A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers
Abstract
:1. Introduction
- Pull-out buffer: Cars at any position in the car sequence can be removed and placed in the backward buffer, and then inserted into the appropriate position as the car sequence advances, so that cars can be moved to any position later in the sequence, and the advancement of the car sequence is limited by the number of cars allowed out of the column.
- Ring buffer: Multiple cars can be selected from the car sequence into the ring buffer, and cars from any position in the ring buffer can be put back into the sequence.
- Automated storage and retrieval system (AS/RS): Consisting of hundreds of buffer points, each buffer point can be accessed individually to generate the desired sequence of cars, and the flexibility of car sequencing is influenced by the number of buffer point locations.
- Parallel buffer: It consists of multiple parallel lanes (Figure 1), where cars from the upstream workshop are put into the parallel lanes, and then the first car of a lane is selected to join the downstream car production sequence according to the needs of the downstream workshop, and cars can only move in one direction in the lane, following the “FIFO” principle.
2. Literature Review
3. Problem Description and Mathematical Model
- 1.
- Each car takes the same amount of time to move one space in either lane of the buffer and can only move in one direction.
- 2.
- The buffer continues to function normally, regardless of fault conditions.
4. DCSPwB Decompositional Algorithm
4.1. Simple Rule-Based Heuristic Entry Algorithm
- 1.
- Select the lane with the best match.
- 2.
- Select the lane with the largest remaining capacity.
- 3.
- Select the lane that takes the shortest amount of time to enter the buffers.
Algorithm 1: Heuristic storage algorithm for simple rules |
4.2. Dynamic Genetic Algorithm
4.2.1. Encoding Method of Solution with Population Initialization
4.2.2. Selection
Algorithm 2: GA TS |
Input: Num of chromosomes in the population n, vector of chromosomes fitness values v, number of parental chromosomes m. return idx |
4.2.3. Dynamic Crossover Algorithm
4.2.4. Dynamic Mutation Algorithm
4.3. Greedy Algorithm for Postponed Car Release
5. Experiments and Results
5.1. Dataset
5.2. Experimental and Computational Results
5.3. The Effect of Buffer Capacity on Car Resequence
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Car Type | A | B | C | D | |
---|---|---|---|---|---|
✓ | ✓ | ||||
✓ | ✓ | ✓ | |||
Amount | 2 | 1 | 1 | 1 |
N | Total number of cars, index i. |
O | Collection of options, index o. |
L | Number of lanes in the buffer, index l. |
V | Capacity per lane. |
Option weights. | |
A continuous sequence of cars, some of which require the option o. | |
The maximum number of cars with option o allowed in a continuous sequence of cars . | |
Capacity constraint, i.e., the maximum number of cars with option o allowed in a continuous sequence of cars . | |
Binary variable: 1, if the car sequence starting from position j satisfies the constraint , 0, otherwise. | |
M | Scaling for (). |
Binary variables: 1, if car i is in lane l, 0, otherwise. | |
Binary variables: 1, if car i is in position j of the sequence, 0, otherwise. | |
Large integers. | |
Binary variables: 1, if car i needs option o, 0, otherwise. | |
The time it takes for a car to move one space in the buffer lane. | |
Time it takes for a car to enter the buffer lane l. | |
Time it takes for a car to exit from the buffer lane l. |
Order of Entering the Car | Car Type | |||
---|---|---|---|---|
1 | K1 | ✓ | ||
2 | K2 | ✓ | ✓ | |
3 | K2 | ✓ | ✓ | |
4 | K1 | ✓ | ||
… | … | … | … | … |
22 | K3 | ✓ | ||
23 | K1 | ✓ | ||
… | … | … | … | … |
Parameters | Value | Unit |
---|---|---|
L | 6 | |
V | 10 | |
9 | s | |
[18, 12, 6, 0, 12, 18] | s | |
[18, 12, 6, 0, 12, 18] | s |
Example | VoiP | GDA | PGDA | GA | DGA | ||||
---|---|---|---|---|---|---|---|---|---|
I_60 | 15.6 | 13.1 | 1.2 | 8.3 | 1.8 | 5.6 | 2.2 | 5.1 | 2.2 |
I_120 | 29.1 | 24.3 | 2.3 | 9.3 | 2.9 | 12.2 | 3.5 | 10.1 | 3.5 |
I_180 | 43 | 38.9 | 3.4 | 14.1 | 4.0 | 19.1 | 4.6 | 19.5 | 4.8 |
I_240 | 57.4 | 53.7 | 4.5 | 22.1 | 5.1 | 27.4 | 6.3 | 25.2 | 6.2 |
I_300 | 73.7 | 71.2 | 5.5 | 34.5 | 6.1 | 39.6 | 7.3 | 37.8 | 7.6 |
I_360 | 89.3 | 85.6 | 6.6 | 46.9 | 7.1 | 50.6 | 8.7 | 48.1 | 8.8 |
II_60 | 13.6 | 13 | 1.2 | 1.2 | 1.9 | 3.2 | 2.3 | 2.8 | 2.2 |
II_120 | 24.8 | 24.8 | 2.1 | 4.2 | 3.0 | 5.6 | 3.4 | 7.6 | 3.5 |
II_180 | 38.2 | 38.8 | 3.1 | 8.6 | 4.2 | 12.6 | 4.9 | 13.2 | 4.7 |
II_240 | 52.1 | 53.4 | 4.1 | 14.2 | 5.6 | 20.8 | 6.1 | 22.8 | 6.3 |
II_300 | 67.1 | 69.5 | 5.2 | 19.8 | 6.9 | 26.2 | 7.4 | 28.1 | 7.5 |
II_360 | 80.7 | 81 | 6.1 | 25.4 | 8.1 | 33.4 | 9.1 | 35.8 | 8.8 |
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Zhang, H.; Ding, W. A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers. Appl. Sci. 2023, 13, 7336. https://doi.org/10.3390/app13127336
Zhang H, Ding W. A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers. Applied Sciences. 2023; 13(12):7336. https://doi.org/10.3390/app13127336
Chicago/Turabian StyleZhang, Haida, and Wensi Ding. 2023. "A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers" Applied Sciences 13, no. 12: 7336. https://doi.org/10.3390/app13127336
APA StyleZhang, H., & Ding, W. (2023). A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers. Applied Sciences, 13(12), 7336. https://doi.org/10.3390/app13127336