Research on Train Loading and Unloading Mode and Scheduling Optimization in Automated Container Terminals
Abstract
:1. Introduction
- In this study, the “full unloading and full loading” and “synchronous loading and unloading” operation modes in RYACT train loading and unloading were researched. To fill a key research gap in the existing literature, an MILP model was established with the objective of minimizing the maximum completion time of ARMG tasks, and the scheduling effects of the two modes were compared.
- An MILP model was established with the objective of minimizing the maximum completion time for ARMG tasks in the case of “non-pre-assign” task arrangement under the “synchronous loading and unloading” mode. It was then compared with “pre-assign” task arrangement in terms of the calculation and completion times.
- The models, solution method, and experimental results presented in this paper have good reference value for managers of the RYACT, helping them to make decisions on equipment scheduling in the RYACT.
2. Literature Review
3. Problem Definition and Formulations
3.1. Problem Description
3.2. Assumptions
- The loading and unloading of containers by the ARMG system does not include shifting activities.
- Containers that have been unloaded from the train will not impact subsequent loading operations.
- The operational speed of the ARMG system remains consistent throughout the modeling process.
- The precise starting and ending positions of container tasks, along with their corresponding coordinate values, are known and accounted for.
- The time required for the ARMG system to both grab and release containers is assumed to be equal, with the initial position of the ARMG system being predetermined.
- To ensure the safety of container handling operations, the trolley will remain stationary during the movement of the ARMG system’s gantry.
3.3. Parameter Description
3.4. Model Formulation
3.4.1. “Full Unloading and Full Loading” Mode
3.4.2. “Synchronous Loading and Unloading” Mode
3.4.3. Considering “Non-Pre-Assignment” of Tasks
- -
- indicates the set of tasks that may conflict among ARMG tasks, where indicates that if the start and end positions of tasks i and j overlap, they may interfere with each other when assigned to two ARMGs.
- -
- indicates the position coordinates of task i in the direction of the railway yard.
- -
- indicates that container task is assigned to ARMG for operation; otherwise, .
- -
- indicates that ARMG starts task immediately after completing task ; otherwise, .
4. Solution Approach
Algorithm 1 Adaptive large neighborhood algorithm | |
1: | Input data: ; |
2: | Set algorithm parameters: |
3: | The number of solutions generated per iteration: ; |
4: | Maximum number of iterations: ; |
5: | The maximum number of iterations with the same optimal value: ; |
6: | The initial solution is generated by RSA and its score is calculated; |
7: | Initialize the data: |
8: | Set iteration number ; |
9: | The score and sequence of the m code of the n iteration; |
10: | Optimal score and corresponding sequence . |
11: | While : |
12: | Determine the list of domain search operators; |
13: | Search the neighborhood of to generate new encodings; . |
14: | For : |
15: | Use Algorithm 1 to calculate the score of ; |
16: | End for; |
17: | Determine the optimal score and corresponding sequence ; |
18: | End while. |
19: | Calculate according to the optimal sequence ; . |
20: | Return . |
5. Numerical Experiments and Results
5.1. Comparison of “Full Unloading and Full Loading” and “Synchronous Loading and Unloading”
- Set the number of tasks to values ranging between 20 and 120, and generate corresponding examples.
- Keep the parameter settings of the ALNS algorithm the same as those in [34].
- For each numerical example of the number of tasks, solve the scenario 10 times and return the minimum value obtained.
5.2. Comparison of the Task Distribution Methods
- -
- Set the number of tasks from 10 to 20 and generate corresponding examples.
- -
- Limit the model solution time to 1200 s.
- -
- Solve the models M2 and M3 using the solver CPLEX and return the experimental results.
- -
- Set the number of tasks to 40, 60, 80, …, 160, and generate corresponding examples.
- -
- Solve the models M2 and M3 using an ALNS algorithm with the same number of iterations (600) and return the experimental results.
- -
- Compare the experimental results between the two models. The experimental results are shown in Table 6.
6. Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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---|---|---|---|---|---|
Vacca et al. [2] | QC scheduling problem | √ | |||
Iris and Lam [4] | QC assignment problem | √ | |||
Luo et al. [8] | Container storage and AGV scheduling | √ | |||
Xiang and Liu [10] | Battery replacement strategy of AGVs | √ | |||
Drungilas et al. [12] | Energy-saving problem of AGVs | √ | |||
Gharehgozli et al. [13] | YCs and yard resource scheduling | √ | |||
Oladugba et al. [18] | Twin ASC sequencing and scheduling | √ | |||
Skaf et al. [23] | Joint scheduling | √ | √ | ||
D. Anghinolfi et al. [31] | Optimization of the operation of loading containers to wagon | √ | |||
Chang et al. [32] | Joint scheduling of equipment | √ | √ | √ | |
Yang et al. [33] | Cooperative scheduling | √ | √ | √ |
Set | Definition |
---|---|
Set of ARMGs indexed by . | |
Set of ARMG tasks for loading containers indexed by and . | |
Set of ARMG tasks for unloading containers indexed by and . | |
Set of ARMG tasks for loading and unloading containers that verify . | |
Set of tasks for loading and unloading containers , where represents a virtual start task; similarly, we can define sets and . | |
Set of tasks for loading and unloading containers verifying , where represents a virtual start task; similarly, we can define and . | |
Set of tasks that may interfere with one another when adjacent ARMGs operate tasks, where . |
Parameter | Definition |
---|---|
The ARMG assigned to task . | |
A 0–1 integer parameter that represents the conflict between the nodes selected in the middle of the moment of tasks and . When its value is 0, it is the middle time of ARMG operation in the RYACT, and when it is 1, it is the middle time of ARMG operation in the train carriage. | |
A 0–1 integer parameter that represents the middle of the moment to avoid conflict between tasks and . When its value is 0, it refers to the middle moment of the starting position, and when it is 1, it refers to the middle moment of the ending position. | |
The operation time of the ARMG for grabbing/releasing containers in the RYACT. | |
The operation time of the ARMG for grabbing/releasing containers on the train. | |
Operation task time of the ARMG for loading/unloading containers. | |
The minimum time interval between ARMG container tasks and . | |
The time the ARMG moves from the end position of container task to the start position of container task . | |
The moving time of the trolley during ARMG operation to complete task . | |
A positive number that is large enough, where . |
Variable | Definition |
---|---|
A binary decision variable that takes the value of if the ARMG starts container task immediately after completing container task ; otherwise, it takes the value of 0. | |
A binary decision variable that takes the value of if task is completed before task ; otherwise, it takes the value of 0, . | |
A real variable representing the start time of task . | |
A real variable representing the end time of task . | |
A real variable representing the midpoint of the moment to grab or release the container for the ARMG operating conflict task . |
Mode | Full Unloading and Full Loading (M1) | Synchronous Loading and Unloading (M2) | |||||
---|---|---|---|---|---|---|---|
Number of Tasks | |||||||
20 | 2830.07 | 2867.49 | 2.68 | 2654.36 | 2753.84 | 2.31 | |
40 | 2615.44 | 2661.64 | 4.57 | 2518.30 | 2566.37 | 4.70 | |
60 | 3557.49 | 3690.65 | 4.89 | 3417.90 | 3535.45 | 4.57 | |
80 | 4750.69 | 4993.32 | 6.27 | 4661.40 | 4910.53 | 5.48 | |
100 | 6009.37 | 6291.13 | 5.68 | 5949.71 | 6190.91 | 5.18 | |
120 | 7581.89 | 7724.49 | 8.25 | 7374.37 | 7593.14 | 7.08 | |
140 | 8620.06 | 8999.28 | 7.61 | 8473.79 | 8946.89 | 7.33 | |
160 | 9906.03 | 10,384.06 | 7.96 | 9736.71 | 9943.30 | 7.58 |
Number of Tasks | “Pre-Assign” Method (M2) | “Non-Pre-Assign” Method (M3) | ||||
---|---|---|---|---|---|---|
10 | 1623.18 | 0.11 | 1512.67 | −6.80 | 3.00 | 2627.27 |
11 | 1607.07 | 0.20 | 1510.14 | −6.03 | 35.89 | 17,845 |
12 | 1683.74 | 0.29 | 1683.74 | 0 | 157.65 | 54,262.06 |
13 | 1766.60 | 0.06 | 1766.60 | 0 | 1201.23 | 2,001,950 |
14 | 1850.19 | 0.72 | 1850.19 | 0 | 1201.40 | 166,761.11 |
15 | 1960.76 | 7.79 | 1960.76 | 0 | 1233.00 | 15,727.98 |
16 | 2094.00 | 1.74 | 2094.00 | 0 | 1202.82 | 69,027.59 |
17 | 2125.84 | 27.44 | — | — | >1200 | — |
18 | 2253.09 | 59.28 | — | — | >1200 | — |
19 | 2334.37 | 84.63 | — | — | >1200 | — |
20 | 2446.46 | 115.10 | — | — | >1200 | — |
40 | 2508.77 | 4.79 | 2508.77 | 0 | 10.58 | 120.88 |
60 | 3514.99 | 4.27 | 3506.47 | −0.24 | 9.66 | 126.23 |
80 | 4655.61 | 5.75 | 4601.04 | −1.17 | 12.50 | 117.39 |
100 | 5949.71 | 5.40 | 5946.44 | −0.05 | 11.80 | 118.52 |
120 | 7371.59 | 7.25 | 7286.47 | −1.15 | 15.50 | 113.79 |
140 | 8477 | 7.37 | 8448.33 | −0.34 | 15.74 | 113.57 |
160 | 9730.31 | 7.81 | 9380.31 | −3.60 | 17.62 | 125.61 |
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Chen, H.; Liu, W.; Oldache, M.; Pervez, A. Research on Train Loading and Unloading Mode and Scheduling Optimization in Automated Container Terminals. J. Mar. Sci. Eng. 2024, 12, 1415. https://doi.org/10.3390/jmse12081415
Chen H, Liu W, Oldache M, Pervez A. Research on Train Loading and Unloading Mode and Scheduling Optimization in Automated Container Terminals. Journal of Marine Science and Engineering. 2024; 12(8):1415. https://doi.org/10.3390/jmse12081415
Chicago/Turabian StyleChen, Hongbin, Wei Liu, Mehdi Oldache, and Amjad Pervez. 2024. "Research on Train Loading and Unloading Mode and Scheduling Optimization in Automated Container Terminals" Journal of Marine Science and Engineering 12, no. 8: 1415. https://doi.org/10.3390/jmse12081415