This paper studies a new automated container terminal (ACT) system which utilizes multistory frame bridges and rail-mounted trolleys to transport containers between the quay and the yard. Beside typical ACT systems use trucks or automated guided vehicles for transporting containers between quay cranes and yard cranes, the new design uses three types of handling machines, namely, ground trolleys (GTs), transfer platforms (TPs), and frame trolleys (FTs). These three types of handling machines collaborate with one another to transport containers. This study decomposes the system into several subsystems. Each subsystem has one TP and several FTs and GTs dedicated to this TP. Then, a Markov chain model is developed to analyze the throughput of TPs. At last, the performance of the new ACT system is estimated. Sensitivity analyzes the numbers, and the processing rates of trolleys are conducted through the numeric experiments.
Port operators face challenges in handling large number of containers which growing fast when global trade increases. At the same time, it is difficult for terminal to expand its capacity fast enough due to insufficient land space, availability of initial investment, and environmental concerns [
In many developed countries where labor cost is very high, we are seeing an increasing use of Automated Container Terminal (ACT) by port operators. For example, rail-mounted gantry cranes (RMGCs) are being used at the Hong Kong International Terminal (HIT) in Hong Kong. Automated stacking cranes (ASCs) are used at the European Combined of Terminal (ECT) in Rotterdam of the Netherlands. It was reported by the port operators that the use of ACT (e.g., Hong Kong International Terminal, Europe Container Terminal, Container Terminal Altenwerder, Thames port, Patrick Terminal, etc.) has helped them to contain direct cost and increase productivity. In most of ACTs, blocks are laid out vertically to the quay when yard cranes are used as the main handling machines in the yard. This layout has benefit from separating the area for seaside operations from land side operations. So, port operators can concentrate on controlling the automatic traffic of different machines for loading and unloading operations while the land side operation is almost impossible to be automated. However, under this yard layout, as the yard cranes need to perform the round-trip travel in a block, the travel time of yard cranes would affect the terminal productivity. In addition, in order to control Automatic Guided Vehicles (AGVs) efficiently, it is necessary to apply advanced operation technologies as well as the high-end hardware technologies.
Recently, Shanghai Zhenhua Port Machinery Company (ZPMC) introduced a new design of ACT which utilizes rail-mounted frame trolleys (FTs) and ground trolleys (GTs) to transport containers in quay and yard side, respectively. Figure
The configuration of the frame bridge based ACT.
FB-ACT has 4 handovers to deliver a container between vessels and yard, which are between quay crane (QC) and FT, FT and TP, TP and GT, GT and yard crane (YC). Each handover will take certain time to transfer a container from one machine to another. The time includes idle/waiting and processing time. However, in the traditional container terminal, there are only two handovers: one is between QC and truck; another is between truck and YC. The increased number of handovers in FB-ACT may decrease the performance of the system.
This study aims to develop a mathematical model for estimating the performance of an FB-ACT in order to assist the decision making of terminal operators who are considering automation as a solution. We try to answer these questions: what is the performance of this new design system with 2 additional handovers between trolleys and TPs? And how does it be affected by certain parameters, such as the number of the trolleys? So that port operators would estimate how many resources are required to achieve a desirable performance level such as annual containers throughput.
The remainder of this paper is organized as follows. Section
FB-ACT introduces a lot of challenges and opportunities for port operators. However, existing research efforts have been devoted to the conventional or AGV-based terminals. For the conventional terminals, Kim et al. recently proposed some analytical methodologies for optimizing the layout design [
The FB-ACT system can be described as a closed-loop material handling system since the three types of machines transport container with one another as described in Section
Recently, Zhen et al. also studied the FB-ACT system [
In this paper, we also divide the whole system into several subsystems. However, we divide the system according to the number of TP. And each subsystem has two closed loops for trolleys and is connected by one TP. Instead of an M/M/c queuing system, we use a Markov chain model to analyze the performance of each subsystem. We also focus on the impact of throughput of TP on the whole system’s performance.
In this paper, we take the same assumptions as mentioned in Zhen et al.’s study [ The pickup and delivery locations of these activities follow the uniform distribution along the quay in horizontal directions and along a side of a block in vertical directions, respectively. This assumption is commonly made in some analytical studies on container terminals [ The number of TPs is the same to the number of blocks, which means a TP is dedicated to a block during a relatively long period. It is also assumed that FTs are dedicated to a TP during a relatively long period. The handling operation of quay cranes (or yard cranes) is represented as the average handling and waiting time of quay cranes (or yard cranes) which is denoted by
Let
In order to study the performance of the sub system, first of all, the behaviors of the trolleys are analyzed. There are two types of operation cycles related to FTs and GTs, respectively, for loading and unloading activities. Those two types of cycles are linked up by TPs as in Figure
Model for the single TP system.
As TP is the machine which transfers the container between a GT and an FT, this study first analyzes the performance of a TP which is dedicated to a block and serving the constant numbers of FTs and GTs. We introduce a two-loop closed line as drawn in Figure
Figure
The handling and transportation activities are performed by three machines proposed in the network model. The unloading operation, for example, can be described by using the network model terms as follows: At first, an FT moves to QS to receive a container. The container is loaded onto the FT by
This system includes three machines and forms two closed loops with finite numbers of trolleys. In the following sections, an analytical model based on the Markov chain is developed to estimate the throughput of the single TP system.
In this section, we analyze the two closed-loop systems as a Markov chain in which the containers are transferred from
Due to the fact that the total number of FTs is
Set
Transition rates of the system form
Event | Condition |
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A FT moves a container from |
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This section provides a systematic way to estimate the throughput of a TP and its relevant analyses including the impact of the delay rates of trolleys and the numbers of trolleys on the throughput of a TP.
With
When there is one FT and one GT in the single TP system, the system states are
Let
Here,
In order to analyze the impact of the delay rates of trolleys (
Throughput of TP with different delay rates of trolleys and the processing rate of TP.
Case |
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1 | 30 | 20 | 60 | 12.7 |
1 | 30 | 25 | 60 | 14.1 |
1 | 30 | 30 | 60 | 15.0 |
1 | 30 | 35 | 60 | 15.7 |
1 | 30 | 40 | 60 | 16.1 |
2 | 30 | 30 | 50 | 13.9 |
2 | 30 | 30 | 55 | 14.5 |
2 | 30 | 30 | 60 | 15.0 |
2 | 30 | 30 | 65 | 15.4 |
2 | 30 | 30 | 70 | 15.8 |
3 | 20 | 30 | 60 | 12.7 |
3 | 25 | 30 | 60 | 14.1 |
3 | 30 | 30 | 60 | 15.0 |
3 | 35 | 30 | 60 | 15.7 |
3 | 40 | 30 | 60 | 16.1 |
In order to further analyze the impact of
Throughput of TP when
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20 | 40 | 60 | 13.3 |
22 | 38 | 60 | 13.9 |
24 | 36 | 60 | 14.4 |
26 | 34 | 60 | 14.7 |
28 | 32 | 60 | 14.9 |
30 | 30 | 60 | 15.0 |
32 | 28 | 60 | 14.9 |
34 | 26 | 60 | 14.7 |
36 | 24 | 60 | 14.4 |
38 | 22 | 60 | 13.9 |
40 | 20 | 60 | 13.3 |
In Section
Under the given quay length denoted by
Tables
Results of sensitivity analysis on different quay length.
Quay length (meters) | Expected number of blocks | Number of FTs per TP | Number of GTs per TP | Terminal throughput (containers/hour) |
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300 | 4 | 1 | 1 | 51.0 |
600 | 8 | 1 | 1 | 101.9 |
900 | 12 | 1 | 1 | 152.9 |
1200 | 16 | 1 | 1 | 203.9 |
Results of sensitivity analysis on different levels of resource requirement.
Quay length (meters) | Expected number of blocks | Number of FTs per TP | Number of GTs per TP | Terminal throughput (containers/hour) |
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900 | 12 | 1 | 1 | 152.9 |
900 | 12 | 2 | 1 | 168.4 |
900 | 12 | 3 | 1 | 169.4 |
900 | 12 | 1 | 2 | 205.3 |
900 | 12 | 2 | 2 | 269.3 |
900 | 12 | 3 | 2 | 279.1 |
900 | 12 | 1 | 3 | 214.8 |
900 | 12 | 2 | 3 | 308.6 |
900 | 12 | 3 | 3 | 331.4 |
The results demonstrate the follows. (1) the terminal throughput increases as the quay length increases. In the same manner, (2) the throughput of system increase as the number of trolleys per TP increases. However, increasing rate is not proportional to the numbers of trolleys. For example, the terminal throughput under the strategy {two FTs, two GTs} is less than the double of the terminal throughput under the strategy {one FT, one GT}. (3) The number of GTs affects the terminal throughput rather than the number of FTs. The reason lies that the delay rate of a GT is smaller than that of an FT. (4) the terminal throughput is influenced by the number of TPs rather than the number of QCs. Suppose that the expected number of QCs is three per berth and the berth length is 300 meter as they are typically known in a conventional container terminal. The estimate terminal throughput is less than the throughput calculated by multiplying the number of QCs and the processing rate of QS (the delay rate of an FT). The results underpin the underlying conjecture of this study in which the TPs are bottlenecks for the operation processes of container flows in FB-ACTs instead of QCs.
This paper introduces a new type of ACT system and makes an explorative study to identify the challenges for the FB-ACT system. It is assumed that a TP is dedicated to a block and the system consists of several single TP systems which serve certain numbers of FTs and GTs. A Markov chain model is developed to analyze the performance of a single TP system in terms of the throughput of a TP. This study further analyzed the number of resources and the terminal configurations by using the developed Markov model. The results show that the throughput of TP increases as its processing rates or the delay rates of the trolleys at quay side and yard side increase. In order to achieve the maximum throughput of TP, the port operator should balance the arriving rate of FTs and GTs by optimizing the traveling speed and workload of FTs and GTs. The terminal throughput increases as the quay length increases or the number of trolleys increases. However, the increasing rate is not proportional to the numbers of trolleys per TP.
This study simplifies the system under the assumptions that there are enough numbers of QCs and YCs. In the future study, it may be necessary to consider the performance of this new system under the certain numbers of QCs and YCs. Different dispatching strategies among FTs, TPs, and GTs are needed to be analyzed. Moreover, uncertain factors in the port operations in ACTs will be investigated in the future [
This research is supported by the National Natural Science Foundation of China (no. 71201099, no. 71101090), Shanghai Pujiang Program (no. 13PJC066), the Ministry of Transport Research Projects (no. 2012-329-810-180), Doctoral Fund of the Ministry of Education Jointly Funded Project (20123121120002, 20123121120004), Shanghai Municipal Education Commission Project (no. 12ZZ148, no. 12ZZ149, and no. 13YZ080), Science and Technology Commission of Shanghai Municipality (no. 10PJ1404700) Shanghai Top Academic Discipline Project-Management Science & Engineering, the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Maritime and Port Authority, Singapore (MPA).