A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal

The scheduling problem in a container terminal is characterized by the coordination of different types of equipment. In this paper, we present an integrated model to schedule the equipment. The objective is to minimize the makespan, or the time it takes to serve a given set of ships. The problem is formulated as a Hybrid Flow Shop Scheduling problem with precedence and Blocking constraints (HFSS-B). A tabu search algorithm is proposed to solve this problem. Certain mechanisms are developed and introduced into the algorithm to assure its quality and efficiency. The performance of the tabu search algorithm is analyzed from the computational point of view.     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

Discrete time model and algorithms for container yard crane scheduling

Container terminal (CT) operations are often bottlenecked by slow YC (yard crane) movements. PM (prime mover) queues in front of the YCs are common. Hence, efficient YC scheduling to reduce the PM waiting time is critical in increasing a CT’s throughput. We develop an efficient model for YC scheduling by taking into account realistic operational constraints such as inter-crane interference, fixed YC separation distances and simultaneous container storage/retrievals. Among them, only inter-crane interference has ever been considered in the literature. The model requires far fewer integer variables than the literature by using bi-index decision variables. We show how the model can be solved quickly using heuristics and rolling-horizon algorithm, yielding close to optimal solutions in seconds. The solution quality and solution time are both better than the literature even with additional constraints considered. The proposed formulations and algorithms can be extended to other problems with time windows and space constraints.     

Integrated scheduling of handling equipment at automated container terminals

To improve the productivities of an automated container terminal, it is important to schedule different types of handling equipment in an integrated way. A mixed-integer programming model, which considers various constraints related to the integrated operations between different types of handling equipment, is formulated. A heuristic algorithm, called multi-layer genetic algorithm (MLGA) is developed with a view to overcome the computation difficulty for solving the mathematical model. A numerical experimentation is carried out in order to evaluate the performance of the algorithm.     

Modeling and solution of the joint quay crane and truck scheduling problem

This paper addresses the joint quay crane and truck scheduling problem at a container terminal, considering the coordination of the two types of equipment to reduce their idle time between performing two successive tasks. For the unidirectional flow problem with only inbound containers, in which trucks go back to quayside without carrying outbound containers, a mixed-integer linear programming model is formulated to minimize the makespan. Several valid inequalities and a property of the optimal solutions for the problem are derived, and two lower bounds are obtained. An improved Particle Swarm Optimization (PSO) algorithm is then developed to solve this problem, in which a new velocity updating strategy is incorporated to improve the solution quality. For small sized problems, we have compared the solutions of the proposed PSO with the optimal solutions obtained by solving the model using the CPLEX software. The solutions of the proposed PSO for large sized problems are compared to the two lower bounds because CPLEX could not solve the problem optimally in reasonable time. For the more general situation considering both inbound and outbound containers, trucks may go back to quayside with outbound containers. The model is extended to handle this problem with bidirectional flow. Experiment shows that the improved PSO proposed in this paper is efficient to solve the joint quay crane and truck scheduling problem.     

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

Due to the variety of technical equipments and terminal layouts, research has produced a multitude of optimization models for seaside operations planning in container terminals. To provide a support in modeling problem characteristics and in suggesting applicable algorithms this paper reviews the relevant literature. For this purpose new classification schemes for berth allocation problems and quay crane scheduling problems are developed. Particular focus is put on integrated solution approaches which receive increasing importance for the terminal management.     

Benefits of a truck appointment system on the service quality of inland transport modes at a multimodal container terminal

Container terminals pay more and more attention to the service quality of inland transport modes such as tucks, trains and barges. Truck appointment systems are a common approach to reduce truck turnaround times. This paper provides a tool to use the truck appointment system to increase not only the service quality of trucks, but also of trains, barges and vessels. We propose a mixed integer linear programming model to determine the number of appointments to offer with regard to the overall workload and the available handling capacity. The model is based on a network flow representation of the terminal and aims to minimize overall delays at the terminal. It simultaneously determines the number of truck appointments to offer and allocates straddle carriers to different transport modes. Numerical experiments, conducted on actual data, quantify the benefits of this combined solution approach. Discrete-event simulation validates the results obtained by the optimization model in a stochastic environment.     

An integrated approach for scheduling health care activities in a hospital

To effectively utilise hospital beds, operating rooms (OR) and other treatment spaces, it is necessary to precisely plan patient admissions and treatments in advance. As patient treatment and recovery times are unequal and uncertain, this is not easy. In response, a sophisticated flexible job-shop scheduling (FJSS) model is introduced, whereby patients, beds, hospital wards and health care activities are respectively treated as jobs, single machines, parallel machines and operations. Our approach is novel because an entire hospital is describable and schedulable in one integrated approach. The scheduling model can be used to recompute timings after deviations, delays, postponements and cancellations. It also includes advanced conditions such as activity and machine setup times, transfer times between activities, blocking limitations and no wait conditions, timing and occupancy restrictions, buffering for robustness, fixed activities and sequences, release times and strict deadlines. To solve the FJSS problem, constructive algorithms and hybrid meta-heuristics have been developed. Our numerical testing shows that the proposed solution techniques are capable of solving problems of real world size. This outcome further highlights the value of the scheduling model and its potential for integration into actual hospital information systems.     

Novel constraints satisfaction models for optimization problems in container terminals

The growth of containerization and transporting goods in containers has created many problems for ports. In this paper, we systematically survey a literature over problems in container terminals. The operations that take place in container terminals are described and then the problems are classified into five scheduling decisions. For each of the decisions, an overview of the literature is presented. After that, each of the decisions is formulated as Constraint Satisfaction and Optimization Problems (CSOPs). The literature also includes simulations and performance in container terminals. To evaluate any solution methods to the decisions and to measure its efficiency, several indicators are suggested.     

Transport operations in container terminals: Literature overview,trends, research directions and classification scheme

Internal transport operations connect the seaside, yard side, and landside processes at container terminals. This paper presents an in-depth overview of transport operations and the material handling equipment used, highlights current industry trends and developments, and proposes a new classification scheme for transport operations and scientific journal papers published up to 2012. The paper also discusses and challenges current operational paradigms of transport operations. Lastly, the paper identifies new avenues for academic research based on current trends and developments in the container terminal industry.     

Storage space allocation models for inbound containers in an automatic container terminal

This paper studies the problem of improving the operations efficiency for retrieving inbound containers in a modern automatic container terminal. In the terminal, when an external truck arrives to collect a container stored in a specific container block, it waits at one end of the block where an automatic stack crane will retrieve the container and deliver it to the truck. With the aim of reducing the expected external truck waiting time which is determined by how the containers are stored in a block, we propose two correlated approaches for the operations efficiency improvement, (1) by designing an optimized block space allocation to store the inbound containers after they are discharged from vessels, and (2) by conducting overnight re-marshaling processes to re-organize the block space allocation after some containers are retrieved. For the block space allocation problem, we consider three optimization models under different strategies of storing containers, namely, a non-segregation model, a single-period segregation model, and a multiple-period segregation model. Optimal solution methods are proposed for all three models. For the re-marshaling problem with a given time limit, we find that the problem is NP-hard and develop a heuristic algorithm to solve the problem. We then use simulation to validate our models and solution approaches. Simulation results reveal important managerial insights such as the advantage of the multiple-period segregation over the myopic single-period segregation, the possibility of overflow of the segregation model, and the benefit of re-marshaling.     

A note on deriving decision rules to locate export containers in container yards

A counterexample is given to illustrate that a key model transformation in the paper entitled “Deriving decision rules to locate export containers in container yards” [Kim, K.H., Park, Y.M., Ryu, K.-R., 2000. Deriving decision rules to locate export containers in container yards. European Journal of Operational Research 124 (1), 89–101] is not correct. Then, the errors in the original derivation of the model transformation are analyzed, and the correct form is presented.     

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.     

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.     

The coordination of transportation and batching scheduling

We study a coordinated scheduling problem of production and transportation in which each job is transported to a single batching machine for further processing. There are m vehicles that transport jobs from the holding area to the batching machine. Each vehicle can transport only one job at a time. The batching machine can process a batch of jobs simultaneously where there is an upper limit on the batch size. Each batch to be processed occurs a processing cost. The problem is to find a joint schedule of production and transportation such that the sum of the total completion time and the total processing cost is optimized. For a special case of the problem where the job assignment to the vehicles is predetermined, we provide a polynomial time algorithm. For the general problem, we prove that it is NP-hard (in the ordinary sense) and present a pseudo-polynomial time algorithm. A fully polynomial time approximation scheme for the general problem is obtained by converting an especially designed pseudo-polynomial dynamic programming algorithm.     

Storage yard operations in container terminals: Literature overview,trends, and research directions

Inbound and outbound containers are temporarily stored in the storage yard at container terminals. A combination of container demand increase and storage yard capacity scarcity create complex operational challenges for storage yard managers. This paper presents an in-depth overview of storage yard operations, including the material handling equipment used, and highlights current industry trends and developments. A classification scheme for storage yard operations is proposed and used to classify scientific journal papers published between 2004 and 2012. The paper also discusses and challenges the current operational paradigms on storage yard operations. Lastly, the paper identifies new avenues for academic research based on current trends and developments in the container terminal industry.     

Group and individual heterogeneity in a stochastic frontier model: Container terminal operators

Container ports are a major component of international trade and the global supply chain. Hence, the improvement of port efficiency can have a significant impact on the wider maritime economy. This paper deconstructs a representation in the existing literature that neglects the heterogeneity of individual and group-specific terminal operators. In its place, we present a hierarchical model to make a connection between efficiency and terminal operator group characteristics. The paper develops a stochastic frontier model that controls not only individual heterogeneity but also group-specific variations. The model decomposes the total stochastic derivation from the frontier into inefficiency, individual heterogeneity, group-specific variations, and noise components, with the estimation being performed using Markov chain Monte Carlo simulations. The validity of the model is tested with a panel of container terminal operator data from 1997-2004. Our findings show that terminal operator groups are important in promoting terminal efficiency at the global level, and that the operators with stevedore backgrounds show a higher efficiency than carriers.     

On maximizing the profit of a satellite launcher: Selecting and scheduling tasks with time windows and setups

At regular times, a satellite launcher company has to plan the use of its launcher to get the maximum profit. In a more formal way, the problem consists of selecting and scheduling a subset of unit-length jobs constrained by capacitated time slots so that the overall cost is a minimum. The data associated with each job are its weight, its time-window and its expected gain when it is performed. With each time slot are associated a setup cost and a capacity. The setup cost of a time slot is due when this time-slot is used to perform at least one job. Moreover the total weight of all jobs scheduled within a time slot is at most the time slot capacity. We first show that the general problem is hard and provide some easy special cases. We then propose a first dynamic-programming polynomial-time algorithm for the special case with unit weights. A second and more efficient dynamic programming algorithm is also provided for the special case of unit weights and agreeable time windows. This last algorithm is finally improved for the special case of equal gains.     

Batch scheduling and common due-date assignment on a single machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.     

工件的运输和继列分批加工协作排序问题

近年来,工件的运输和加工协作排序问题在物流和供应链管理领域得到广泛关注. 讨论了先用 $\ m$ 台车辆将工件从等待区域运输到继列分批处理机处, 再进行分批加工的协作排序问题, 加工一批工件需要支付一定的费用, 目标为最小化工件的总完工时间与批的加工费用之和. 在工件的加工时间都相等的情况下, 如果工件运输方案确定, 给出了多项式时间的动态规划算法; 如果工件运输方案不确定, 证明了该问题是{\, NP}-难的, 给出了车辆返回时间 $\ t=0$ 时, 最差性能比等于 $\ 2-\frac{1}{m}$ 的近似算法.