Crane Scheduling Research Articles

A Branch-and-Price Algorithm to Solve a Quay Crane Scheduling Problem

Abstract As the maritime industry grows rapidly in size, more attention is being paid to to a wide range of aspects of problems faced at ports with respect to the efficient allocation of resources. A very important seaside planning problem that has received large attention in literature lately is the quay crane scheduling problem (QCSP). The problem involves the creation of a work schedule for the available quay cranes at the port to empty the containers from a vessel or given set of vessels. These optimization problems can be very complex and since they involve a large number of variables and constraints, the use of a commercial solver is impractical. In this paper, we reformulate a problem currently available in the literature to a Dantzig-Wolfe formulation that can be solved by column generation. We then develop a branch-and-price algorithm, which is an exact method, to effectively solve mixed integer programs with very large instances. The algorithm is first tested on a formulation currently available in literature with a small instance and will then be tested on large instances.

Migrating Birds Optimization for the Seaside Problems at Maritime Container Terminals

Sea freight transportation involves moving huge amounts of freights among maritime locations widely spaced by means of container vessels. The time required to serve container vessels is the most relevant indicator when assessing the competitiveness of a maritime container terminal. In this paper, two main logistic problems stemming from the transshipment of containers in the seaside of a maritime container terminal are addressed, namely, the Berth Allocation Problem aimed at allocating and scheduling incoming vessels into berthing positions along the quay and the Quay Crane Scheduling Problem, whose objective is to schedule the loading and unloading tasks associated with a container vessel. For solving them, two Migrating Birds Optimization (MBO) approaches are proposed. The MBO is a recently proposed nature-inspired algorithm based on theV-formation flight of migrating birds. In this algorithm, a set of solutions of the problem at hand, called birds, cooperate among themselves during the search process by sharing information within aV-line formation. The computational experiments performed over well-known problem instances reported in the literature show that the performance of our proposed MBO approaches is highly competitive and presents a better performance in terms of running time than the best approximate approach proposed in the literature.

A follow-up survey of berth allocation and quay crane scheduling problems in container terminals

Abstract This paper surveys recent publications on berth allocation, quay crane assignment, and quay crane scheduling problems in seaport container terminals. It continues the survey of Bierwirth and Meisel (2010) that covered the research up to 2009. Since then, there was a strong increase of activity observed in this research field resulting in more than 120 new publications. In this paper, we classify this new literature according to the features of models considered for berth allocation, quay crane scheduling and integrated approaches by using the classification schemes proposed in the preceding survey. Moreover, we identify trends in the field, we take a look at the methods that have been developed for solving new models, we discuss ways for evaluating models and algorithms, and, finally, we light up potential directions for future research.

A Study of Rescheduling Strategies for the Quay Crane Scheduling Problem under Random Disruptions

Providing a suitable answer to different types of unforeseen changes in optimization problems is one challenging goal. This paper addresses the Quay Crane Scheduling Problem under random disruptions, whose goal is to determine the sequences of transshipment operations performed by a set of quay cranes in order to load and unload containers onto/from a berthed container vessel. An evolutionary algorithm is used to find an initial solution of the problem with completely deterministic data, whereas several rescheduling strategies are integrated into a dynamism management system aimed at keeping a proper quality level after a random disruption. Computational experiments indicate that using knowledge about previous static problems can largely improve the performance of the implemented schedule.

A genetic algorithm heuristic for solving the quay crane scheduling problem with time windows

One of the most important operations in marine container terminals is quay crane scheduling. The quay crane scheduling problem (QCSP) involves scheduling groups of containers to be loaded and unloaded by each quay crane. It also requires addressing practical issues such as minimum spacing between quay cranes and precedence relationships between container groups. This study addresses the QCSP with one additional consideration: time availability of quay cranes. This problem is referred to as QCSP with time windows (QCSPTW) in the literature. This article discusses the genetic algorithm (GA) developed to solve the QCSPTW. It builds on a previously developed GA to solve the QCSP by the authors. The results of a large set of numerical experiments using benchmark instances highlight several key characteristics of the proposed solution approach: (i) the developed GA can provide near optimal solutions in a faster time for medium and large-sized instances (overall average gap is less than 3 per cent), and (ii) the developed GA leads to an improvement in the solution quality (lower vessel turnaround time) for instances with fragmented time windows (time windows that are broken up into two or more non-contiguous segments).

Integrated internal truck, yard crane and quay crane scheduling in a container terminal considering energy consumption

Container terminals mainly include three types of handling equipment, i.e., quay cranes (QCs), internal trucks (ITs) and yard cranes (YCs). Due to high cost of the handling equipment, container terminals can hardly purchase additional handling equipment. Therefore, the reasonable scheduling of these handling equipment, especially coordinated scheduling of the three types of handling equipment, plays an important role in the service level and energy-saving of container terminal. This paper addresses the problem of integrated QC scheduling, IT scheduling and YC scheduling. Firstly, this problem is formulated as a mixed integer programming model (MIP), where the objective is to minimize the total departure delay of all vessels and the total transportation energy consumption of all tasks. Furthermore, an integrated simulation-based optimization method is developed for solving the problem, where the simulation is designed for evaluation and optimization algorithm is designed for searching solution space. The optimization algorithm integrates genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, where the GA is used for global search and the PSO is used for local search. Finally, numerical experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can coordinate the scheduling of the three types of handling equipment and can realize the optimal trade-off between time-saving and energy-saving.

Quay crane scheduling with dual cycling

In this article, the dual cycling quay crane scheduling problem (D-QCSP) with hatches is addressed to minimize the operation cycles of quay cranes. The problem is decomposed into two sub-problems: the intra-group stage (sequencing stacks within each hatch) and the inter-group stage (scheduling all hatches). A new stack sequencing method is constructed for stacks of each hatch, which is modelled as a two-machine non-permutation flow shop scheduling problem. By removing inner gaps using left-shifting, the adapted hatch scheduling sub-problem is modelled as a two-machine grouped flow shop scheduling problem, which contains more precise processing times. A composite heuristic is proposed for the D-QCSP. Based on the derived lower bound, the heuristic is compared with the best existing heuristics on a large number of instances. Experimental results illustrate that the proposal outperforms the existing methods on all instances and dual cycling needs many fewer quay crane operating cycles than single cycling.

Integrated quay crane and yard truck scheduling for unloading inbound containers

To lower vessel turn time, it is crucial that the operations of quay cranes, yard trucks, and yard cranes are well coordinated. Most studies have sought to optimize each of these processes independently. Since the operations by quay cranes and yard trucks are highly interrelated it is necessary to develop and solve these operations in an integrated manner that reflects the characteristics of the marine container terminals. This study developed a mixed integer programming model for scheduling quay cranes and yard trucks jointly. The integrated model explicitly considered real-world operational constraints such as precedence relationships between containers, blocking, quay crane interference, and quay crane safety margin. To solve the integrated optimization model, a genetic algorithm (GA) combined with a greedy algorithm was developed. The results indicated that the solutions obtained from the integrated model are superior to those obtained from the non-integrated approach. The GA solutions demonstrated that the developed integrated model is solvable within reasonable time for an operational problem.

Yard crane scheduling in a container terminal for the trade-off between efficiency and energy consumption

Green transportation has recently been the focus of the transportation industry to sustain the development of global economy. Container terminals are key nodes in the global transportation network and energy-saving is a main goal for them. Yard crane (YC), as one type of handling equipment, plays an important role in the service efficiency and energy-saving of container terminals. However, traditional methods of YC scheduling solely aim to improve the efficiency of container terminals and do not refer to energy-saving. Therefore, it is imperative to seek an appropriate approach for YC scheduling that considers the trade-off between efficiency and energy consumption. In this paper, the YC scheduling problem is firstly converted into a vehicle routing problem with soft time windows (VRPSTW). This problem is formulated as a mixed integer programming (MIP) model, whose two objectives minimize the total completion delay of all task groups and the total energy consumption of all YCs. Subsequently, an integrated simulation optimization method is developed for solving the problem, where the simulation is designed for evaluating solutions and the optimization algorithm is designed for exploring the solution space. The optimization algorithm integrates the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm, where the GA is used for global search and the PSO is used for local search. Finally, computational experiments are conducted to validate the performance of the proposed method.

A note on a model for quay crane scheduling with non-crossing constraints

This article studies the quay crane scheduling problem with non-crossing constraints, which is an operational problem that arises in container terminals. An enhancement to a mixed integer programming model for the problem is proposed and a new class of valid inequalities is introduced. Computational results show the effectiveness of these enhancements in solving the problem to optimality.

A Lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem

Decisions on the quay crane assignment problem and the quay crane scheduling problem are typically made independently. However, the efficiency of container terminals can be increased when these decisions are made simultaneously due to the interrelation between quay crane assignment and scheduling. A mathematical formulation for the integrated quay crane assignment and scheduling problem (QCASP) is developed in this paper. Practical considerations are incorporated in the model, such as quay crane (QC) interference. A Lagrangian relaxation is proposed for the model. Feasible solutions are then obtained from the proposed heuristic. Computational results are provided for the proposed Lagrangian relaxation.

The Integrated Yard Truck and Yard Crane Scheduling and Storage Allocation Problem at Container Terminals

The storage block allocation, the yard truck and yard crane scheduling are three separate sub-problems in container terminals, playing an important role in the efficiency of port discharging operations. This paper proposes an integer programming model considering these three problems as a whole. The objective is to minimize the time when all the unloading operations have been completed and all containers have been stacked at storage block. A Local Sequence-Cut (LSC) method is developed to solve the problem.

Review on the Berth Allocation and Quay Cranes Assignment Problems in Container Terminal

In recent decade, containers become an important part of the world's economy. With the growth in offshore trade, problems about container and port are attention by research scholars in many countries. In the study on the problem in container ports, Berth Allocation and Quay Crane Scheduling problem are very important; optimization of the two problems can improve the efficient of container ports. In this paper, we describe and classify the main Berth Allocation Processes and Quay Crane Scheduling and present a survey of methods for their single optimization and integrate optimization.

The Integrated Berth and Quay Crane Scheduling Problem in Container Terminals

With the current development of the berth and quay crane in China, minimizing the total time of all ships stopping at the port, and maximizing the utilization rate of quay cranes to reduce the waiting time in the queue at the anchorage are the key to success in the field of container terminals. The objective of this paper is to minimize the total time of all stopped ships at the port and to maximize the operation efficiency of quay cranes. Compared with single berth and quay crane allocation, this paper analyzes the berth-quay crane as a whole, and an integer programming model with some constraints is built for this problem. Then the heuristic algorithm is used in this paper to optimize the problem and gain the solution. This paper provides a guide for practical operation.

Scheduling small number of quay cranes with non-interference constraint

Quay crane (QC) scheduling significantly affects the turn-around time of a container vessel, and it plays an important role in container terminal operation. Lee et al. (An approximation algorithm for quay crane scheduling with non-interference constraints in port container terminals, Presented at Tristan VI, Phuket, June 10–15, 2007) present a 2-approximation algorithm for QC scheduling problem with non-interference constraint. In this paper we revisit Lee’s heuristic for the scenario with small number of QCs, and prove that it is 4/3 and 5/3-approximation for the case with two QCs and the case with three QCs respectively.

An analytical framework for integrated maritime terminal scheduling problems with time windows

Container transport, an integral part of intercontinental trade, has steadily increased over the past few decades. The productivity of such a system, in part, hinges on the efficient allocation of terminal resources such that the container transit time is minimized. This study provides an analytical framework, which entails efficient scheduling of quay and yard cranes, to minimize the time spent by containers at a terminal. A mixed-integer programming model is developed to capture the two-stage multi-processor characteristic of the problem, where each crane has specific time window availability. A genetic algorithm equipped with a novel decoding procedure is developed. The mixed-integer model is tested on a number of problem instances of varying sizes to gain managerial insights.

Erratum to: Crane scheduling for opportunistic remarshaling of containers in an automated stacking yard

Erratum to: Crane scheduling for opportunistic remarshaling of containers in an automated stacking yard

An Integrated Quay Crane Assignment and Scheduling Problem

As maritime container transport is developing rapidly, the need arises for efficient operations at container terminals. One of the most important determinants of container handling efficiency is the productivity of quay cranes, which are responsible for unloading and loading operations for container vessels. For this reason, the Quay Crane Assignment Problem (QCAP) and the Quay Crane Scheduling Problem (QCSP) have received increasing attention in the literature and the present paper deals with the integration of these interrelated problems. A formulation is developed for the Quay Crane Assignment and Scheduling Problem (QCASP), which accounts for crane positioning conditions and a Genetic Algorithm (GA) is developed to solve the QCASP. Both the model formulation and the solution methodology are presented in detail and computational analysis is conducted in order to evaluate the performance of the proposed GA. The results obtained from the GA are compared with the results from an exact technique, thus providing complete information about the performance of the heuristic in terms of solution quality.

Scheduling multiple factory cranes on a common track

A heuristic algorithm is presented for scheduling the movement of multiple factory cranes mounted on a common track. The cranes must complete a sequence of tasks at locations along the track without crossing paths, while adhering as closely as possible to a factory production schedule. The algorithm creates a decision tree of possible states of the crane system, which evolves over time as tasks are assigned and sequenced. By identifying and removing inferior states from the tree, the algorithm efficiently generates provably optimal or near-optimal crane schedules, depending on the complexity of the problem instance.

A Polynomially Solvable Case for Solving Crane Scheduling Problem in Batch Annealing Process

This paper investigates a special case for scheduling of the multi-crane operations in batch annealing process in an iron and steel enterprise so that the completion time of the last annealed coil (makespan) is minimized. Additional no-delay and no-buffer constraints for taking fully advantage of machines are considered. No-delay constraints for machine unloading means technological requires fixed heating time and cooling time that once the heating (cooling) is completed, the furnace (cooler) must be unloaded immediately without any delay by crane. No-buffer constraints for machine unloading means the time gap between the unloading time of one machine for one job and its start time on the next job is exactly equal to the corresponding transportation time. We prove that this problem can be solved optimally in polynomial time where the starting time and ending time of every possible crane movement are formulated.