Integrated Scheduling of Automated Yard Cranes and Automated Guided Vehicles with Limited Buffer Capacity of Dual-Trolley Quay Cranes in Automated Container Terminals
Abstract
:1. Introduction
2. Literature Review
3. Problem Description and Formulation
3.1. Assumptions
- Any piece of equipment can handle one container at a time.
- The scheduling of a QC and the allocation of export containers are known;
- QCs are homogeneous and have the same buffer capacity;
- Each YC serves a specific yard block and contains one type of container, export or import;
- There are four different conditions for any two consecutive containers handled by the same equipment; AGV, QC’s main trolley, or QC’s portal trolley:
- Handling two consecutive import containers;
- Handling two consecutive export containers;
- Handling an export container before an import one;
- Handling an import container before an export one.
3.2. Notations
3.2.1. Sets and Parameters
Set of QCs. | |
Set of YCs. | |
Set of yard blocks. | |
Set of available slots in each block. | |
Set of yard locations. | |
Set of all containers. Each container is defined by its number and its assigned quay crane. | |
Set of import containers (jobs), | |
Set of export containers (jobs), | |
Set of the containers in the buffer beneath each quay crane, | |
Set of all containers beside the starting dummy container. | |
Set of all containers beside the ending dummy container. | |
Set of all containers, including dummy starting and ending jobs. | |
Indices for QCs. | |
Indices for blocks. | |
Indices for the available slots in each block. | |
Indices for containers (jobs), job means that container is handled by quay crane , and job means that container is handled by quay crane . | |
Dummy starting job. | |
Dummy ending job. | |
Indices for yard locations, location is slot n in block b, and location is slot in block . | |
Handling time of container by the main trolley of its assigned quay carne. | |
Handling time of container by the portal trolley of its assigned quay crane. | |
The transportation time of AGV for export container from its assigned block to its assigned quay crane. | |
AGV’s transportation time from quay crane to block | |
AGV’s transportation time between quay crane and quay crane . | |
AGV’s traveling time from the block that container is located to block , . | |
The handling time of YC to transfer export container from its assigned slot to the transfer point in front of its assigned block. | |
The transportation time of YC between the transfer point of block b to the location | |
YC’s transportation time from the assigned location of the import container to the assigned location of the import container . | |
A large number | |
The capacity of the buffer beneath each QC | |
Total number of AGVs |
3.2.2. Decision Variables
=1; if an AGV, scheduled to deliver the container , has just delivered container . =0; otherwise | |
=1; if the import container is assigned to the location . =0; otherwise. | |
=1; if the YC of block b is scheduled to handle both import containers and consecutively. =0; otherwise. | |
=1; if a YC is scheduled to handle both export containers and consecutively. =0; otherwise. | |
=1; if the job is located in the buffer beneath QC when the QC starts to handle job =0; otherwise. |
3.2.3. Decision Variables
The starting time of the main trolley of quay crane k to handle container i | |
The starting time of the portal trolley of quay crane k to handle container i | |
The starting time of YC to handle container (i,k) | |
=1; if block b is assigned to the import container (i,k). =0; otherwise. It is an intermediated variable: | |
The quay crane k’s waiting time to start handling container i | |
The AGV’s waiting time until quay crane k starts to handle container i | |
=1; if there is an available slot in the buffer beneath quay crane l when the QC starts to handle job j =0; otherwise. |
3.3. Mathematical Model
4. Results and Discussion
- Investigating the effect of the integrating the scheduling of YCs and AGVs considering the limited QCs buffer capacity on completion time, AGV utilization, and QC utilization;
- Investigating the effects of using the QCs buffer capacity with different sizes;
- Investigating the impact of using single-trolley QCs instead of dual-trolley QCs.
4.1. Investigating the Effect of the Integrating the Scheduling of YCs and AGVs on Completion Time, AGV Utilization, and QC Utilization
4.2. Investigating the Effect of Using the QC Buffer Capacity with Different Sizes
4.3. Investigating the Impact of Using Single-Trolley QCs Instead of Dual-Trolley QCs
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Instances | Number of Containers | AGV/YC | Optimum Solution | |||||
---|---|---|---|---|---|---|---|---|
Computational Time (s) | Completion Time (s) | Average AGV Waiting Time (s) | Average QC Waiting Time (s) | AGV Utilization (%) | QC Utilization (%) | |||
1 | 5 | 2/2 | 0.016 | 519 | 64.95 | 382 | 87.49 | 26.40 |
2 | 6 | 2/2 | 0.021 | 602 | 60 | 376 | 90.03 | 37.54 |
3 | 10 | 2/2 | 0.202 | 994 | 78 | 588 | 92.15 | 40.85 |
4 | 10 | 3/2 | 0.073 | 794 | 127 | 413 | 84.01 | 47.98 |
5 | 15 | 3/2 | 0.596 | 998 | 120 | 485 | 87.98 | 51.40 |
6 | 20 | 3/2 | 8 | 1451 | 159 | 626 | 89.04 | 56.86 |
7 | 25 | 3/2 | 46 | 1808 | 190 | 787 | 89.49 | 56.47 |
8 | 25 | 3/3 | 59 | 1793 | 183 | 756 | 89.79 | 57.84 |
9 | 25 | 5/3 | 5 | 1479 | 310 | 455 | 79.04 | 69.24 |
10 | 30 | 5/3 | 11 | 1809 | 263 | 570 | 85.46 | 68.49 |
11 | 40 | 6/4 | 110 | 2002 | 309 | 235 | 84.57 | 88.26 |
12 | 50 | 6/4 | 711 | 2261 | 358 | 262 | 84.84 | 88.90 |
13 | 60 | 6/4 | 1324 | 2822 | 409 | 325 | 85.51 | 88.48 |
14 | 70 | 6/4 | --- | --- | --- | --- | --- | --- |
Instances | Number of Containers | AGV/YC | Optimum Solution | |||
---|---|---|---|---|---|---|
Computational Time (s) | Completion Time (s) | AGV Utilization (%) | QC Utilization (%) | |||
1 | 5 | 2/2 | 0.009 | 553 | 84.45 | 35.99 |
2 | 6 | 2/2 | 0.02 | 620 | 88.39 | 33.71 |
3 | 10 | 2/2 | 0.191 | 1079 | 90.82 | 41.89 |
4 | 10 | 3/2 | 0.05 | 808 | 80.82 | 48.39 |
5 | 15 | 3/2 | 0.563 | 1052 | 86.69 | 53.23 |
6 | 20 | 3/2 | 6.513 | 1483 | 88.00 | 58.26 |
7 | 25 | 3/2 | 30.999 | 1810 | 85.91 | 59.89 |
8 | 25 | 3/3 | 21.667 | 1842 | 89.03 | 60.26 |
9 | 25 | 5/3 | 2.5 | 1532 | 78.72 | 70.23 |
10 | 30 | 5/3 | 11.04 | 1833 | 82.54 | 69.50 |
11 | 40 | 6/4 | 94.535 | 2091 | 80.54 | 88.47 |
12 | 50 | 6/4 | 272.419 | 2374 | 80.88 | 89.51 |
13 | 60 | 6/4 | 1431.354 | 2971 | 80.88 | 88.59 |
Instances | Number of Containers | AGV/YC | Optimum Solution | |||
---|---|---|---|---|---|---|
Computational Time (s) | Completion Time (s) | AGV Utilization (%) | QC Utilization (%) | |||
1 | 5 | 2/2 | 0.009 | 543.00 | 80.48 | 39.96 |
2 | 6 | 2/2 | 0.025 | 651 | 84.79 | 42.55 |
3 | 10 | 2/2 | 2 | 1045 | 85.36 | 43.44 |
4 | 10 | 3/2 | 0.074 | 845 | 75.98 | 54.08 |
5 | 15 | 3/2 | 0.646 | 1066 | 82.55 | 60.88 |
6 | 20 | 3/2 | 13 | 1565 | 83.39 | 61.47 |
7 | 25 | 3/2 | 70 | 1817 | 82.61 | 63.29 |
8 | 25 | 3/3 | 66 | 1889 | 84.33 | 65.64 |
9 | 25 | 5/3 | 3 | 1541 | 75.60 | 85.01 |
10 | 30 | 5/3 | 13 | 1843 | 81.88 | 81.71 |
11 | 40 | 6/4 | 82 | 2210 | 76.02 | 90.41 |
12 | 50 | 6/4 | 236 | 2728 | 76.83 | 89.96 |
13 | 60 | 6/4 | 449 | 3259 | 77.29 | 89.90 |
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Naeem, D.; Eltawil, A.; Iijima, J.; Gheith, M. Integrated Scheduling of Automated Yard Cranes and Automated Guided Vehicles with Limited Buffer Capacity of Dual-Trolley Quay Cranes in Automated Container Terminals. Logistics 2022, 6, 82. https://doi.org/10.3390/logistics6040082
Naeem D, Eltawil A, Iijima J, Gheith M. Integrated Scheduling of Automated Yard Cranes and Automated Guided Vehicles with Limited Buffer Capacity of Dual-Trolley Quay Cranes in Automated Container Terminals. Logistics. 2022; 6(4):82. https://doi.org/10.3390/logistics6040082
Chicago/Turabian StyleNaeem, Doaa, Amr Eltawil, Junichi Iijima, and Mohamed Gheith. 2022. "Integrated Scheduling of Automated Yard Cranes and Automated Guided Vehicles with Limited Buffer Capacity of Dual-Trolley Quay Cranes in Automated Container Terminals" Logistics 6, no. 4: 82. https://doi.org/10.3390/logistics6040082
APA StyleNaeem, D., Eltawil, A., Iijima, J., & Gheith, M. (2022). Integrated Scheduling of Automated Yard Cranes and Automated Guided Vehicles with Limited Buffer Capacity of Dual-Trolley Quay Cranes in Automated Container Terminals. Logistics, 6(4), 82. https://doi.org/10.3390/logistics6040082