This paper investigates an integrated QC and SV scheduling problem constrained by apron buffer capacity. In this problem, the decisions to make include the bay-to-QC assignment, the QC-bay sequence, the QC-job sequence, the job-to-SV assignment and the SV-job sequence. First, a mixed-integer linear programming model is formulated for this problem to minimize the makespan. Second, the relationships and interactive variables among the four segments of constraints of the proposed model (i.e., scheduling QCs for vessel bays, sequencing jobs handled by a QC in each bay, scheduling SVs for jobs, apron buffer capacity constraints for each vessel bay) are analyzed to present three rules: vessel block rule, near-to-far rule and full-buffer rule. Finally, a sequential insertion algorithm, a greedy insertion algorithm and an improved genetic algorithm are proposed to solve mid- and large-sized cases for the problem. Numerical experiments show that the algorithms perform well, compared to the off-the-shelf solver. Based on these experiments, managerial implications are discussed for container terminal operations and management.

Multi-resource collaborative scheduling problem of automated terminal considering the AGV charging effect under COVID-19

Since the COVID-19 ravaged the global terminals, the Automated Container Terminal (ACT) has become one of important approach to promote the stronger quick response capacity to deal with the uncertainty that COVID-19 brought to the terminal. This research takes Automated Guided Vehicle (AGV) and their effects into account the multi-resource collaborative scheduling model to tradeoff ACT operational efficiency and energy savings. Firstly, the dual-cycle strategy of QC and the pooling strategy of AGV are given, which coordinates the scheduling of Quay Cranes (QCs), Yard Cranes (YCs) and other equipment. Furthermore, a multi-resource collaborative scheduling optimization model is proposed which roots from the principle of the Blocking-type Hybrid Flow Shop Problem (B–HFSP) with the objectives of minimizing the makespan of QC and the transportation energy consumption. And simultaneously, a mixed algorithm SA-GA is designed for solving this mixed integer programming model by an optimizing effect of Simulated Annealing on Genetic algorithms. Numerical experiments show that the model in this research is effective. The convergence of SA-GA is effective for small-scale cases and superior for large-scale cases. Considering both goals of high efficiency and energy saving, the Pareto solution set and collaborative scheduling solution take a priority to ensure that the bottlenecked QC runs efficiently. Here and now the average idle rate of QC is about [14%, 35%] lower than that of other equipment. The collaborative scheduling model constructed above not only has reference value for other multi-device and multi-stage scheduling problem, but also enhance the integrated decision-making ability of the ACT in the post-epidemic era.

Quay crane scheduling with time windows constraints for automated container port

The traditional quay crane of the container terminal is gradually transitioning to automation, which significantly changes the loading and unloading operation mode of the quay crane. In this paper, we study the sequence scheduling of automated quay crane (AQC) with time window constraints. First, the process of AQC handling operation is decomposed, and the mechanism model for AQC operation is established. Then, a mixed integer linear programming model is formulated to optimize the scheduling of AQC considering the time window constraints. Finally, the effectiveness of the optimization model is verified by arithmetic examples, and the management insights of energy efficiency optimization of the quay crane scheduling are given through scenario analysis.