Crane Scheduling Problem Research Articles

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.

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

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.

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.

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.

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.

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.

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.

A study on deep reinforcement learning-based crane scheduling model for uncertainty tasks

Abstract Aiming at the crane scheduling problem for uncertainty tasks in multi-crane scheduling situation, this article proposes a deep reinforcement learning-based crane scheduling modeling method that is not dependent on mathematical planning and has certain generality. First, the crane scheduling process is integrated into deep reinforcement learning framework in which the orbit space of the crane and the transportation task is environmental information and crane is the intelligent agent. Second, the interactive mode between reinforcement learning algorithm and environment is adjusted to adapt to the combined learning of multi-crane scheduling model. Last, the crane scheduling model for uncertainty tasks is constructed by optimizing reward discount factor, learning rate, and reward function intensive mode. Testing of the model is carried out based on practical crane scheduling in one steelmaking workshop. Scheduling proposal is generated and all crane tasks are completed within the planned time, which verifies the feasibility of this model. Results show that compared with manual scheduling plan, the scheduling proposal based on the new model reduces total task completion time by 11.52%, time of collision of crane routes decreases by 57.14%, and negative crane transportation distance shortens by 55.26%. The high efficiency of the scheduling model is therefore verified.

Integrated Berth and Crane Scheduling Problem Considering Crane Coverage in Multi-Terminal Tidal Ports under Uncertainty

In this work, we study the integrated berth and crane scheduling problem in a tidal port with multiple terminals, considering the uncertainties, tides, maximum coverage of cranes and interference between cranes. For coping with the uncertainties, a certain number of randomly generated samples are used to evaluate the solutions, and slack variables are introduced to reduce the impact caused by the variation in vessel arrival and crane operational efficiency. A novel nonlinear mixed integer programming model is first formulated for the problem to minimize the sum of expectation and variance of costs under all samples. An improved adaptive genetic algorithm, combining a simulated annealing mechanism and greedy construction strategy, is developed and implemented by MATLAB. The feasibility and validity of the algorithm and the benefits of multi-terminal collaborative scheduling strategy under uncertainty are evaluated through numerical experiments. The results show that the algorithm can obtain feasible scheduling solutions with higher quality. Compared to the strategy that considers either the uncertainty or the multi-terminal collaborative mechanism, the resulting solution considering both can effectively reduce the cost and improve the competitiveness of the port.

Multi-shuttle crane scheduling in automated storage and retrieval systems

We study a shared-storage automated storage and retrieval system (AS/RS) with one crane capable of carrying multiple unit loads. In a shared-storage system, items to be stored are not pre-assigned to dedicated shelf spaces. Therefore, given a set of storage and retrieval requests, the crane scheduling problem consists of deciding which requests are processed together in the same tour, determining the sequence in which the requests are processed, and assigning each storage request to an available slot on the shelf. We reformulate the problem as a special type of capacitated vehicle routing problem, which we use to close some open questions regarding the time complexity of related geometric routing problems. The reformulation allows us to tap into the rich and mature vehicle routing toolbox from the literature to propose a new exact solution approach. We show that this method is capable of solving large instances to optimality, outperforming previous methods from the literature. We use our new approach to derive multiple insights. Specifically, we show that system throughput can be predicted from the capacity of the crane via a simple rule. We also determine the optimal shape of a shelf and investigate the value of having knowledge of multiple requests when planning the crane schedule. Finally, we demonstrate that our approach can easily be extended to solve a whole family of multi-shuttle crane scheduling problems.

Crane scheduling for end-of-aisle picking: Complexity and efficient solutions based on the vehicle routing problem

To relieve human order pickers from unproductive walking through a warehouse, parts-to-picker systems deliver demanded stock keeping units (SKUs) toward picking workstations. In a wide-spread parts-to-picker setup, a crane-operated automated storage and retrieval system (ASRS) delivers bins with demanded SKUs toward an end-of-aisle picking workstation and returns them back into the rack once the picks are completed. We consider the scheduling of the crane that operates subsequent dual commands. Each dual command combines a retrieval request for another SKU bin demanded at the picking workstation with a storage request, where a bin that has already been processed and passed through the bin buffer is returned to its dedicated storage position in the ASRS. This system setup in general and the resulting crane scheduling problem in particular have been an active field of research for more than 30 years. We add the following contributions to this stream of research: We finally prove that the crane scheduling problem is strongly NP-hard. Furthermore, we show that, although only a single vehicle (namely, the crane) is applied, the problem is equivalent to the traditional vehicle routing problem (VRP). This opens the rich arsenal of very efficient VRP solvers, which substantially outperform existing tailor-made algorithms from the literature. • We consider end-of-aisle picking in modern warehouses. • We finally settle the complexity status of the resulting crane scheduling problem. • We show that the problem is transferable to the vehicle routing problem. • This allows us to solve large instances and to gain managerial insights.

Decomposition Algorithms for the Unidirectional Quay Crane Scheduling Problems

Decomposition Algorithms for the Unidirectional Quay Crane Scheduling Problems

Digital-twin driven energy-efficient multi-crane scheduling and crane number selection in workshops

In multi-crane systems, interference between cranes frequently occurs, and a significant amount of energy is wasted to avoid these interferences. Energy-efficient multi-crane scheduling and employing the required number of cranes are critical for saving energy. The energy consumption of a crane varies during operation; thus, it is important to accurately and effectively evaluate the operational energy consumption of a crane for different working phases. Digital twins (DTs) have various advantages such as virtual reality interaction, real-time mapping, and dynamic performance evaluation. Therefore, a DT-driven energy-efficient multi-crane scheduling and crane number selection approach is proposed in this study. The crane scheduling problem was described and modeled by considering energy consumption. Subsequently, a DT framework was established. Under this framework, a multi-crane system based on simulation was built in a virtual space. After inputting tasks into the virtual multi-crane system, a solution was generated based on the crane scheduling rules, interference detection, and avoidance methods. Then, the energy consumption of the program was evaluated. Finally, a case study was considered to illustrate the advantages of the proposed method.

The integrated quay crane assignment and scheduling problems with carbon emissions considerations

The continuous worldwide growth in container terminals’ traffic has pushed further the need for innovative research in ports’ operations. The quay crane assignment and scheduling problems are the prominent focus of such research but lack, to date, carbon emission considerations despite forecasts predicting that emissions from maritime transportation will exponentially increase in the absence of regulatory policies. The objective of this paper aims at filling this gap by solving the integrated quay crane assignment and scheduling problem with consideration of carbon regulatory policies. Two mathematical models of the problem are formulated using mixed integer programming (MIP), to capture the effects of carbon taxation and carbon cap-and-trade, respectively. The sensitivity analysis conducted shows that the primary focus of a port should be minimizing the berthing time of vessels which is highly impacted by the number of QCs assigned to each vessel.

A Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem

The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed to tackle the drawbacks of the EDAs, i.e., the lack of diversity of solutions and poor ability of exploitation. The hybridization approach, used in this investigation, uses a distance based ranking model and the moth-flame algorithm. The distance based ranking model is in charge of modelling the solution space distribution, through an exponential function, by measuring the distance between solutions; meanwhile, the heuristic moth-flame determines who would be the offspring, with a spiral function that identifies the new locations for the new solutions. Based on the results, the proposed scheme, called QCEDA, works to enhance the performance of those other EDAs that use complex probability models. The dispersion results of the QCEDA scheme are less than the other algorithms used in the comparison section. This means that the solutions found by the QCEDA are more concentrated around the best value than other algorithms, i.e., the average of the solutions of the QCEDA converges better than other approaches to the best found value. Finally, as a conclusion, the hybrid EDAs have a better performance, or equal in effectiveness, than the so called pure EDAs.

Compact ILP formulations for a class of solutions to berth allocation and quay crane scheduling problems

Compact ILP formulations for a class of solutions to berth allocation and quay crane scheduling problems

A robust multiobjective model for the integrated berth and quay crane scheduling problem at seaside container terminals

The ever increasing demand for container transportation has led to the congestion of maritime container terminals in the world. In this work, the two interrelated problems of berth and quay crane scheduling are considered in an integrated multiobjective mathematical model. A special character of this model is that the arrival times of vessels and the failure (working) times of quay cranes are not deterministic and can vary based on some scenarios. Hence, a robust model is devised for the problem having three objectives of minimising the deviations from target berthing locations and times as well as departure delays of all vessels. This robust optimisation seeks to minimise the value of the objectives regarding all the scenarios. An exact solution approach based on the \U0001d716-constraint method by the Gurobi software is applied. Moreover, regarding the complexity of the problem, two Simulated Annealing (SA) based metaheuristics, namely a Multi-Objective Simulated Annealing (MOSA) and a Pareto Simulated Annealing (PSA) approach are adapted with a novel solution encoding scheme. The three methods are compared based on some multiobjective metrics and a statistical test. The advantage of the integration of berth and quay crane scheduling is examined as well.

Optimization Approach for Yard Crane Scheduling Problem with Uncertain Parameters 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 in the 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 small-scale 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. Large-scale experiments are performed to study the operation efficiency of the storage yard with different handling volumes assigned to each yard crane.