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.
4.2. Parameter Definition
N is the number of containers.
is the number of transshipment containers.
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.
is the EC of the AGV loading container moving one meter.
is the EC of the AGV unloading container moving one meter.
is the EC of the external truck loading container moving one meter.
is the EC of the external truck unloading container moving one meter.
is the EC of the YC loading container moving one meter.
is the EC of the YC unloading container moving one meter.
is the EC of the YC spreader loading container moving one meter in the vertical direction.
is the EC of the YC spreader loading container moving one meter in the horizontal direction.
is the EC of the YC spreader unloading container moving one meter in the vertical direction.
is the EC of the YC spreader unloading container moving one meter in the horizontal direction.
The EC
in the parallel layout yard can be calculated as follows.
,
,
,
are respectively the EC generated by the four stages in
Section 3.
4.3. The EC Model in the Parallel Layout
consists of four parts of EC.
is the EC of the AGV loading container moving from seaside origin (
O) to the YC, and
is the corresponding moving distance of the AGV.
is the EC of the AGV unloading container moving from the YC to seaside destination (
D), and
is the corresponding moving distance of the AGV.
is the EC of the YC unloading container moving, and
is the corresponding moving distance of the YC.
is the EC of the YC spreader.
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
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
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
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,
is the corresponding moving distance of the YC spreader. Stage five is the EC of the YC spreader horizontally moving above the AGV, and
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
is the corresponding moving distance of the YC spreader.
consists of four parts of EC.
is the EC of the external truck unloading container moving from the landside origin (
O) to the YC, and
is the corresponding moving distance of the external truck.
is the EC of the external truck loading container moving from the YC to the landside destination (
D), and
is the corresponding moving distance of the external truck.
is the EC of the YC unloading container moving, and
is the corresponding moving distance of the YC.
is the EC of the YC spreader.
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
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
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
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,
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
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
is the corresponding moving distance of the YC spreader.
consists of four parts of EC.
is the EC of the external truck loading container moving from the landside origin (
O) to the YC, and
is the corresponding moving distance of the external truck.
is the EC of the external truck unloading container moving from the YC to the landside destination (
D), and
is the corresponding moving distance of the external truck.
is the EC of the YC unloading container moving, and
is the corresponding moving distance of the YC.
is the EC of the YC spreader.
is similar to
in that it also consists of six energy consuming stages, and
,
,
,
,
,
are the corresponding moving distances of the YC spreader for each stage.
consists of four parts of EC.
is the EC of the AGV unloading container moving from the seaside origin (
O) to the YC, and
is the corresponding moving distance of the AGV.
is the EC of the AGV loading container moving from the YC to the seaside destination (
D), and
is the corresponding moving distance of the AGV.
is the EC of the YC unloading container moving, and
is the corresponding moving distance of the YC.
is the EC of the YC spreader.
is similar to
in that it also consists of six energy consuming stages, and
,
,
,
,
,
are the corresponding moving distances of the YC spreader for each stage.
4.4. The EC Model in the Perpendicular Layout
The EC
in the perpendicular layout yard can be calculated as follows.
,
,
,
are respectively the EC generated by the four stages in
Section 3.
consists of three parts of EC.
is the EC of the AGV loading container moving from the seaside origin (
O) to the seaside of the yard, and
is the corresponding moving distance of the AGV.
is the EC of the AGV unloading container moving from the seaside of the yard to seaside destination (
D), and
is the corresponding moving distance of the AGV.
is the EC of the YC.
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
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
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
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
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
is the corresponding moving distance of the YC. Stage six is the EC of the YC spreader horizontally moving above the AGV, and
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
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.
consists of three parts of EC.
is the EC of the AGV unloading container moving from the seaside origin (
O) to seaside of the yard, and
is the corresponding moving distance of the AGV.
is the EC of the AGV loading container moving from the seaside of the yard to the seaside destination (
D), and
is the corresponding moving distance of the AGV.
is the EC of the YC.
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
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
is the corresponding moving distance of the YC. Stage three is the EC of the YC spreader horizontally moving above the target container, and
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
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
is the corresponding moving distance of then YC spreader. Stage six is the EC of the YC horizontally moving above the external truck, and
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
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.
consists of three parts of EC.
is the EC of the external truck loading container moving from the landside origin (
O) to the landside of the yard, and
is the corresponding moving distance of the AGV.
is the EC of the external truck unloading container moving from the landside of the yard to the landside destination (
D), and
is the corresponding moving distance of the external truck.
is the EC of the YC.
is similar to
in that it also consists of seven energy consuming stages, and
,
,
,
,
,
,
are the corresponding moving distances of the YC and YC spreader for each stage.
consists of three parts of EC.
is the EC of the AGV unloading container moving from the seaside origin (
O) to the seaside of the yard, and
is the corresponding moving distance of the AGV.
is the EC of the AGV loading container moving from the seaside of the yard to the seaside destination (
D), and
is the corresponding moving distance of the AGV.
is the EC of the YC.
is similar to
in that it also consists of seven energy consuming stages, and
,
,
,
,
,
,
are the corresponding moving distances of the YC and YC spreader for each stage.
According to Equations (1) and (22), the difference in the EC
can be calculated as follows:
If is greater than 0, it means that the parallel layout consumes more energy compared to the perpendicular layout. In contrast, if is less than 0, the parallel layout consumes less energy than the perpendicular layout.
can be calculated as follows:
–
can be calculated as shown in
Table 3.