Integrated scheduling of a container handling system with simultaneous loading and discharging operations

The integrated scheduling of container handling systems aims to optimize the coordination and overall utilization of all handling equipment, so as to minimize the makespan of a given set of container tasks. A modified disjunctive graph is proposed and a mixed 0–1 programming model is formulated. A heuristic algorithm is presented, in which the original problem is divided into two subproblems. In the first subproblem, contiguous bay crane operations are applied to obtain a good quay crane schedule. In the second subproblem, proper internal truck and yard crane schedules are generated to match the given quay crane schedule. Furthermore, a genetic algorithm based on the heuristic algorithm is developed to search for better solutions. The computational results show that the proposed algorithm can efficiently find high-quality solutions. They also indicate the effectiveness of simultaneous loading and discharging operations compared with separate ones.     

A workload balancing genetic algorithm for the quay crane scheduling problem

This paper proposes a novel genetic algorithm to deal with the quay crane scheduling problem (QCSP), which is known to be one of the most critical tasks in terminal operations because its efficiency and the quality of the schedule directly influence the productivity of the terminal. QCSP has been studied intensively in recent years. Algorithms in this field are concerned in the solution quality obtained and the required computational time. As QCSP is known to be NP-hard, heuristic approaches are widely adopted. The genetic algorithm proposed is constructed with a novel workload balancing heuristics, which is capable of considering the loading conditions of different quay cranes (QCs) during the reassignment of task-to-QC. The idea is modelled as a fuzzy logic controller to guide the mutation rate and mutation mechanism of the genetic algorithm. As a result, the proposed algorithm does not require any predefined mutation rate. Meanwhile, the genetic algorithm can more adequately reassign tasks to QCs according to the QCs’ loading condition throughout the evolution. The proposed algorithm has been tested with the well-known benchmark problem sets in this field and produces some new best solutions in a much shorter computational time.     

Joint planning for yard storage space and home berths in container terminals

Yard planning is essential for efficient operations in container terminals, especially for ports with limited storage space. To improve the utilisation of space and the efficiency of container handling in a terminal, operators require flexible yard space planning strategies to manage job workloads and yard-to-berth transportation costs. In previous studies, the inter-related decision making process for berths and yards has normally been studied separately, and yard planning models are designed with deterministic inputs of berths, where many existing terminals are operating with sub-optimal efficiency. In this paper, we consider different policies of the scattered stacking strategy for export containers and analyse the entire cycle of container handling from yard block to home berth, where the home berth is a quay section which includes the preferred berthing place of a vessel upon its arrival. We analyse three stacking policies, namely exclusive, cross-area, and buffer-area stacking policies, and formulate the planning problem for yard storage and related home berths into MILP (mixed integer linear programming) models. Solutions are obtained with a two-stage approach method. The numerical analysis demonstrates that the workload imbalance can be significantly reduced by implementing either the cross-area or buffer-area container stacking policy.     

Evaluation of a hybrid genetic tabu search framework on job shop scheduling benchmark problems

It has been well established that to find an optimal or near-optimal solution to job shop scheduling problems (JSSPs), which are NP-hard, one needs to harness different features of many techniques, such as genetic algorithms (GAs) and tabu search (TS). In this paper, we report usage of such a framework which exploits the diversified global search and the intensified local search capabilities of GA and TS, respectively. The system takes its input directly from the process information in contrast to having a problem-specific input format, making it versatile in dealing with different JSSP. This framework has been successfully implemented to solve industrial JSSPs. In this paper, we evaluate its suitability by applying it on a set of well-known job shop benchmark problems. The results have been variable. The system did find optimal solutions for moderately hard benchmark problems (40 out of 43 problems tested). This performance is similar to, and in some cases better than, comparable systems, which also establishes the versatility of the system. However for the harder benchmark problems it had difficulty in finding a new improved solution. We analyse the possible reasons for such a performance.     

Quay crane scheduling in container terminals

The problem of scheduling identical quay cranes moving along a common linear rail to handle containers for a ship is studied. The ship has a number of container-stacking compartments called bays, and only one quay crane can work on a bay at the same time. The objective of the scheduling problem is to find the work schedule for each quay crane which minimizes the ship’s stay time in port. Finding the optimal solution of the scheduling problem is computationally intractable and a heuristic is proposed to solve it. The heuristic first decomposes the difficult multi-crane scheduling problem into easier subproblems by partitioning the ship into a set of non-overlapping zones. The resulting subproblems for each possible partition are solved optimally by a simple rule. An effective algorithm for finding tight lower bounds is developed by modifying and enhancing an effective lower-bounding procedure proposed in the literature. Computational experiments were carried out to evaluate the performance of the heuristic on a set of test problems randomly generated based on typical terminal operations data. The computational results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 4.8% above their lower bounds.     

Synchronization of yard truck scheduling and storage allocation in container terminals

Yard truck scheduling and storage allocation, as two separate subproblems in port operations, have been extensively studied in the past decades. However, from the operational point of view, they are highly interdependent. This article proposes an integer programming model in which yard truck scheduling and storage allocation problems are formulated as a whole for heterogeneous import containers. Different stacking times at yard blocks is modelled as well. The objective of the proposed model is to reduce the congestion and waiting time of yard trucks in the terminal so as to decrease the makespan of discharging containers. Owing to the inherent computational complexity, a genetic algorithm and a greedy heuristic algorithm have been designed. Computational experiments show that the proposed genetic algorithm and greedy algorithm are both effective in solving the studied problem.     

Modelling a resilient yard template under storage demand fluctuations in a container terminal

This article investigates the generation of a resilient yard template, which has the property of resilience under storage demand fluctuations. A stochastic programming model is formulated aiming at minimizing the risk of containers without available storage slots being assigned in the designated area. Furthermore, a corresponding particle swarm optimization algorithm is proposed for solving the model. Finally, numerical experiments are conducted to verify the effectiveness of the proposed model and solution approaches.     

An effective heuristic for scheduling a yard crane to handle jobs with different ready times

In land-constrained port container terminals, yard cranes are commonly used for handling containers in a container yard to load containers onto or unload containers from trucks. However, yard cranes are bulky, slow and need to move frequently between their work locations. As it is common that the container flow in a terminal is bottlenecked by yard crane operations, effective work schedules of yard cranes are needed to increase the terminal’s throughput. This article studies the problem of scheduling a yard crane to perform a given set of container handling jobs with different ready times. The objective is to minimize the sum of job waiting times. It is noted that the scheduling problem is NP-complete. This research develops a heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. The performance of the heuristic is evaluated by a set of test problems generated on the basis of real-life terminal operations data. Indeed, the computational results show that the proposed heuristic can find effective solutions for the scheduling problem.     

Optimizing the landside operation of a container terminal

This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three-stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short-term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most 8% above a lower bound on optimal RMG utilization. Research supported by Patrick Technology and Systems, the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), and the German Research Foundation Research Center Mathematics for key technologies: Modelling, simulation, and optimization of real-world processes (Matheon).     

Development and simulation analysis of real-time yard crane control systems for seaport container transshipment terminals

As more and more container terminals open up all over the world, terminal operators are discovering that they must increase quay crane work rates to remain competitive. In this paper, we develop a real-time yard crane control system and show that a terminal’s long-run average quay crane rate depends on the portion of this system that dispatches yard cranes in the storage area in real time. Several real-time yard crane dispatching systems are evaluated by a fully-integrated, discrete event simulation model of a pure transshipment terminal that is designed to reproduce the multi-objective, stochastic, real-time environment at an RTGC-based, multiple-berth facility. Results indicate that yard cranes should prioritize the retrieval of containers from the stacks, rather than the storage of containers into stacks. Also, the yard crane dispatching system should not only consider the trucks already waiting for service in the yard, but also the trucks that are heading towards the yard. The experiments provide the first direct connection in the literature between real-time yard crane control systems and long-run performance at a seaport container terminal. We also make a qualitative comparison between rule-based and look-ahead yard crane dispatching schemes, and discuss deadlocking issues in detail.     

Disruption recovery model for berth and quay crane scheduling in container terminals

This article addresses the problem of recovering berth and quay crane (QC) schedules in container terminals when disruptions occur after a subset of operations has been processed. Firstly, models for simultaneous optimization of berth and QC schedules are developed. Then, two strategies, namely, QC rescheduling strategy and berth reallocation strategy are proposed to tackle disruptions and recover the berth and QC schedule, and models for the two strategies are developed respectively. To solve the disruption recovery models, algorithms based on local rescheduling and tabu search are designed. Finally, numerical experiments are provided to illustrate the validity of the proposed model and algorithms.     

Scheduling operations of a rail crane and container deliveries between rail and port terminals

This article addresses the problem of scheduling container transfer operations in rail terminals. The overall problem can be divided into three smaller problems: constructing a dual-cycle delivery task by matching inbound and outbound containers; determining parking positions for trucks; and sequencing the delivery tasks for transfer by the rail crane. This article provides a mathematical model to obtain the optimal solutions to these problems, and suggests genetic and heuristic algorithms to reduce computational time when solving larger problems. Numerical experiments are conducted to validate the performance of the suggested heuristic algorithms.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

A modified generalized extremal optimization algorithm for the quay crane scheduling problem with interference constraints

The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.     

Scheduling the operations of a double-load crane in slab yards

This paper studies a double-load crane scheduling problem (DLCSP) in steel slab yards. A slab yard stores slabs in stacks. To prepare for use in production, some slabs need to be moved from one place to another. These movement tasks are performed by a double-load crane which can hold up to two slabs simultaneously. Given a set of tasks and possibly precedence relationships among them, the scheduling problem is to allocate the tasks to double-load operations and determine the schedule for the crane to perform the tasks so as to minimise the makespan. The problem is first formulated as a mixed integer linear programming (MILP) model with variables representing the order of tasks. Based on properties of the problem, it is then reformulated from a crane operation perspective. Computational experiments are carried out on practical data collected from a steel company. The results show that both models can solve practical sized problems optimally, with the second model being more efficient.     

A decision-tree stacking heuristic minimising the expected number of reshuffles at a container terminal

Reshuffling containers, one of the daily operations at a container terminal, is time consuming and increases a ship’s berthing time. We propose a decision-tree heuristic to minimise the expected number of reshuffles when arriving containers should be stacked in a block of containers with an arbitrary number of piles. The heuristic algorithm uses the optimal solutions of a stochastic dynamic programming model. Since the total number of states of the dynamic programming model increases exponentially, the model can only solve small-scale problems in a reasonable time. To solve large-scale problems, the heuristic uses the results of the exact model for small-scale problems to generate generalised decision trees. These trees can be used to solve problems with a realistic number of piles. The numerical experiments show the effectiveness of the algorithm. For small-scale problems, the trees can quickly make optimal decisions. For large-scale problems, the decision-tree heuristic significantly outperforms stacking policies commonly used in practice. Using the decision trees, we can compare the performance of a shared-stacking policy, which allows containers of multiple ships to be stacked on top of each other, with a dedicated-stacking policy. Shared-stacking appears to outperform dedicated-stacking.     

港口集装箱码头轮胎式龙门吊优化调度研究

随着贸易全球化的到来,集装箱运输业飞速发展,港口集装箱码头受到越来越多的重视。轮胎式龙门吊体积大,作业效率低,该环节 已经成为码头作业的瓶颈。提出了轮胎式龙门吊优化调度混合整数规划模型,研究了定量作业条件下的龙门吊优化调度问题,通过实际案例分 析为码头管理者提供决策支持。     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

Assembly block location and sequencing for flat transporters in a planar storage yard of shipyards

Assembly block location and sequencing are two important and related problems for scheduling a flat transporter to perform block storage and transport within a planar storage yard in shipyards. They affect not only the transport efficiency of storage yards but also the productivity and coordination of related workshops. This paper addresses the block location and sequencing at the same time with the purpose of reducing unproductive moves. A heuristic approach is proposed based on a sequencing strategy, a location selecting procedure for the incoming blocks and a policy for relocating blocks. A tabu search algorithm is proposed to improve the solution. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed approach.     

A tabu search algorithm for simultaneous machine/AGV scheduling problem

Machines and automated guided vehicles (AGVs) scheduling problems are two essential issues that need to be addressed for the efficiency of the overall production system. The purpose of this paper is to study the simultaneous scheduling problem of machines and AGVs in a flexible manufacturing system (FMS) since the global optimum cannot be reached by considering each of them individually. In this paper, a mixed integer linear programming (MILP) model is developed with the objective of makespan minimisation. The MILP model consists of the following two constraint sets: machines and AGVs scheduling sub-problems. As both sub-problems are known to be NP-hard, a heuristic algorithm based on tabu search (TS) is proposed to get optimal or near to optimal solution for large-size problems within reasonable computation time. The proposed algorithm includes a novel two-dimensional solution representation and the generation of two neighbour solutions, which are alternately and iteratively applied to improve solutions. Moreover, an improved lower bound calculation method is introduced for the large-size problems. Computational results show the superior performance of the TS algorithm for the simultaneous scheduling problem.