Crane Scheduling Research Articles

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.

A column generation approach for the crane scheduling with sidekick in a perpendicular automated yard block

In a new container terminal design, the perpendicular block is equipped with a Rail Mounted Gantry crane (RMG) and a sidekick Ground Trolley (GT). The RMG can handle containers by itself, or utilize the sidekick GT for container delivery. Unlike the traditional crane scheduling problem (CSP), the makespan is not merely determined by the job sequence, but also affected by the GT allocation and the RMG-GT synchronization. This novel optimization problem is defined as the crane scheduling problem with sidekick (CSP-S). It can be formulated as a mixed integer programming model to explicitly determine the GT allocation and the handover points. When the choice of handover points is remodeled as an implicit decision, the CSP-S can be transformed into an arc-based surrogate model. Based on the solution patterns of the surrogate model, it is found that the RMG-GT working plan can be decomposed into smaller “segments”. Each segment consists of two intertwined paths of the RMG and the GT respectively. A column generation approach is proposed, where the segments can be generated by a multi-attribute labeling algorithm based on the surrogate model. This solution approach can optimally solve the traditional CSP, and outperforms all benchmark methods under the CSP-S. This can be attributed to the multi-attribute labeling algorithm, which accurately controls the RMG-GT synchronization. Numerical experiments showed that the column generation approach could be well implemented under the rolling-horizon manner in practice. It improved the “Nearest Job” strategy and the TSP-based method by more than 10 % and 5 % respectively under the CSP-S. Experiments also revealed that the RMG-GT system would benefit from a faster GT, but the marginal contribution of the GT speed was gradually reducing.

An Iterative Re-Optimization Framework for the Dynamic Scheduling of Crossover Yard Cranes with Uncertain Delivery Sequences

In yard-crane scheduling problems, as loading operations take priority over unloading, the delivery sequence of unloading from the quaysides to the yard is uncertain. The delivery sequence changes may make crane scheduling more difficult. As a result, the crane operations schedules developed statically become suboptimal or even infeasible. In this paper, we propose a dynamic scheduling problem considering uncertain delivery sequences. A mixed-integer linear program is developed to assign tasks to cranes and minimize the makespan of crane operations. We propose an iterative solution framework in which the schedules are re-optimized whenever the delivery sequence change is revealed. A genetic algorithm is proposed to solve the problem, and a greedy algorithm is designed to re-optimize and update the solution. To make the updated solution take effect as soon as possible, regarding batch-based task assignment, the tasks in the scheduling period are divided into several batches. In this case, the instant requests arising from the delivery sequence change are added to corresponding batch tasks and re-optimized together with the tasks of this batch. In addition, a relaxation model is formulated to derive a lower bound for demonstrating the performance of the proposed algorithm. Experimental results show that the average gap between the algorithm and the lower bound does not exceed 5%. The greedy insertion algorithm can re-optimize the instant requests in time. Therefore, the proposed iterative re-optimization framework is feasible and has the advantages (necessity) of batch-based task assignment.

Storage strategy of outbound containers with uncertain weight by data-driven hybrid genetic simulated annealing algorithm.

It is necessary to ensure the ship's stability in container ship stowage and loading and unloading containers. This work aims to reduce the container dumping operation at the midway port and improve the efficiency of ship transportation. Firstly, the constraint problem of the traditional container ship stacking is introduced to realize the multi-condition mathematical model of the container ship, container, and wharf. Secondly, a Hybrid Genetic and Simulated Annealing Algorithm (HGSAA) model is proposed for the container stacking and loading stacking in the yard. The specific container space allocation and multi-yard crane adjustment scheme are studied. Finally, the effectiveness of the multi-condition container ship stowage model is verified by numerical experiments by changing the number of outbound containers, storage strategies, storage yards, and bridges. The experimental results show that the HGSAA mode converges to 106.1min at the 751st iteration. Of these, the non-loading and unloading time of yard bridge 1 is 3.43min. The number of operating boxes is 25. The non-loading and unloading time of yard bridge 2 is 3.2min, and the operating box volume is 25 boxes. The objective function of the genetic algorithm converges when it iterates to generation 903 and 107.9min. Among them, the non-loading and unloading time of yard bridge 1 is 4.1min. The non-loading and unloading time of yard bridge 2 is 3.1min. Therefore, the proposed HGSAA has a faster convergence speed than the genetic algorithm and can obtain relatively good results. The proposed container stacking strategy can effectively solve the specific container allocation and multi-yard crane scheduling problems. The finding provides a reference for optimizing container scheduling and improving shipping transportation efficiency.

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.

Models and algorithms for a yard crane scheduling problem in container ports

This paper addresses the scheduling of a yard crane in an automated container block, considering its relationships with the other terminal subsystems. Containers coming into the block to be stored have release times, indicating the moment at which they arrive from ships or trucks. Containers being retrieved have due times, indicating when they will be required by other subsystems. The problem can be seen as a pickup routing problem and also as a one-machine scheduling problem. As a starting point, integer linear models were developed for both approaches. Then, to obtain good solutions for large instances, several heuristic algorithms, coupled with a local search, were proposed. An extensive computational study, based on a newly generated benchmark, shows the limits of the exact methods and the quality of the solutions obtained by the heuristics.

Joint Optimization of Pre-Marshalling and Yard Cranes Deployment in the Export Block

To improve the efficiency of loading operation by researching the optimization of the pre-marshalling operation scheme in the export container block between the time when the ship stowage chart was published and the beginning time of loading, a two-stage mixed integer programming model was established. The first stage established an optimization model of the container reshuffling location, based on the objective function of the least time-consuming operation of a single-bay-yard crane, and designed an improved artificial bee colony algorithm to solve it. Based on the first stage, an optimization model of yard crane configuration and scheduling was built to minimize the maximum completion time of the yard crane in the export block, and an improved genetic algorithm was designed to solve the built model. Through comparative analysis, the performance of our algorithm was better than CPLEX and traditional heuristic algorithms. It could still solve the 30 bays quickly, and the solving quality was 8.53% and 11.95% higher than GA and TS on average, which verified the effectiveness of the model and the science of the algorithm and could provide a reference for improving the efficiency of port operation.

A Novel Benchmark Environment for Dynamic Factory Crane Scheduling

In dynamic warehouse operations, factory crane scheduling is a challenging problem to be solved. The interplay between a number of cranes requires good coordination to efficiently handle requested transport orders within the warehouse. The objective is to maximize the throughput and therefore minimize the makespan of crane schedules for a given set of transport orders and resulting crane moves. However, in real world processes, uncertainty is a key factor that needs to be considered. New transport orders arrive without prior announcement during the planning window, as the exact timing of vehicles responsible for inbound and outbound flows are often available only on short notice. Furthermore, events such as crane maintenance or operator breaks must be dealt with accordingly. To further the algorithmic research where these challenging events in the domain of dynamic factory crane scheduling must be tackled, we propose an open-source simulation model that serves as a novel benchmark.

Optimization Approach for Yard Crane Scheduling Problem using genetic algorithm in Container Terminals

As the core operational issue in container terminals, yard crane scheduling problem directly affects the overall operation efficiency of port connecting highway or railway transportation and sea transportation. In practice, the scheduling of yard cranes is subject to many uncertain factors, so the scheme may be inapplicable and needs to be adjusted. From the perspective of proactive strategy, considering fluctuations in arrival time of external trucks as well as varied handling volume of yard cranes,a stochastic programming model is established in this paper to obtain a fixed scheme with the minimum expected value of yard crane makespan and total task waiting time over all the scenarios. The scheme does not require rescheduling when facing different situations. Subsequently, two algorithms based on certain rules are proposed to obtain the yard crane operation scheme in the deterministic environment, which are taken as the basic solution inthe uncertain conditions, and then a tailored genetic algorithm is adopted to find the optimal solution with good adaptability to the uncertain scenarios. Finally, we use smallscale examples to compare the performance of algorithms in the deterministic and uncertain environment and then analyze the relationship between different yard crane configurations and the number of tasks. Largescale experiments are performed to study the operation efficiency of the storage yard with different handling volumes assigned to each yard crane.

Service scheduling optimization for multiple tower cranes considering the interval time of the cross-tasks.

The key issues that have always affected the production yield of the construction industry are delays and cost overruns, especially when dealing with large-scale projects and super-high buildings in which multiple tower cranes with overlapping areas are often deployed because of urgent due date and limited space. The service scheduling of tower cranes, which act as the crucial site equipment for lifting and transporting materials, is one of the main problems not only related to the construction progress and project cost but also affecting equipment health, and it may bring security risks. The current work presents a multi-objective optimization model for a multiple tower cranes service scheduling problem (MCSSP) with overlapping areas while achieving maximum interval time of cross-tasks and minimum makespan. For the solving procedure, NSGA-Ⅱ is employed with double-layer chromosome coding and simultaneous coevolutionary strategy design, which can obtain a satisfactory solution through effectively allocating tasks within overlapping areas to each crane and then prioritizing all the assigned tasks. The makespan was minimized, and stable operation of tower cranes without collision was achieved by maximizing the cross-tasks interval time. A case study of the megaproject Daxing International Airport in China has been conducted to evaluate the proposed model and algorithm. The computational results illustrated the Pareto front and its non-dominant relationship. The Pareto optimal solution outperforms the results of the single objective classical genetic algorithm in terms of overall performance of makespan and interval time of cross-tasks. It also can be seen that significant improvement in the time interval of cross-tasks can be achieved at the cost of a tiny increase in makespan, which means effective avoidance of the tower cranes entering the overlapping area at the same time. This can help eliminate collision, interference and frequent start-up and braking of tower cranes, leading to safe, stable and efficient operation on the construction site.

Energy-oriented crane scheduling in steel coil storages: Evaluation of heuristic approaches

Steel production is an energy-intense industry. Besides the production process itself, accompanying logistic processes are characterized by a high energy demand due to the weight of the products. We consider a steel coil storage, where a gantry crane stores and retrieves steel coils of up to 35 tons. An energy-oriented approach for the scheduling of crane operations can help save energy and lower operational costs. In industrial settings, crane operators require swift assistance in sequencing crane operations and assigning storage places for the coils. Therefore, we develop different heuristic approaches for the energy-oriented crane scheduling problem and compare them based on a case study derived from a German steel manufacturer.

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>

Discrete-time and continuous-time scheduling approaches for crane-assisted pipeless process plants

In pipeless process plants that employ cranes to transfer material-containing-vessels between equipment, scheduling of cranes along with the equipment-operations on vessels is crucial from a productivity perspective. The workings of such crane-assisted pipeless process plants can differ from each other depending on the nature of their set-ups and product(s) produced. For the scheduling of such plants which currently lack substantive research in the literature, it is important to explore and develop general methods, and the current work is an endeavor in this direction. Mixed integer linear programming (MILP) based models are developed in this work using the discrete-time and precedence-based continuous-time approaches. While the modeling using the discrete-time approach is developed from scratch, that based on the continuous-time approach is a continuation from our prior work (Aravind et al., 2021). We compare the two approaches and draw generic model-agnostic insights about the aptness of the approaches to suit the practical requirements of implementation, through computational studies. Modeling based on the continuous-time approach is found to be favored from a computational perspective despite its inherent complexity in construction.

An allocation approach for external truck tasks appointment in automated container terminal

Ports are the key connection of sea and land transportation. The coordination of container collection and distribution directly affect the handling efficiency of port in the entire supply chain. The optimization of tasks appointment for external trucks is crucial to improving the efficiency of container collection and distribution. The layout of the interchange points of external trucks are streamlined in automated container terminals where external trucks are commonly affected by the seaside operations. The traditional methods of external trucks assignment are inadequately applicable. In this paper an optimization model for the tasks appointment of external trucks is established for the joint optimization of external truck appointment and automated rail mounted gantry crane (ARMG) scheduling in the yard. Multiple objectives are generated including the balance of appointment among periods of time and between blocks. In this model the capacity constraints of the loading operations of external truck and moving operations of ARMGs between the seaside and landside are comprehensively considered. The model is solved by CPLEX and verified through sensitivity analysis. Different task appointment modes and various scenarios are compared and suggestions for selecting an optimization strategy are proposed. The experimental results show that the task appointment solutions effectively prevent the queuing of trucks, and balance the ARMG handling in automated container terminals, and herein the port efficiency is enhanced and the satisfaction of the carriers is promoted accordingly. It is also suggested that terminal managers should consider yard operations, operation capacity and the length of appointment period when considering the optimization of a task appointment schedule. While keeping optimize the appointment modes according to the operational conditions to improve the balance between the seaside and landside operations and reduce the idle of the ARMGs.

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.

Multiple equipment scheduling and AGV trajectory generation in U-shaped sea-rail intermodal automated container terminal

As a key development direction of future ports, automated container terminals will play a crucial part in the development of multimodal transportation. Based on the newly constructed U-shaped yard layout in sea-rail intermodal container terminal, this paper focuses on the integrated scheduling of horizontal transport equipment and handling equipment, as well as path planning for AGVs. A bi-level programming model is established to obtain the yard crane scheduling scheme and determine the specific trajectories of AGVs with the goal of minimizing the makespan and total waiting time of AGVs and trucks. We design a spatio-temporal greedy strategy based bi-level genetic algorithm to schedule tasks and resolve conflicts in light of the multi-objective and hierarchical characteristics of the problem. Results indicate that the proposed algorithm could resolve the path conflicts effectively and obtain the integrated scheme that hardly affect the operation process of sea-rail intermodal containers.

Intelligent scheduling of double-deck traversable cranes based on deep reinforcement learning

ABSTRACT Cranes are used extensively in manufacturing workshops to move jobs, but their high complexity and dynamics lead to difficult workshop production scheduling. To address this issue, this article proposes a deep reinforcement learning-based method combined with discrete event simulation to minimize the makespan of the double-deck traversable crane flexible job-shop scheduling problem (DTCFJSP). Specifically, the problem is first formulated as a finite Markov decision process by introducing state representation, an action space and a reward function. Then, a new double-deep Q-learning network is incorporated to create a selection strategy for optimal actions in different states. The results of experiments conducted in this study show that the average efficiency of the double-deck traversable crane is approximately 12% higher than that of regular cranes, and the application of deep reinforcement learning in crane scheduling is feasible and effective.

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.

Simulation-Based Optimization Approaches for Dealing with Dual-Command Crane Scheduling Problem in Unit-Load Double-Deep AS/RS Considering Energy Consumption

Automated storage/retrieval systems (AS/RS) have been increasingly used to support operations in manufacturing firms, warehouses, and distribution centers. Usually, AS/RSs are expensive. To achieve a good return on investment (ROI), an AS/RS must operate optimally. This research focuses on solving the crane scheduling problem, which has a great and immediate impact on the performance of an AS/RS. To optimize the design and operations of an AS/RS, many past studies have applied the simulation approach. However, the simulation and optimization have been often loosely coupled, resulting in a rigorous and labor-intensive optimization procedure. Using population- and evolution-based metaheuristics to deal with the crane scheduling problem of an AS/RS is one of the research trends. However, the whale optimization algorithm (WOA) and its variants have not been used for this purpose. To address the said gaps, this research first proposes a framework for coupling the simulation and optimization closely, in which various heuristics/metaheuristics, including first-come first-serve (FCFS), RANDOM, WOA, genetic algorithms (GAs), particle swarm optimization (PSO), and especially an improved WOA (IWOA), together with dynamic programming (DP), have been used as alternative sequencing methods. Based on this framework, different simulation-based optimization approaches have been developed for solving the dual-command crane scheduling problem in a unit-load double-deep AS/RS. The experimental results show that IWOA+DP outperforms the others in terms of energy consumption.