Research on Energy Saving Effect of Parallel and Perpendicular Yard Layouts under Different Proportions of Transshipment at the Automated Container Terminal

Abstract

The proportions of container transshipment is the key factor in determining the proportion of automated guided vehicle (AGV) and external container truck operations. In terms of parallel and perpendicular layouts of automated container terminals (ACTs), varying proportions of container transshipment result in different proportions of AGVs and external container truck operations, subsequently leading to distinct impacts on energy consumption (EC) for each ACT layout. This paper deemed EC as the primary evaluation criterion, established an EC model encompassing yard cranes (YCs) and container trucks, and investigated the EC of parallel and perpendicular layouts at different proportions of container transshipment. The results indicate that when the proportions of container transshipment were less than 17%, the parallel layout had lower EC; when it was between 17% and 21%, there was not much difference between the two layouts; when it was greater than 21%, the perpendicular layout had lower EC. This conclusion was based on an ideal environment established in this paper. When making decisions, decision makers should use this model as a starting point and adapt it flexibly to the actual situation of the port, in order to arrive at a reasonable and feasible plan.

1. Introduction

More and more goods tend to choose container transport [1]. An ACT can improve the productive efficiency and reduce the EC, leading to a surge in the number of ACTs currently operational or under construction [2,3]. Ref. [4] presented an overview of ACTs operational worldwide. There are several types of ACT layout designs including parallel, perpendicular, and U-shaped layout designs, and [5] provided a comprehensive account of the characteristics of each of these designs. Despite the distinct advantages and usage scenarios of each layout design, terminal operators often find it challenging to determine the most suitable layout. This is primarily due to the numerous factors that influence decision making in practical scenarios.

Since Port Rotterdam built the first ACT in 1992, extensive research has been conducted on ACTs to aid terminal operators in making informed decisions [6]. As the number of operational ACTs continues to grow, yard layout has become a key factor to improve the ACT performance [7]. Previous studies on ACT layout design have primarily focused on analyzing internal yard factors to assess the terminal performance. This includes evaluating the operational efficiency of different layout types, optimizing the yard dimensions (block length and width), and adjusting the storage strategies. However, until recently, there has been a notable scarcity of literature exploring the impact of container transshipment on the ACT layout. Container transshipment is an important transportation service [8]. For instance, Port of Singapore renowned as the world’s largest transshipment hub, it handles over 85% of its containers for onward shipment to other ports [9]. The proportion of container transshipment is an important external factor that significantly influences yard operations, and this proportion varies significantly among different ports. Therefore, understanding how this factor affects the layout and determining which layout is more suitable for transit ports with a high proportion of container transshipment is crucial. In this paper, we aim to address these questions by studying the terminal EC performance of parallel and perpendicular layouts in various proportions of container transshipment.

This paper consists of six sections. The research background of ACTs is introduced in Section 1. Section 2 summarizes and reviews the previous research work. Then, we describe the problem of container transshipment influencing the EC in Section 3. Subsequently, Section 4 focuses on developing an EC model for both parallel and perpendicular ACT layouts. In Section 5, we carry out model solving and the calculation analysis of the example. Finally, we present our conclusions and propose directions for further research in Section 6.

2. Related Work

Since the 1990s, the development of equipment automation has significantly improved the efficiency of port operations [10,11,12]. Rapid economic growth has spurred terminal operators to adopt ACTs as a means in which to increase their handling capacity [13,14]. However, the construction and management of ACTs involve substantial capital investment and require the careful consideration of numerous factors. Consequently, numerous studies have been conducted to enhance the management of ACTs [6]. Ref. [15] mainly offered a review of the outlooks on ACT layout. It specifically compared the performance of various ACT layouts and explored how specific factors impacted the performance of a given ACT layout. These various ACT layouts were mainly the parallel layout, perpendicular layout, and U-shaped layout [16].

2.1. Comparing Different Types of ACT Layout

Regarding the aspect of performance comparison among different types of ACT layouts, several studies have provided valuable insights. Ref. [17] studied the AGV system in parallel and perpendicular layouts, and the simulation results demonstrated that the number and operation efficiency of AGVs were affected by the layout of the yard. Based on the requirements of sustainable development, Ref. [5] conducted a comprehensive simulation study on ACT layouts, evaluating them in terms of environment, economic, and efficiency. The research indicated that the U-shaped layout design excelled in terms of EC and operation cost. Ref. [18] evaluated EC and carbon dioxide emissions with parallel and perpendicular layouts. Their results showed that the carbon dioxide emissions were relatively similar between the two layouts. Ref. [19] designed a separate lane in the yard to separate the internal and external trucks. Compared to the perpendicular layout, the parallel layout had better performance in the trucks’ waiting time and yard operation efficiency. In order to improve the comprehensive efficiency of the ACT, Ref. [20] constructed a set of evaluation index systems including yard layout and equipment allocation, and verified the feasibility of the system.

2.2. ACT Layout Influenced by Relevant Factors

Regarding the aspect of ACT layout performance influenced by relevant factors, various studies have delved into the specifics. Ref. [21] investigated how the block width affects the traditional container terminal performance under a parallel layout and provided optimal block width recommendations for the terminal layout design. This study is also applicable to ACTs. Ref. [22] evaluated the ACT performance considering multiple factors including yard layouts. Numerical experiments were conducted, offering insights into resource optimization and layout design. Ref. [23] studied different layout patterns for reefer containers within yard blocks, specifically focusing on how they impacted ACT productivity in a perpendicular layout. Their results indicated that the internal block layout was a key factor influencing the terminal performance. Ref. [24] focused on testing variables within the handshake area in a perpendicular layout to optimize the layout. Ref. [25] studied the impact of different crane systems and block dimensions on the terminal’s performance under a perpendicular layout. Ref. [26] analyzed and designed an ACT layout considering carbon emissions under a perpendicular layout. The result indicated that the optimal ACT layout design sequence for sustainable port development is in designing a sufficiently long block area, appropriately increasing the outside truck driving area, and properly reducing the AGV driving area. Ref. [27] studied the blocks’ allocation in an ACT yard. Experiments showed that the block-sharing strategy had good performance in improving equipment utilization and lowering the terminal operating costs. Ref. [28] studied the EC and operational costs in different ACT layouts, while Ref. [29] proposed a new high operation platform mode for ACTs. This mode had two operation platforms. Their simulation results showed that this new mode could improve the ACT operation efficiency. Some studies on common container terminals (non-ACTs) also have guiding significance for this paper. Ref. [21] studied the influence of the block width on the performance of a marine container terminal, and obtained the optimal block width ranges by constructing a comprehensive calculation model including ships, quay cranes (QCs), YCs, and container. In another paper, Ref. [30] studied the effect of the block on the performance of a marine container terminal, while Ref. [31] studied the storage layout of transit containers in the yard, and put forward an optimization model to improve the efficiency of transit containers in the container terminal.

In the literature, various studies have been conducted to design ACT layouts by considering factors such as the EC, block dimensions, and equipment configuration. However, there is a notable gap in research regarding the influence of container transshipment on the ACT layout. To address this, we selected the proportion of container transshipment as a variable parameter to investigate two key questions: (1) whether container transshipment affects the ACT layout, and (2) how it specifically affects the ACT layout.

3. Problem Description

3.1. The Parallel Layout and Perpendicular Layout of ACT

To address the questions posed in Section 2, we designed a square area to serve as the block stacking area for the ACT yard. Both parallel and perpendicular layout designs were created based on this square area, as illustrated in Figure 1 and Figure 2. This square area design ensured that the two layouts remained as similar as possible, featuring the same number of blocks, identical block dimensions, and an equal number of rail-mounted gantry cranes (RMGs).

3.2. The Operation Process of the ACT

To ensure that the proportion of container transshipment remained the sole variable parameter, this study tried to keep all other conditions the same. The operation process of the ACT comprises four phases, as shown in Figure 3.

Phase 1 (container transfer from ship to yard): Both transshipment and non-transshipment import containers are moved from QCs to the yard by AGVs, and stacked in blocks by RMGs.

Phase 2 (container dispatch from yard to hinterland): The non-transshipment containers are moved to the hinterland by external trucks. The remaining containers are designated for re-export as transshipment containers.

Phase 3 (container arrival from hinterland to yard): The exported containers originating from the hinterland are brought to the yard by external trucks and stacked by RMGs in the blocks.

Phase 4 (container transfer from yard to ship): All of the exported containers, both transshipment and non-transshipment, are moved by AGVs to QCs and then subsequently loaded onto ships.

3.3. The Influence of Container Transshipment

There are numerous distinctions between Figure 1 and Figure 2.

(1)

The block layouts differ between the two ACT designs.

(2)

In the parallel layout, container trucks travel a greater distance compared to the perpendicular layout, whereas YCs have a shorter travel distance.

(3)

Non-cantilever RMGs are used in the parallel layout, while cantilever RMGs are used in the perpendicular layout.

(4)

In the parallel layout, external trucks can drive directly into the yard to transport containers, whereas in the perpendicular layout, container handling occurs at the landside.

When ACTs with different layouts handle the same containers, these distinctions make the RMGs, AGVs, and external trucks have different operational paths and ECs. When we studied the influence of container transshipment based on these differences, we found that the proportion of container transshipment affected the proportion of work of the RMGs, AGVs, and external trucks, which then affected their ECs. This study developed the EC model and explored the balance point of EC in two layouts by changing the proportion of container transshipment.

4. Theoretical Model

Factors such as operational efficiency, EC, and yard shape are all considerations that port operators need to comprehensively evaluate when choosing between parallel or perpendicular layout designs. This paper added the element of container transshipment to these considerations, increasing the complexity of the problem. To gain a more direct understanding of the impact of the container transshipment, this paper adopted the controlled variable method to conduct related research. Specifically, assuming that both parallel and perpendicular layouts could meet the port operation requirements in terms of operational efficiency, and the yard shape was suitable for both layout forms, this paper considered only the factor of operational EC. That is, we investigated which parallel layout or perpendicular layout had a lower EC under different container transfer rates. To address the proposed problem, two EC models on the parallel layout and perpendicular layout were separately developed, which mainly considered the EC coming from the RMGs, AGVs, and external trucks in the yard. Additionally, several assumptions were made to simplify the problem and highlight the research focus.

4.1. Model Assumptions

The relevant assumptions were as follows.

(1)

The study was carried out under ideal conditions, so there was no energy loss and no waiting time.

(2)

All containers were 20 ft standard containers and a heavy box.

(3)

Although the proportion of container transshipment is typically derived from long-term container port throughput statistics, this study considered a single import and export process to represent this proportion. As illustrated in Figure 3, if α is the proportion of container transshipment and N is the number of imported containers, then there are αN containers to be exported after N containers of imported container stacking in the yard. During this period, (1 − α)N imported containers were transported to the hinterland, and (1 − α)N exported containers coming from the hinterland were transported to the yard, waiting for export.

(4)

The imported/exported containers were uniformly distributed across blocks, ensuring a consistent operational process for each block. This distribution is shown in Figure 4 and Figure 5.

(5)

For containers entering and leaving the yard in parallel layout, the operation order of the YCs is from right to left. For containers entering the yard in a perpendicular layout, the operation order of the YCs is from seaside to landside. For containers leaving the yard in a perpendicular layout, the operation order of the YCs is from landside to seaside.

(6)

The origin (O) and destination (D) of the AGVs and external trucks in the yard are shown in Figure 4 and Figure 5.

(7)

AGVs drive in a counterclockwise direction, while external trucks drive in a clockwise direction.

(8)

Both container trucks and YCs maintain a constant speed during operation.

4.2. Parameter Definition

N is the number of containers.

$N_t$ is the number of transshipment containers.

$N_n$ is the number of non-transshipment containers.

i is the imported container.

j is a container destined for the hinterland.

k is a container from the hinterland.

t is the transshipment container.

$E_a^l$ is the EC of the AGV loading container moving one meter.

$E_a^u$ is the EC of the AGV unloading container moving one meter.

$E_e^l$ is the EC of the external truck loading container moving one meter.

$E_e^u$ is the EC of the external truck unloading container moving one meter.

$E_y^l$ is the EC of the YC loading container moving one meter.

$E_y^u$ is the EC of the YC unloading container moving one meter.

$E_s^{+l}$ is the EC of the YC spreader loading container moving one meter in the vertical direction.

$E_s^{-l}$ is the EC of the YC spreader loading container moving one meter in the horizontal direction.

$E_s^{+u}$ is the EC of the YC spreader unloading container moving one meter in the vertical direction.

$E_s^{-u}$ is the EC of the YC spreader unloading container moving one meter in the horizontal direction.

The EC $E^{-}$ in the parallel layout yard can be calculated as follows. $E_1^{-}$, $E_2^{-}$,$E_3^{-}$, $E_4^{-}$ are respectively the EC generated by the four stages in Section 3.

$$E^{-}=E_1^{-}+E_2^{-}+E_3^{-}+E_4^{-}$$

(1)

4.3. The EC Model in the Parallel Layout

(1)

$E_1^{-}$

$E_1^{-}$ consists of four parts of EC. $E_{1a}^{-l}$ is the EC of the AGV loading container moving from seaside origin (O) to the YC, and $L_i^{1l}$ is the corresponding moving distance of the AGV. $E_{1a}^{-u}$ is the EC of the AGV unloading container moving from the YC to seaside destination (D), and $L_i^{1u}$ is the corresponding moving distance of the AGV. $E_{1y}^{-}$ is the EC of the YC unloading container moving, and $L_y^1$ is the corresponding moving distance of the YC. $E_{1s}^{-}$ is the EC of the YC spreader.

$$E_1^{-}=E_{1a}^{-l}+E_{1a}^{-u}+E_{1y}^{-}+E_{1s}^{-}$$

(2)

$$E_{1a}^{-l}=\sum _{i\in N}\left(L_i^{1l}{E}_a^l\right)$$

(3)

$$E_{1a}^{-u}=\sum _{i\in N}\left(L_i^{1u}{E}_a^u\right)$$

(4)

$$E_{1y}^{-}=L_y^1{E}_y^u$$

(5)

$E_{1s}^{-}$ consists of six EC stages. The first stage is the EC of the YC spreader vertically lifting container from the AGV to the specified height, and $X_{1i}^1$ is the corresponding moving distance of the YC spreader. The second stage is the EC of YC spreader loading container horizontally moving for the specified distance, and $X_{2i}^1$ is the corresponding moving distance of the YC spreader. The third stage is the EC of the YC spreader vertically lowering the container to yard, and $X_{3i}^1$ is the corresponding moving distance of the YC spreader. The fourth stage is the EC of the YC spreader vertically lifting to the specified height, $X_{4i}^1$ is the corresponding moving distance of the YC spreader. Stage five is the EC of the YC spreader horizontally moving above the AGV, and $X_{5i}^1$ is the corresponding moving distance of the YC spreader. The sixth stage is the EC of the YC spreader vertically lowering to the AGV to prepare to lift the next container, and $X_{6i}^1$ is the corresponding moving distance of the YC spreader.

$$E_{1s}^{-}=\sum _{i\in N}\left(X_{1i}^1{E}_s^{+l}+X_{2i}^1{E}_s^{-l}+X_{3i}^1{E}_s^{+l}+X_{4i}^1{E}_s^{+u}+X_{5i}^1{E}_s^{-u}+X_{6i}^1{E}_s^{+u}\right)$$

(6)

(2)

$E_2^{-}$

$E_2^{-}$ consists of four parts of EC. $E_{2e}^{-u}$ is the EC of the external truck unloading container moving from the landside origin (O) to the YC, and $L_j^{2u}$ is the corresponding moving distance of the external truck. $E_{2e}^{-l}$ is the EC of the external truck loading container moving from the YC to the landside destination (D), and $L_j^{2l}$ is the corresponding moving distance of the external truck. $E_{2y}^{-}$ is the EC of the YC unloading container moving, and $L_y^2$ is the corresponding moving distance of the YC. $E_{2s}^{-}$ is the EC of the YC spreader.

$$E_2^{-}=E_{2e}^{-u}+E_{2e}^{-l}+E_{2y}^{-}+E_{2s}^{-}$$

(7)

$$E_{2e}^{-u}=\sum _{j\in N_n}\left(L_j^{2u}{E}_e^u\right)$$

(8)

$$E_{2e}^{-l}=\sum _{j\in N_n}\left(L_j^{2l}{E}_e^l\right)$$

(9)

$$E_{2y}^{-}=L_y^2{E}_y^u$$

(10)

$E_{2s}^{-}$ consists of six EC stages. The starting point is the moment that the YC spreader vertically lowers the previous container to the external truck. One is the EC of the YC spreader vertically lifting from the external truck to the specified height, and $X_{1j}^2$ is the corresponding moving distance of the YC spreader. The second stage is the EC of the YC spreader horizontally moving for the specified distance, and $X_{2j}^2$ is the corresponding moving distance of the YC spreader. The third stage is the EC of the YC spreader vertically lowering to prepare to lift the container, and $X_{3j}^2$ is the corresponding moving distance of the YC spreader. Stage four is the EC of the YC spreader vertically lifting the container to the specified height, $X_{4j}^2$ is the corresponding moving distance of the YC spreader. Stage five is the EC of the YC spreader loading container horizontally moving above the external truck, and $X_{5j}^2$ is the corresponding moving distance of the YC spreader. Stage six is the EC of the YC spreader vertically lowering the container to the external truck, and $X_{6j}^2$ is the corresponding moving distance of the YC spreader.

$$E_{2s}^{-}=\sum _{j\in N_n}\left(X_{1j}^2{E}_s^{+u}+X_{2j}^2{E}_s^{-u}+X_{3j}^2{E}_s^{+u}+X_{4j}^2{E}_s^{+l}+X_{5j}^2{E}_s^{-l}+X_{6j}^2{E}_s^{+l}\right)$$

(11)

(3)

$E_3^{-}$

$E_3^{-}$ consists of four parts of EC. $E_{3e}^{-l}$ is the EC of the external truck loading container moving from the landside origin (O) to the YC, and $L_k^{3l}$ is the corresponding moving distance of the external truck. $E_{3e}^{-u}$ is the EC of the external truck unloading container moving from the YC to the landside destination (D), and $L_k^{3u}$ is the corresponding moving distance of the external truck. $E_{3y}^{-}$ is the EC of the YC unloading container moving, and $L_y^3$ is the corresponding moving distance of the YC. $E_{3s}^{-}$ is the EC of the YC spreader.

$$E_3^{-}=E_{3e}^{-l}+E_{3e}^{-u}+E_{3y}^{-}+E_{3s}^{-}$$

(12)

$$E_{3e}^{-l}=\sum _{k\in N_n}\left(L_k^{3l}{E}_e^l\right)$$

(13)

$$E_{3e}^{-u}=\sum _{k\in N_n}\left(L_k^{3u}{E}_e^u\right)$$

(14)

$$E_{3y}^{-}=L_y^3{E}_y^u$$

(15)

$E_{3s}^{-}$ is similar to $E_{1s}^{-}$ in that it also consists of six energy consuming stages, and $X_{1k}^3$, $X_{2k}^3$, $X_{3k}^3$, $X_{4k}^3$, $X_{5k}^3$, $X_{6k}^3$ are the corresponding moving distances of the YC spreader for each stage.

$$E_{3s}^{-}=\sum _{k\in N_n}\left(X_{1k}^3{E}_s^{+l}+X_{2k}^3{E}_s^{-l}+X_{3k}^3{E}_s^{+l}+X_{4k}^3{E}_s^{+u}+X_{5k}^3{E}_s^{-u}+X_{6k}^3{E}_s^{+u}\right)$$

(16)

(4)

$E_4^{-}$

$E_4^{-}$ consists of four parts of EC. $E_{4a}^{-u}$ is the EC of the AGV unloading container moving from the seaside origin (O) to the YC, and $L_p^{4u}$ is the corresponding moving distance of the AGV. $E_{4a}^{-l}$ is the EC of the AGV loading container moving from the YC to the seaside destination (D), and $L_p^{4l}$ is the corresponding moving distance of the AGV. $E_{4y}^{-}$ is the EC of the YC unloading container moving, and $L_y^4$ is the corresponding moving distance of the YC. $E_{4s}^{-}$ is the EC of the YC spreader.

$$E_4^{-}=E_{4a}^{-u}+E_{4a}^{-l}+E_{4y}^{-}+E_{4s}^{-}$$

(17)

$$E_{4a}^{-u}=\sum _{p\in N}\left(L_p^{4u}{E}_a^u\right)$$

(18)

$$E_{4a}^{-l}=\sum _{p\in N}\left(L_p^{4l}{E}_a^l\right)$$

(19)

$$E_{4y}^{-}=L_y^4{E}_y^u$$

(20)

$E_{4s}^{-}$ is similar to $E_{2s}^{-}$ in that it also consists of six energy consuming stages, and $X_{1p}^4$, $X_{2p}^4$, $X_{3p}^4$, $X_{4p}^4$, $X_{5p}^4$, $X_{6p}^4$ are the corresponding moving distances of the YC spreader for each stage.

$$E_{4s}^{-}=\sum _{p\in N}\left(X_{1p}^4{E}_s^{+u}+X_{2p}^4{E}_s^{-u}+X_{3p}^4{E}_s^{+u}+X_{4p}^4{E}_s^{+l}+X_{5p}^4{E}_s^{-l}+X_{6p}^4{E}_s^{+l}\right)$$

(21)

4.4. The EC Model in the Perpendicular Layout

The EC $E^{+}$ in the perpendicular layout yard can be calculated as follows. $E_1^{-}$, $E_2^{-}$,$E_3^{-}$, $E_4^{-}$ are respectively the EC generated by the four stages in Section 3.

$$E^{+}=E_1^{+}+E_2^{+}+E_3^{+}+E_4^{+}$$

(22)

(1)

$E_1^{+}$

$E_1^{+}$ consists of three parts of EC. $E_{1a}^{+l}$ is the EC of the AGV loading container moving from the seaside origin (O) to the seaside of the yard, and $D_i^{1l}$ is the corresponding moving distance of the AGV. $E_{1a}^{+u}$ is the EC of the AGV unloading container moving from the seaside of the yard to seaside destination (D), and $D_i^{1u}$ is the corresponding moving distance of the AGV. $E_{1y}^{+}$ is the EC of the YC.

$$E_1^{-}=E_{1a}^{+l}+E_{1a}^{+u}+E_{1y}^{+}$$

(23)

$$E_{1a}^{+l}=\sum _{i\in N}\left(D_i^{1l}{E}_a^l\right)$$

(24)

$$E_{1a}^{+u}=\sum _{i\in N}\left(D_i^{1u}{E}_a^u\right)$$

(25)

$E_{1y}^{+}$ consists of seven EC stages. The first stage is the EC of the YC spreader vertically lifting container from the AGV to the specified height, and $Y_{1i}^1$ is the corresponding moving distance of the YC spreader. Stage two is the EC of the YC loading container horizontally moving along the track for a specified distance, and $Y_{2i}^1$ is the corresponding moving distance of the YC. Stage three is the EC of the YC spreader vertically lowering the container to the yard, and $Y_{3i}^1$ is the corresponding moving distance of the YC spreader. Stage four is the EC of the YC spreader vertically lifting to the specified height, and $Y_{4i}^1$ is the corresponding moving distance of the YC spreader. Stage five is the EC of the YC horizontally moving above the seaside of the yard, and $Y_{5i}^1$ is the corresponding moving distance of the YC. Stage six is the EC of the YC spreader horizontally moving above the AGV, and $Y_{6i}^1$ is the corresponding moving distance of the YC spreader. Stage seven is the EC of the YC spreader vertically lowering to the AGV to prepare to lift the next container, and $Y_{7i}^1$ is the corresponding moving distance of the YC spreader. For a clearer comprehension of the YC movement, we summarized the moving direction of the YC and YC spreader in seven stages, as shown in

Table 1. The moving direction of the YC and YC spreader in seven stages for $E_1^{+}$.

Moving Direction	YC	YC Spreader
Stage 1	Motionless	Vertical upward moving
Stage 2	Moving horizontally parallel to YC track	Moving horizontally parallel to the YC track
Stage 3	Motionless	Vertical downward moving
Stage 4	Motionless	Vertical upward moving
Stage 5	Moving horizontally parallel to YC track	Moving horizontally parallel to the YC track
Stage 6	Motionless	Moving horizontally perpendicular to the YC track
Stage 7	Motionless	Vertical downward moving

.

$$E_{1y}^{+}=\sum _{i\in N}\left(Y_{1i}^1{E}_s^{+l}+Y_{2i}^1{E}_y^l+Y_{3i}^1{E}_s^{+l}+Y_{4i}^1{E}_s^{+u}+Y_{5i}^1{E}_y^u+Y_{6i}^1{E}_s^{-u}+Y_{7i}^1{E}_s^{+u}\right)$$

(26)

(2)

$E_2^{+}$

$E_2^{+}$ consists of three parts of EC. $E_{2e}^{+u}$ is the EC of the AGV unloading container moving from the seaside origin (O) to seaside of the yard, and $D_j^{2u}$ is the corresponding moving distance of the AGV. $E_{2e}^{+l}$ is the EC of the AGV loading container moving from the seaside of the yard to the seaside destination (D), and $D_j^{2l}$ is the corresponding moving distance of the AGV. $E_{2y}^{+}$ is the EC of the YC.

$$E_2^{+}=E_{2e}^{+u}+E_{2e}^{+l}+E_{2y}^{+}$$

(27)

$$E_{2e}^{+u}=\sum _{j\in N_n}\left(D_j^{2u}{E}_e^u\right)$$

(28)

$$E_{2e}^{+l}=\sum _{j\in N_n}\left(D_j^{2l}{E}_e^l\right)$$

(29)

$E_{2y}^{+}$ consists of seven EC stages. The starting point is the moment that the YC spreader vertically lowers the previous container to the external truck. One is the EC of the YC spreader vertically lifting from the external truck to the specified height, and $Y_{1j}^2$ is the corresponding moving distance of the YC spreader. Stage two is the EC of the YC unloading the container horizontally, moving along the track for specified distance, and $Y_{2j}^2$ is the corresponding moving distance of the YC. Stage three is the EC of the YC spreader horizontally moving above the target container, and $Y_{3j}^2$ is the corresponding moving distance of the YC spreader. Stage four is the EC of the YC spreader vertically lowering to prepare to lift the container, and $Y_{4j}^2$ is the corresponding moving distance of the YC spreader. Stage five is the EC of the YC spreader vertically lifting the container to the specified height, and $Y_{5j}^2$ is the corresponding moving distance of then YC spreader. Stage six is the EC of the YC horizontally moving above the external truck, and $Y_{6j}^2$ is the corresponding moving distance of the YC. Stage seven is the EC of the YC spreader vertically lowering the container to then external truck, and $Y_{7j}^2$ is the corresponding moving distance of then YC spreader. For a clearer comprehension of the YC movement, we summarized the moving direction of the YC and YC spreader in seven stages, as shown in

Table 2. The moving direction of the YC and YC spreader in seven stages for $E_2^{+}$.

Moving Direction	YC	YC Spreader
Stage 1	Motionless	Vertical upward moving
Stage 2	Moving horizontally parallel to YC track	Moving horizontally parallel to the YC track
Stage 3	Motionless	Moving horizontally perpendicular to the YC track
Stage 4	Motionless	Vertical downward moving
Stage 5	Motionless	Vertical upward moving
Stage 6	Moving horizontally parallel to the YC track	Moving horizontally parallel to the YC track
Stage 7	Motionless	Vertical downward moving

.

$$E_{2y}^{+}=\sum _{j\in N_n}\left(Y_{1j}^2{E}_s^{+u}+Y_{2j}^2{E}_y^u+Y_{3j}^2{E}_s^{-u}+Y_{4j}^2{E}_s^{+u}+Y_{5j}^2{E}_s^{+l}+Y_{6j}^2{E}_y^l+Y_{7j}^2{E}_s^{+l}\right)$$

(30)

(3)

$E_3^{+}$

$E_3^{+}$ consists of three parts of EC. $E_{3e}^{+l}$ is the EC of the external truck loading container moving from the landside origin (O) to the landside of the yard, and $D_k^{3l}$ is the corresponding moving distance of the AGV. $E_{3e}^{+u}$ is the EC of the external truck unloading container moving from the landside of the yard to the landside destination (D), and $D_k^{3u}$ is the corresponding moving distance of the external truck. $E_{3y}^{+}$ is the EC of the YC.

$$E_3^{+}=E_{3e}^{+l}+E_{3e}^{+u}+E_{3y}^{+}$$

(31)

$$E_{3e}^{+l}=\sum _{k\in N_n}\left(D_k^{3l}{E}_e^l\right)$$

(32)

$$E_{3e}^{+u}=\sum _{k\in N_n}\left(D_k^{3u}{E}_e^u\right)$$

(33)

$E_{3y}^{+}$ is similar to $E_{1y}^{+}$ in that it also consists of seven energy consuming stages, and $Y_{1k}^3$, $Y_{2k}^3$, $Y_{3k}^3$, $Y_{4k}^3$, $Y_{5k}^3$, $Y_{6k}^3$, $Y_{7k}^3$ are the corresponding moving distances of the YC and YC spreader for each stage.

$$E_{3y}^{+}=\sum _{k\in N_n}\left(Y_{1k}^3{E}_s^{+l}+Y_{2k}^3{E}_y^l+Y_{3k}^3{E}_s^{+l}+Y_{4k}^3{E}_s^{+u}+Y_{5k}^3{E}_y^u+Y_{6k}^3{E}_s^{-u}+Y_{7k}^3{E}_s^{+u}\right)$$

(34)

(4)

$E_4^{+}$

$E_4^{+}$ consists of three parts of EC. $E_{4a}^{+u}$ is the EC of the AGV unloading container moving from the seaside origin (O) to the seaside of the yard, and $D_p^{4u}$ is the corresponding moving distance of the AGV. $E_{4a}^{+l}$ is the EC of the AGV loading container moving from the seaside of the yard to the seaside destination (D), and $D_p^{4l}$ is the corresponding moving distance of the AGV. $E_{4y}^{+}$ is the EC of the YC.

$$E_4^{+}=E_{4a}^{+u}+E_{4a}^{+l}+E_{4y}^{+}$$

(35)

$$E_{4a}^{+u}=\sum _{p\in N}\left(D_p^{4u}{E}_a^u\right)$$

(36)

$$E_{4a}^{+l}=\sum _{p\in N}\left(D_p^{4l}{E}_a^l\right)$$

(37)

$E_{4y}^{+}$ is similar to $E_{2y}^{+}$ in that it also consists of seven energy consuming stages, and $Y_{1p}^3$, $Y_{2p}^3$, $Y_{3p}^3$, $Y_{4p}^3$, $Y_{5p}^3$, $Y_{6p}^3$, $Y_{7p}^3$ are the corresponding moving distances of the YC and YC spreader for each stage.

$$E_{4y}^{+}=\sum _{p\in N}\left(Y_{1p}^4{E}_s^{+u}+Y_{2p}^4{E}_y^u+Y_{3p}^4{E}_s^{-u}+Y_{4p}^4{E}_s^{+u}+Y_{5p}^4{E}_s^{+l}+Y_{6p}^4{E}_y^l+Y_{7p}^4{E}_s^{+l}\right)$$

(38)

According to Equations (1) and (22), the difference in the EC $∆E$ can be calculated as follows:

$$∆E=E^{-}-E^{+}$$

(39)

If $∆E$ is greater than 0, it means that the parallel layout consumes more energy compared to the perpendicular layout. In contrast, if $∆E$ is less than 0, the parallel layout consumes less energy than the perpendicular layout.

$∆E$ can be calculated as follows:

$$∆E={\alpha }_1{E}_a^l+{\alpha }_2{E}_a^u+{\alpha }_3{E}_e^l+{\alpha }_4{E}_e^u+{\alpha }_5{E}_y^l+{\alpha }_6{E}_y^u+{\alpha }_7{E}_s^{+l}+{\alpha }_8{E}_s^{+u}+{\alpha }_9{E}_s^{-l}+{\alpha }_{10}{E}_s^{-u}$$

(40)

${\alpha }_1$–${\alpha }_{10}$ can be calculated as shown in

Table 3. Formula of coefficients.

Coefficients	Formula of Coefficients
${\alpha }_1$	$\left({\displaystyle \sum _{i\in N}}{L}_i^{1l}+{\displaystyle \sum _{p\in N}}{L}_p^{4l}\right)-\left({\displaystyle \sum _{i\in N}}{D}_i^{1l}+{\displaystyle \sum _{p\in N}}{D}_p^{4l}\right)$
${\alpha }_2$	$\left({\displaystyle \sum _{i\in N}}{L}_i^{1u}+{\displaystyle \sum _{p\in N}}{L}_p^{4u}\right)-\left({\displaystyle \sum _{i\in N}}{D}_i^{1u}+{\displaystyle \sum _{p\in N}}{D}_p^{4u}\right)$
${\alpha }_3$	$\left({\displaystyle \sum _{j\in N_n}}{L}_j^{2l}+{\displaystyle \sum _{k\in N_n}}{L}_k^{3l}\right)-\left({\displaystyle \sum _{j\in N_n}}{D}_j^{2l}+{\displaystyle \sum _{k\in N_n}}{D}_k^{3l}\right)$
${\alpha }_4$	$\left({\displaystyle \sum _{j\in N_n}}{L}_j^{2u}+{\displaystyle \sum _{k\in N_n}}{L}_k^{3u}\right)-\left({\displaystyle \sum _{j\in N_n}}{D}_j^{2u}+{\displaystyle \sum _{k\in N_n}}{D}_k^{3u}\right)$
${\alpha }_5$	$-{\displaystyle \sum _{i\in N}}\left(Y_{2i}^1\right)-{\displaystyle \sum _{j\in N_n}}\left(Y_{6j}^2\right)-{\displaystyle \sum _{k\in N_n}}\left(Y_{2k}^3\right)-{\displaystyle \sum _{p\in N}}\left(Y_{6p}^4\right)$
${\alpha }_6$	$L_y^1+L_y^2+L_y^3+L_y^4-{\displaystyle \sum _{i\in N}}\left(Y_{5i}^1\right)-{\displaystyle \sum _{j\in N_n}}\left(Y_{2j}^2\right)-{\displaystyle \sum _{k\in N_n}}\left(Y_{5k}^3\right)-{\displaystyle \sum _{p\in N}}\left(Y_{2p}^4\right)$
${\alpha }_7$	${\displaystyle \sum _{i\in N}}\left(X_{1i}^1+X_{3i}^1-Y_{1i}^1-Y_{3i}^1\right)+{\displaystyle \sum _{j\in N_n}}\left(X_{4j}^2+X_{6j}^2-Y_{5j}^2-Y_{7j}^2\right)+{\displaystyle \sum _{k\in N_n}}\left(X_{1k}^3+X_{3k}^3-Y_{1k}^3-Y_{3k}^3\right)+{\displaystyle \sum _{p\in N}}\left(X_{4p}^4+X_{6p}^4-Y_{5p}^4-Y_{7p}^4\right)$
${\alpha }_8$	${\displaystyle \sum _{i\in N}}\left(X_{4i}^1+X_{6i}^1-Y_{4i}^1-Y_{7i}^1\right)+{\displaystyle \sum _{j\in N_n}}\left(X_{1j}^2+X_{3j}^2-Y_{1j}^2-Y_{4j}^2\right)+{\displaystyle \sum _{k\in N_n}}\left(X_{4k}^3+X_{6k}^3-Y_{4k}^3-Y_{7k}^3\right)+{\displaystyle \sum _{p\in N}}\left(X_{1p}^4+X_{3p}^4-Y_{1p}^4+Y_{4p}^4\right)$
${\alpha }_9$	${\displaystyle \sum _{i\in N}}\left(X_{2i}^1\right)+{\displaystyle \sum _{j\in N_n}}\left(X_{5j}^2\right)+{\displaystyle \sum _{k\in N_n}}\left(X_{2k}^3\right)+{\displaystyle \sum _{p\in N}}\left(X_{5p}^4\right)$
${\alpha }_{10}$	${\displaystyle \sum _{i\in N}}\left(X_{5i}^1-Y_{6i}^1\right)+{\displaystyle \sum _{j\in N_n}}\left(X_{2j}^2-Y_{3j}^2\right)+{\displaystyle \sum _{k\in N_n}}\left(X_{5k}^3-Y_{6k}^3\right)+{\displaystyle \sum _{p\in N}}\left(X_{2p}^4-Y_{3p}^4\right)$

.

5. Calculation and Analysis

5.1. Example Description

The core area of the automated terminal yard is a square (150 m × 150 m). Both parallel layout yard and perpendicular layout yard have 5 blocks, and the number of bays, rows and ties in one block are respectively 24, 10, and 4. To simplify the calculations, in the example presented in this paper, the number of imported containers was set to 4800 TEU. For the proportion of container transshipment, to ensure that decimals did not appear in the container calculations, a took the values as shown in

Table 4. The value of α and the corresponding number of transshipment containers ($N_t$).

α (%)	${\mathit{N}}_{\mathit{t}}$ (TEU)	α (%)	${\mathit{N}}_{\mathit{t}}$ (TEU)
0	0	54	2600
4	200	58	2800
8	400	63	3000
13	600	67	3200
17	800	71	3400
21	1000	75	3600
25	1200	79	3800
29	1400	83	4000
33	1600	88	4200
38	1800	92	4400
42	2000	96	4600
46	2200	100	4800
50	2400	/	/

.

$d$ is the distance between the centers of two adjacent blocks, and was set to 30 m. As shown in Figure 4 and Figure 5, assuming that the route of container trucks is rectangular, the length and width of the routes taken by the AGVs and external trucks are respectively shown in

Table 5. The length and width of the container truck routes.

Routes	${\mathit{l}}_1$	${\mathit{l}}_2$	${\mathit{l}}_3$	${\mathit{l}}_4$	${\mathit{l}}_5$	${\mathit{S}}_1$	${\mathit{S}}_2$	${\mathit{S}}_3$	${\mathit{S}}_4$	${\mathit{S}}_5$	${\mathit{l}}_{\mathit{a}}$	${\mathit{S}}_{\mathit{e}}$
Length (m)	150	150	150	150	150	160	160	160	160	160	150	160
Width (m)	30	90	90	150	150	150	150	90	90	30	30	30

.

5.2. Model Calculation

(1)

Calculation of EC Per Unit Distance

According to assumption (8), $E_a^l$, $E_a^u$, $E_e^l$, $E_e^u$, $E_y^l$, $E_y^u$, $E_s^{+l}$, $E_s^{+u}$, $E_s^{-l}$, $E_s^{-u}$ can be calculated by the following equations:

$$E_a^l={\mu }_t(m_a+m_c)g$$

(41)

$$E_a^u={\mu }_t{m}_{a}g$$

(42)

$$E_e^l={\mu }_t(m_e+m_c)g$$

(43)

$$E_a^u={\mu }_t{m}_{e}g$$

(44)

$$E_e^l={\mu }_r(m_y+m_c)g$$

(45)

$$E_a^u={\mu }_r{m}_{y}g$$

(46)

$$E_s^{+l}=(m_s+m_c)g$$

(47)

$$E_s^{+u}=m_{s}g$$

(48)

$$E_s^{-l}={\mu }_s(m_s+m_c)g$$

(49)

$$E_s^{-u}={\mu }_s{m}_{s}g$$

(50)

In Equations (41)–(50):

$m_a$ is the quality of the AGV, $m_e$ is the quality of the external truck, $m_c$ is the quality of the heavy container, $m_y$ is the quality of the YC, $m_s$ is the quality of the YC spreader, ${\mu }_t$ is the coefficient of friction between the truck and ground, ${\mu }_r$ is the coefficient of friction between the YC and rail, ${\mu }_s$ is the coefficient of friction between the spreader and YC, and $g$ is the gravitational acceleration.

(2)

Calculation of Coefficients

Taking Block $B_1$ as an example, the container operation sequence for the non-transshipment container bay in the parallel layout is as follows:

The container operation sequence at Phase 1 in Section 3 is shown in Figure 6.

The container operation sequence at Phase 2 in Section 3 is shown in Figure 7.

The container operation sequence at Phase 3 in Section 3 is the exact opposite of that in Figure 7 where the operation sequence is in reverse order from 40 to 1. Likewise, the container operation sequence at Phase 4 in Section 3 is the exact opposite of that in Figure 6, also being in reverse order from 40 to 1.

In the case of the transshipment container bay, there were only two operation phases: Phase 1 and Phase 4. The container operation sequences for both Phase 1 and Phase 4 were the same as those of the non-transshipment container bay.

The container operation sequence in the perpendicular layout was the same as that in the parallel layout. Taking Phase 1 of a certain bay of Block $B_1$ as an example, the container operation sequence is shown in Figure 8.

Based on the conditions above-mentioned, the calculation formula for the coefficient can be obtained, as shown in

Table 6. The calculation formula of the coefficient.

Coefficients	Formula of Coefficients
${\alpha }_1$	${\displaystyle \frac{24dN}{5}}$
${\alpha }_2$	${\displaystyle \frac{24dN}{5}}$
${\alpha }_3$	${\displaystyle \frac{24d{N}_n}{5}}$
${\alpha }_4$	${\displaystyle \frac{24d{N}_n}{5}}$
${\alpha }_5$	$-120000c_l-\left({\displaystyle \frac{N_n\ast N_n}{200}}+N_n\right)c_l$
${\alpha }_6$	$-119560c_l-{\displaystyle \frac{{9N}_n}{10}}{c}_l-{\displaystyle \frac{N_n\ast N_n}{200}}{c}_l$
${\alpha }_7$	$0$
${\alpha }_8$	$0$
${\alpha }_9$	$11N{c}_w+11N_n{c}_w$
${\alpha }_{10}$	$9N{c}_w+9N_n{c}_w$

. For a detailed calculation process regarding the moving distance of devices like the YC and YC spreader, readers can refer to another paper [29] by the authors.

As $N_n=(1-\alpha )N$, $∆E$ can be expressed in terms of a quadratic equation of one variable (Equation (51)).

$$∆E=a{\alpha }^2+b\alpha +c$$

(51)

In Equation (51):

$$a=-{\displaystyle \frac{{\mu }_r{m}_{y}g{c}_l{N}^2}{100}}-{\displaystyle \frac{{{\mu }_r{m}_{c}g{c}_{l}N}^2}{200}}$$

(52)

$$\begin{gathered} b=-{\displaystyle \frac{48{\mu }_t{m}_{e}gdN}{5}}-{\displaystyle \frac{24{\mu }_t{m}_{c}gdN}{5}}+{\displaystyle \frac{{\mu }_r{m}_{y}g{c}_l\left(N^2+95N\right)}{50}} \\ \hspace{1em}\hspace{1em}+{\displaystyle \frac{{\mu }_r{m}_{c}g{c}_l\left(N^2+100N\right)}{100}}-{20\mu }_s{m}_{s}gN{c}_w-11{\mu }_s{m}_{c}gN{c}_w \end{gathered}$$

(53)

$$\begin{gathered} c={\displaystyle \frac{48{\mu }_t{m}_{a}gdN}{5}}+{\displaystyle \frac{48{\mu }_t{m}_{c}gdN}{5}}+{\displaystyle \frac{48{\mu }_t{m}_{e}gdN}{5}}-{\displaystyle \frac{{\mu }_r{m}_{y}g{c}_l\left(N^2+190N+23956000\right)}{100}} \\ \hspace{1em}\hspace{1em}-{\displaystyle \frac{{\mu }_r{m}_{c}g{c}_l\left(N^2+200N+24000000\right)}{200}}+40{\mu }_s{m}_{s}gN{c}_w+22{\mu }_s{m}_{c}gN{c}_w \end{gathered}$$

(54)

The relevant parameters are shown in

Table 7. The values of the relevant parameters.

Parameters	${\mathit{m}}_{\mathit{a}}$	${\mathit{m}}_{\mathit{c}}$	${\mathit{m}}_{\mathit{e}}$	${\mathit{m}}_{\mathit{y}}$	${\mathit{m}}_{\mathit{s}}$	$\mathit{g}$	${\mathit{\mu }}_{\mathit{t}}$	${\mathit{\mu }}_{\mathit{r}}$	${\mathit{\mu }}_{\mathit{s}}$	${\mathit{c}}_{\mathit{l}}$	${\mathit{c}}_{\mathit{w}}$
Values	20,000 kg	30,000 kg	10,000 kg	40,000 kg	2000 kg	9.81 m/s2	0.024	0.015	0.015	6.1 m	2.44 m

.

Then, we obtained the computational results as shown in

Table 8. The value of $∆E$ corresponding to α.

α (%)	$∆\mathit{E}$ (109 J)	α (%)	$∆\mathit{E}$ (109 J)
0	−2.86	54	3.13
4	−2.25	58	3.38
8	−1.67	63	3.66
13	−0.98	67	3.85
17	−0.45	71	4.02
21	0.04	75	4.16
25	0.51	79	4.27
29	0.96	83	4.36
33	1.37	88	4.43
38	1.86	92	4.45
42	2.22	96	4.45
46	2.55	100	4.43
50	2.85	/	/

and Figure 9.

As illustrated in Figure 9, when the proportion of container transshipment was less than 17%, the parallel layout had lower EC; when it was between 17% and 21%, there was not much difference between the two layouts; when it was greater than 21, the perpendicular layout had a lower EC. This indicates that the proportion of container transshipment is an important parameter in which to choose the type of ACT layout, and different values of $\alpha$ apply to different yard layouts.

6. Conclusions and Future Work

As the number of ACTs increases, selecting the appropriate layout has become a significant challenge. To address this problem, we proposed comparing the EC of perpendicular and parallel layouts with different proportions of container transshipment from the perspective of promoting sustainable development. The major contributions of this paper with respect to other research are as follows:

(1)

According to the literature review, this study is the first to propose and analyze the influence of container transshipment on the ACT layout. To gain a more direct understanding of the impact of the container transshipment, this paper adopted the controlled variable method to conduct related research.

(2)

Different values of $\alpha$ apply to different yard layouts. Taking the example in this paper, when $\alpha \le 17$%, the parallel layout was more suitable; when $\alpha \ge 21\%$, the perpendicular layout was more suitable; when $17\mathrm{\%}<\alpha <21$%, there was not much difference between the two layouts. Choosing the appropriate ACT layout according to the container transshipment can effectively reduce the port EC and enhance sustainable development.

The calculation method presented in this paper has generally applicability. However, when it comes to specific ports, decision makers should use this model as a starting point and adapt it flexibly to the actual situation of the port, in order to arrive at a reasonable and feasible plan.

We believe that in the future, we need to continue to strengthen our work in three areas. Firstly, the research primarily relies on theoretical models and computational simulations. In future studies, we advise enhancing the model to incorporate more realistic factors such as the actual operation flow of the equipment, variable container sizes, stochastic operational delays, and energy losses due to equipment inefficiencies. Additionally, we recommend introducing advanced mathematical techniques to solve this model. Secondly, we will consider more indicators like operational efficiency, cost-effectiveness, terminal sizes, and so on, and employ multi-objective optimization models and techniques to identify layout configurations. Thirdly, the calculation scale of the example should be improved, the operation scenario should be set for the simultaneous loading and unloading operation of multiple large container ships, and the operating area should be expanded to allow more QCs, YCs, and container trucks to run, which is closer to the daily operations of large ACTs.