Quay Crane Allocation Research Articles

Optimizing the Allocation of Quay Cranes and Prime Movers for Container Handling Operations

Optimizing the Allocation of Quay Cranes and Prime Movers for Container Handling Operations

Optimizing berth-crane allocation considering tidal effects using chaotic quantum whale optimization algorithm

With the normalization of the global epidemic, shipping has gradually resumed, resulting in a surge in port throughput. Terminal managers are having great difficulty in making container ports be stable, orderly, and efficient. For small and medium-sized ports, making full use of the tidal water level to increase the operation time of large ships significantly improves the efficiency of port operations. Therefore, considering the impact of tidal factors on the operation of container ports, this paper firstly proposes a new berths and quay cranes allocation optimization model, T-B&QC, that minimizes the distance between the actual berthing berth and the preferred berth, the port time cost of ships and the number of quay crane movements as the optimization objectives, under constraints that consider tidal factors. Then, to solve the T-B&QC model using chaotic mapping and quantum theory, the Whale Optimization Algorithm (WOA) is integrated by using the Chaotic Quantum Rotating Gate Algorithm (CQRGA) and the Quantum Not Gate Algorithm (QNGA), whale coding rules are designed, and the Feasible-Integer Processing Algorithm (WF-IP) is established. Afterwards, the Chaotic Quantum Whale Optimization Algorithm, CQWOA, is proposed. Finally, the CQWOA is used to develop a new berth and quay crane allocation optimization method, T-B&QC_CQWOA. Subsequently, data from an actual seaport container port is used to test the reliability and superiority of the proposed distributing approach and the established optimizing algorithm. Numerical results demonstrate that the proposed distributing approach outperforms the classical distribution models that are selected herein, and the CQWOA yields a coordinated schedule of higher quality than the others in the process of solving the model.

Integrated rescheduling optimization of berth allocation and quay crane allocation with shifting strategies

Container terminal operations are a core aspect of vessel operations in ports and necessitate an intelligent rescheduling approach to manage complex uncertainty scenarios. This paper investigates the problem of berth allocation and quay crane (QC) assignment with shifting strategies. A variable-length rolling mechanism (VLRM) is designed to identify uncertainty scenarios and determine the optimal rescheduling time point. Notably, we introduce a novel cross-wharf shifting movements strategy (CWSM) and develop a rescheduling model that accounts for constraints related to tidal time windows. The proposed Adaptive Large Neighborhood Search algorithm (ALNS) is tailored to solve this problem effectively. Computational results from various instance sizes validate the efficacy of both the model and the ALNS algorithm. These results demonstrate that the ALNS algorithm exhibits distinct advantages in solution quality and computational time for large-scale instances. Furthermore, the inclusion of tidal time window constraints significantly amplifies the complexity of uncertainty scenarios, emphasizing their importance and the impossibility of neglecting them. The cross-wharf shifting movements strategy, presented herein, effectively mitigates the impact of uncertainty scenarios within a defined scope while enhancing adjustment flexibility.

A survey on computational intelligence approaches for intelligent marine terminal operations

AbstractMarine container terminals (MCTs) play a crucial role in intelligent maritime transportation (IMT) systems. Since the number of containers handled by MCTs has been increasing over the years, there is a need for developing effective and efficient approaches to enhance the productivity of IMT systems. The berth allocation problem (BAP) and the quay crane allocation problem (QCAP) are two well‐known optimization problems in seaside operations of MCTs. The primary aim is to minimize the vessel service cost and maximize the performance of MCTs by optimally allocating berths and quay cranes to arriving vessels subject to practical constraints. This study presents an in‐depth review of computational intelligence (CI) approaches developed to enhance the performance of MCTs. First, an introduction to MCTs and their key operations is presented, primarily focusing on seaside operations. A detailed overview of recent CI methods and solutions developed for the BAP is presented, considering various berthing layouts. Subsequently, a review of solutions related to the QCAP is presented. The datasets used in the current literature are also discussed, enabling future researchers to identify appropriate datasets to use in their work. Eventually, a detailed discussion is presented to highlight key opportunities along with foreseeable future challenges in the area.

A column generation approach for the quay crane allocation problem considering uncertain operation efficiency

This study constructs a mixed integer programming model for the integrated quay crane allocation problem to minimize vessels’ waiting time and delay time cost. Taking the uncertainty of quay crane operation efficiency into consideration, this study constructs a stochastic programming model and a distributional robust chance constraint (DRCC) model. In addition, column generation is applied to solve the three proposed models. Moreover, this paper uses real-world data from Shanghai Yangshan Port to verify the effectiveness of proposed model and algorithm. To prove the robustness of the DRCC model, this study conducts an uncertain parameters sensitivity analysis, and analyzes the performance of the models proposed above. The results show that the proposed DRCC model has better anti-interference ability. The conclusion drawn from this study has potential implications for resource allocation within port operations.

Berth and quay crane allocation and scheduling problem with renewable energy uncertainty: A robust exact decomposition

Container terminals are moving towards using renewable energy sources to manage their operations and cope with the traditional ones impacting the environment. However, renewable energy sources are limited, more costly, uncertain, and supplied in a non-continuous way. To improve operations’ sustainability, terminals are called to alternate between traditional and renewable energy sources. In this context, this paper proposes a multi-objective mathematical model to solve the berth and quay crane allocation and scheduling problem (BACASP), considering energy uncertainty and operations’ sustainability. The model considers two conflicting objectives: maximising renewable energy usage and minimising operational and energy costs. A robust version of the model is proposed to handle the uncertainty of renewable energy availability, whose objective is to optimize the worst-case scenario. Since many uncertain scenarios are involved, a simple commercial solver could not solve the model, even for small instances. Thus, we propose an exact decomposition algorithm that alleviates the model complexity, based on novel reinforcement procedures including novel set partitioning and valid inequalities, lower bounds, a warm-up scenario picking formula, speed up upper bounds, and a max–min MIP cutting procedure. A series of experiments show how the proposed approach helped tighten the model bounds, improve algorithm convergence, and alleviate computational time. We also conduct an economic analysis to assess the value of integration of energy parameters within BACASP. An additional investigation is made to show how Pareto optimal curves are sensitive to the price and availability of renewable energy uncertain scenarios.

A novel robust exact decomposition algorithm for berth and quay crane allocation and scheduling problem considering uncertainty and energy efficiency

In container terminals, electricity price variation has a tangible impact on the operating cost of port equipment, especially the quay crane (QC). Accordingly, significant operational cost savings could be realized via careful planning. This study addresses, for the first time, berth allocation and QC assignment and scheduling problem (BACASP) considering energy price variations. A novel mathematical model is developed to minimize both energy costs and vessel tardiness. Furthermore, we consider the uncertainty in QC processing time and vessel arrival time, based on which we propose a robust formulation that optimizes the worst-case scenario. This study also highlights why robustness is essential for cost-cutting considering the energy prices in the BACASP. The model is unable to achieve optimality using CPLEX, even for small instances. Thus, a novel exact decomposition algorithm is proposed to solve the problem over a reasonable computational time. Its novelty lies in four proposed strengthening procedures designed and embedded within the algorithm. To test the algorithm, several instances are generated based on the literature and real data of a port partner. Then, several experiments are conducted to highlight the impact of implementing the four strengthening procedures and demonstrate how considering energy constraints within the BACASP leads to significant cost savings.

An integrated container terminal scheduling problem with different‐berth sizes via multiobjective hydrologic cycle optimization

Integrated berth and quay crane allocation problem (BQCAP) are two essential seaside operational problems in container terminal scheduling. Most existing works consider only one objective on operation and partition of quay into berths of the same lengths. In this study, BQCAP is modeled in a multiobjective setting that aims to minimize total equipment used and overall operational time and the quay is partitioned into berths of different lengths, to make the model practical in the real-world and complex quay layout setting. To solve the new BQCAP efficiently, a multiobjective hydrologic cycle optimization algorithm is devised considering problem characteristics and historical Pareto-optimal solutions. Specifically, the quay crane of the large vessel in all Pareto-optimal solutions is rearranged to increase the chance of finding a good solution. Besides, worse solutions are probabilistic retained to maintain diversity. The proposed algorithm is applied to a real-world terminal scheduling problem with different sizes from a container terminal company. Experimental results show that our algorithm generally outperforms the other well-known peer algorithms and its variants on solving BQCAP, especially in finding the Pareto-optimal solutions range.

Simultaneous Allocation and Scheduling of Quay Cranes, Yard Cranes, and Trucks in Dynamical Integrated Container Terminal Operations

We present a dynamical modeling of integrated (end-to-end) container terminal operations using finite state machine (FSM) framework where each state machine is represented by a discrete-event system (DES) formulation. The hybrid model incorporates the operations of quay cranes (QC), internal trucks (IT), and yard cranes (YC) and also the selection of storage positions in container yard (CY) and vessel bays. The QC and YC are connected by the IT in our models. As opposed to the commonly adapted modeling in container terminal operations, in which the entire information/inputs to the systems are known for a defined planning horizon, in this research we use real-time trucks, crane, and container storage operations information, which are always updated as the time evolves. The dynamical model shows that the predicted state variables closely follow the actual field data from a container terminal in Tanjung Priuk, Jakarta, Indonesia. Subsequently, using the integrated container terminal hybrid model, we proposed a model predictive algorithm (MPA) to obtain the near-optimal solution of the integrated terminal operations problem, namely the simultaneous allocation and scheduling of QC, IT, and YC, as well as selecting the storage location for the inbound and outbound containers in the CY and vessel. The numerical experiment based on the extensive Monte Carlo simulation and real dataset show that the MPA outperforms by 3-6% both of the policies currently implemented by the terminal operator and the state-of-the-art method from the current literature.

Discretization-Strategy-Based Solution for Berth Allocation and Quay Crane Assignment Problem

The continuous berth allocation and quay crane assignment problem considers the size of berths and ships, the number of quay cranes, the dynamic ships and non-crossing constraints of quay cranes. In this work, a mixed-integer linear programming model of this problem is established, aiming at minimizing the total stay time and delay penalty of ships. To solve the model, the continuous berth is separated into discrete segments via a proposed discretization strategy. Thereafter, a large neighborhood search algorithm composed of the random removal operator and relaxed sorting-based insertion operator and a backtracking comparison-based constraint repair strategy are proposed. The effectiveness of the model and algorithm presented is verified via real-life instances with different characteristics, and the performances of different combinations of removal operators and insertion operators in the large neighborhood search algorithmic framework are analyzed. Numerical results show that the large neighborhood search algorithm can optimally solve the small-scale instances in a reasonable time. Meanwhile, the results of large-scale instances show that the large neighborhood search algorithm incorporating the discretization strategy is more efficient than other genetic algorithms based on continuous optimization. With the proposed approach, high-quality berth and quay crane allocation results can be obtained efficiently.

Port Container Terminal Quay Crane Allocation Based on Simulation and Machine Learning Method

Port Container Terminal Quay Crane Allocation Based on Simulation and Machine Learning Method

A Collaborative Berth Planning Approach for Disruption Recovery

Traditionally, terminal operators create an initial berthing plan before the arrival of incoming vessels. This plan involves decisions on when and where to load or discharge containers for the calling vessels. However, disruptive unforeseen events (i.e., arrival delays, equipment breakdowns, tides, or extreme weather) interfere with the implementation of this initial plan. For terminals, berths and quay cranes are both crucial resources, and their capacity limits the efficiency of port operations. Thus, one way to minimize the adverse effects caused by disruption is to ally different terminals to share berthing resources. In some challenging situations, terminal operators also need to consider the extensive transshipment connections between feeder and mother vessels. Therefore, in this work, we investigate a collaborative variant of the berth allocation recovery problem which focuses on the collaboration among terminals and transshipment connections between vessels. We propose a mixed-integer programming model to (re)-optimize the initial berth and quay crane allocation plan and develop a Squeaky Wheel Optimization metaheuristic to find near-optimal solutions for large-scale instances. The results from the performed computational experiments, considering multiple scenarios with disruptive events, show consistent improvements of up to 40% for the suggested collaborative strategy (in terms of costs for the terminal operators).

Berth and quay crane allocation and scheduling with worker performance variability and yard truck deployment in container terminals

In a container terminal, the quay cranes (QCs) are the main equipment involved in the core activities. According to a bottleneck principle, the productivity rate of QCs is related to both worker productivity and deployed yard trucks. Yet, in the literature, the berth and quay cranes allocation and scheduling problems were addressed separately from these two parameters. In contrast, practitioners confirm their important impact on cranes productivity and efficiency. This paper proposes a new extension of the berth and quay cranes allocation and scheduling problems considering worker performance variability and yard truck deployment constraints. First, we formulate the problem as a mixed-integer linear program to minimize the vessels departure time under many practical regulations involving the work roster constraints specific to container terminals and the trucks utilization congestion targets. Additionally, the study provides a computationally efficient method to find a lower bound. We also show that integrative planning minimizes the vessels departure time compared to the separated decision-making process. Second, to build good solutions in a reasonable time, we propose a heuristic and a Variable Neighborhood Search (VNS) with a new architecture and settings designed to suit the novel issues of the tackled problem. The algorithm is tested on real time data sets and outperforms a commercial solver. This study originates from our experience with a multinational company managing a container terminal. Thus, we have embedded the proposed resolving methods in a decision-support system for our industrial partner.

Combined Configuration of Container Terminal Berth and Quay Crane considering Carbon Cost

Berths and quay cranes are scarce resources in the container terminal system. If the equipment is reasonably planned, the service quality might be improved and the operation cost of the terminal would be reduced. In addition, the competition among ports is not only the competition of the terminal service quality, throughput, and scale but also the competition of low-energy consumption and low pollution. In order to reduce carbon dioxide emissions, this paper developed a multiobjective optimization model for the joint allocation of container terminal berths and Quay cranes. The model is developed based on preference of ships for berths, and the impact of carbon emission cost on terminal operations have been considered. The carbon cost from two aspects, namely, reducing the operation cost of ships and minimizing the average waiting time and departure delay of ships, has been considered. The improved adaptive genetic algorithm has been used to solve the model. A container terminal in Ningbo has been used as a case study. The carbon emission cost of the berths and quay cranes operation system has been calculated. The influence of the variation in carbon emission cost on the berths and quay cranes configuration scheme has been evaluated. The result proves that considering the carbon cost can make the berths and quay cranes operation more green and reasonable. It can be seen that the objective function value of the joint scheme is 5.92% lower than that of the traditional scheme, and the terminal operation cost of carbon emission constraints is 11.76% lower than that of no carbon emission constraints.

A Fuzzy Optimization Model for the Berth Allocation Problem and Quay Crane Allocation Problem (BAP + QCAP) with n Quays

This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.

Energy-Efficient and Integrated Allocation of Berths, Quay Cranes, and Internal Trucks in Container Terminals

Despite a significant number of studies that have focused on the operational efficiency of container terminals, existing literature has paid little attention to improving energy efficiency, e.g., energy consumption and negative externalities in container terminals. Most researchers consider energy-saving goals when allocating berths and quay cranes to vessels, assuming that internal trucks are in sufficient supply. Furthermore, recent studies have revealed that shortage of internal trucks has become an issue that greatly affects the operational and energy efficiencies of container terminals. This work presents a planning model that integrates berth allocation, quay crane assignment, and internal truck assignment problems. The developed model contributes to existing literature by including energy-saving goals in the integrated planning of these problems, as well as including important realistic factors such as shortages of internal trucks and handling time estimations, thus producing a reliable handling plan that achieves energy and cost savings without additional truck investment. To solve realistic problems, a Lagrangian relaxation-based method is developed. Furthermore, the benefits of the developed approach are demonstrated by comparing it to an existing approach. On average, our approach could improve the solutions of the integrated problem with different numbers of internal trucks by 6% compared to the solutions obtained using the existing approach.

Combining mixed integer programming and constraint programming to solve the integrated scheduling problem of container handling operations of a single vessel

In the container terminals of seaports, the container handling system consists of a variety of container handling machines such as quay cranes, internal yard trucks, and yard cranes. This study applies a holistic approach to the integrated scheduling of these machines for the container handling operations of a single vessel. We formulate this special hybrid flow shop scheduling problem through both mixed integer programming (MIP) and constraint programming (CP) techniques. Then we develop an easily-implemented approach that combines the strengths of MIP and CP. First, the MIP model, which only considers quay crane scheduling, is solved by an MIP solver, and a quay crane allocation plan is retrieved from the MIP solution. Then, this quay crane allocation plan is fed to the CP model, warm-starting the branch-and-prune algorithm built in a CP optimizer. Our numerical experiments reveal that this hybrid MIP/CP approach can solve the large-sized instances with up to 1000 containers, 6 quay cranes, 36 yard trucks, and 15 yard cranes to optimality with a gap of less than 3.31%, within a solution time of 2 minutes. If we increase the solution time to 5 minutes, this hybrid approach solves larger instances with up to 1400 containers to optimality with a gap of less than 1.41%. The state-of-the-art dedicated algorithms reported in the literature (which address an easier version of the same problem by ignoring non-crossing constraints and safety margins between quay cranes) are only able to find solutions for real-life instances with up to 500 containers within the solution time of 2930 or 5221 seconds, leaving a 4% or an unknown optimality gap. Thus, this study improves the solution of this integrated scheduling problem in terms of the instance size, solution efficiency, and solution optimality.

Discrete-Event Systems Modeling and the Model Predictive Allocation Algorithm for Integrated Berth and Quay Crane Allocation

In this paper, we study the problem of integrated berth and quay crane allocation (I-BCAP) in general seaport container terminals and propose the model predictive allocation (MPA) algorithm and preconditioning methods for solving the I-BCAP. First, we propose a dynamical modeling framework based on discrete-event systems (DESs), which describes the operation of a berthing process with multiple discrete berthing positions and multiple quay cranes. Second, based on the discrete-event model, we propose the MPA algorithm for solving the I-BCAP using the model predictive control (MPC) principle with a rolling event horizon. The validation and performance evaluation of the proposed modeling framework and allocation method are done using: 1) extensive Monte Carlo simulations with realistically generated datasets; 2) real dataset from a container terminal in Tanjung Priuk port, located in Jakarta, Indonesia; and 3) real life field experiment at the aforementioned container terminal. The numerical simulation results show that our proposed MPA algorithm can improve the efficiency of the process where the total handling and waiting cost is reduced by approximately 6%–9% in comparison with the commonly adapted method of first-come first-served (FCFS) (for the berthing process) combined with the density-based quay cranes allocation (DBQA) strategy. Moreover, the proposed method outperforms the state-of-the-art hybrid particle swarm optimization (HPSO)-based and genetic algorithm (GA)-based method proposed in the recent literature. The real life field experiment shows an improvement of about 6% in comparison with the existing allocation method used in the terminal.

Reactive strategy for discrete berth allocation and quay crane assignment problems under uncertainty

This study examines the simultaneous allocation of berths and quay cranes under discrete berth situations with uncertainty at container terminals. First, a mixed-integer programming model that considers practical constraints with the objective of minimizing the baseline cost is formulated to obtain a baseline schedule. However, in reality, different disruptions, i.e., deviation of vessels’ arrival times, deviation of vessels’ loading and unloading operation times, calling of unscheduled vessels, and breakdown of quay cranes, will occur when executing the baseline schedule. Thereby, a reactive strategy, which takes the baseline schedule as a reference and aims to minimize the recovery cost, is proposed. Given that the cost value cannot simulate the choices of decision makers in reality, a behavior perception-based disruption model is proposed to effectively simulate a practical situation. A rolling horizon heuristic is presented to derive good feasible solutions. Computational tests are reported to show (i) the effectiveness of the proposed approach to solve a set of real instances to optimality; and (ii) the performance of proposed reactive strategy to conduct different disruptions; (iii) the comparisons between the proposed reactive strategy and proactive strategy.

A genetic algorithm for solving the quay crane scheduling and allocation problem

International sea-freight container transportation has grown dramatically over the last years and container terminals represent nowadays a key actor in the global shipping network. The management of a container terminal is a complex process that involves many decisions. Among the problems to be solved, there are the spatial allocation of containers on the terminal yard, allocation of ships to berths and cranes, scheduling priorities and operations in order to minimize ship’s turnaround time, one of the main indicators of the terminal performance for the shipping companies. An efficient use of quay cranes is crucial, since quay cranes are highly expensive and represent one of the most scarce resources in the terminal. The quay crane allocation problem aims to efficiently assign quay cranes to vessels that must be operated over a given time horizon. The allocated cranes must be sufficient to complete the workload within the given time window, although many configurations are possible. In this paper, we will mainly focus on the quay crane scheduling problem, considering other logistic activities as given. This problem can be split into two sub-problems. First, specific quay cranes must be assigned to specific tasks. Second, a detailed schedule of the loading and unloading moves for each quay crane should be constructed. In this case, the number of quay cranes assigned to the vessel is assumed to be known in advance. The paper presents a solution for solving the quay crane scheduling and allocation problem that is based on working with modern optimization techniques such as genetic algorithms. The genetic algorithms are soft computing techniques that are used for optimization and search. Thus, the solution is obtained through a C++ built on simulation model that, over the analytical modelling of container’s terminals activity, has the main advantage of providing a greater level of detail and avoids too many simplifications. Also, three different scenarios that describe operational situations have been taken into account.