Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows
Abstract
:1. Introduction
2. Literature Review
2.1. The Truck–Trailer Routing Problem for Prefabricated Components
2.2. Existing Solution Methods for the TTRP
3. Problem Description and Model Formulation
3.1. Problem Description
3.2. The Mathematical Formulation for the CTTRPTW
3.2.1. Fixed Costs
3.2.2. Fuel Consumption Costs
3.2.3. Carbon Emissions Costs
3.2.4. Customer Satisfaction with Soft Time Windows
4. Solution Algorithm
5. Computational Experiments
5.1. Description of the Test Instances
5.2. Computational Results and Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Reference | Solution Algorithm | Constraints | Carbon | ||
---|---|---|---|---|---|
C | T | O | |||
Chao [15] | Tabu search algorithm | ✔ | |||
Tan et al. [16] | Evolutionary algorithm | ✔ | |||
Lin et al. [4] | Simulated annealing algorithm | ✔ | |||
Niu et al. [17] | Particle swarm optimization algorithm | ✔ | |||
Regnier-Coudert et al. [6] | Greedy algorithm | ✔ | |||
Li et al. [18] | Benders decomposition algorithm | ✔ | ✔ | ||
Bartolini and Schneider [19] | Branch-and-cut algorithm | ✔ | |||
Wang et al. [11] | Adaptive large neighborhood search algorithm | ✔ | ✔ | ||
Davila-Pena et al. [20] | Clarke–Wright algorithm | ✔ | |||
Current paper | Tabu search and simulated annealing algorithm | ✔ | ✔ | ✔ |
Notations | Definitions |
---|---|
Decision Variables | |
) (1 if used, 0 otherwise) | |
) (1 if used, 0 otherwise) | |
Binary variable, indicating whether truck k is used (1 if used, 0 otherwise) | |
Integer variable, representing the number of deliveries made to node j | |
Continuous decision variable, representing the transported load on arc (i,j) in truck k | |
Parameters | |
Departure costs for the driver | |
Wages paid to the driver | |
Driver’s reward for the number of successful deliveries | |
Fuel consumption rate per unit distance when an empty truck is hauling an empty trailer (liters/km) | |
Fuel consumption rate per unit distance of an empty truck running alone (liters/km) | |
Fuel consumption per unit distance of full load complete vehicles (truck + trailer) (liters/km) | |
Fuel consumption per unit distance of full load complete trucks without trailers (liters/km) | |
Effective fuel consumption rate of vehicles on arc (i,j) | |
Rated load capacity of a truck without a trailer (tons) | |
Rated load capacity of a vehicle (truck + trailer) (tons) | |
Unit fuel consumption costs (yuan/liter) | |
Unit carbon emissions costs (yuan/kg) | |
Carbon emissions produced per unit of fuel consumed | |
Unit penalty costs for delays in the delivery | |
The time for truck k arriving at the construction site s | |
Demand at node i |
No. | Coordinate (X, Y) | Demand | Earliest Time | Latest Time | Customer Type |
---|---|---|---|---|---|
0 | 35, 54 | - | - | - | - |
1 | 45, 68 | 10 | 912 | 967 | 1 |
2 | 45, 70 | 30 | 825 | 870 | 1 |
3 | 42, 66 | 10 | 65 | 146 | 1 |
4 | 42, 68 | 10 | 727 | 782 | 1 |
5 | 42, 65 | 10 | 15 | 67 | 1 |
6 | 40, 69 | 20 | 621 | 702 | 0 |
7 | 40, 66 | 20 | 170 | 225 | 1 |
8 | 38, 68 | 20 | 255 | 324 | 0 |
9 | 38, 70 | 10 | 534 | 605 | 0 |
10 | 35, 66 | 10 | 357 | 410 | 0 |
11 | 35, 69 | 10 | 448 | 505 | 0 |
12 | 30, 70 | 20 | 652 | 721 | 0 |
13 | 27, 60 | 30 | 30 | 92 | 0 |
14 | 27, 70 | 10 | 567 | 620 | 0 |
15 | 25, 65 | 40 | 384 | 429 | 0 |
16 | 25, 70 | 40 | 475 | 528 | 1 |
17 | 23, 62 | 20 | 99 | 148 | 0 |
18 | 20, 60 | 20 | 179 | 254 | 1 |
19 | 20, 65 | 10 | 278 | 345 | 1 |
20 | 30, 50 | 10 | 10 | 73 | 0 |
21 | 30, 52 | 20 | 914 | 965 | 0 |
22 | 28, 52 | 20 | 812 | 883 | 0 |
23 | 28, 55 | 10 | 732 | 777 | 0 |
24 | 25, 50 | 10 | 65 | 144 | 0 |
25 | 25, 52 | 40 | 169 | 224 | 0 |
Type | Problems | Characteristic |
---|---|---|
R | R1 | Customers are disperses with narrow time windows, limited vehicle capacities, and short route durations. |
R2 | Customers are disperses with wider time windows, larger vehicle capacities, and longer route durations. | |
C | C1 | Customers are clustered with narrow time windows, limited vehicle capacities, and short route durations. |
C2 | Customers are clustered with wider time windows, larger vehicle capacities, and longer route durations. | |
RC | RC1 | A mix of dispersed and clustered customers, characterized by narrow time windows, limited vehicle capacities, and short route durations. |
RC2 | A mix of dispersed and clustered customers, characterized by narrow time windows, limited vehicle capacities, and short route durations. |
Total Costs | Carbon Emissions Costs | Solution Time (Seconds) | |
---|---|---|---|
Initial solution | 63,311.144 | 9102.299 | 0.365 |
CPLEX | 52,566.208 | 7120.329 | 0.498 |
SA | 62,826.109 | 9002.213 | 0.330 |
TS | 60,936.506 | 8612.295 | 0.366 |
DASA-TS | 52,393.315 | 6909.462 | 0.306 |
Original Problem | CPLEX | DASA-TS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Case | VCs | TCs | Total Costs | Total Carbon Emissions Costs | Solution Time (Seconds) | Total Costs | Total Carbon Emissions Costs | Solution Time (Seconds) | ||
Test 1 (25) | 1 | RC101 | 10 | 15 | 165,967.8361 | 27,020.0414 | 0.004 | 165,082.3034 | 26,769.6817 | 0.290 |
2 | RC101 | 15 | 10 | 166,253.2252 | 26,909.2786 | 0.004 | 164,213.5527 | 27,015.2373 | 0.274 | |
3 | RC201 | 10 | 15 | 167,080.2769 | 27,265.3359 | 0.005 | 166,784.0610 | 27,240.8108 | 0.234 | |
4 | RC201 | 15 | 10 | 168,250.7589 | 26,754.0413 | 0.005 | 168,413.3385 | 26,267.7567 | 0.213 | |
Test 2 (50) | 5 | RC101 | 20 | 30 | 487,822.3078 | 92,160.1587 | 0.006 | 473,366.3021 | 91,477.1735 | 0.372 |
6 | RC101 | 20 | 30 | 484,050.9021 | 93,906.4925 | 0.680 | 479,588.2613 | 92,397.5703 | 0.413 | |
7 | RC201 | 20 | 30 | 474,065.1031 | 89,321.3705 | 0.705 | 473,366.3021 | 88,373.1735 | 0.376 | |
8 | RC201 | 37 | 13 | 498,091.0120 | 95,898.1453 | 0.604 | 497,410.7872 | 92,075.2418 | 0.432 | |
Test 3 (100) | 9 | RC101 | 40 | 60 | 1,711,778.8260 | 321,391.4460 | 10.307 | 1,709,710.6087 | 318,306.7923 | 6.631 |
10 | RC101 | 60 | 40 | 2,431,076.3334 | 449,232.2015 | 8.135 | 2,289,416.4772 | 435,534.6520 | 6.583 | |
11 | RC201 | 40 | 60 | 1,785,390.2267 | 337,956.7135 | 12.307 | 1,751,653.6209 | 323,420.5884 | 7.598 | |
12 | RC201 | 60 | 40 | 2,200,800.9498 | 413,090.6721 | 9.110 | 2,061,096.9005 | 394,213.6461 | 8.309 |
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Zhou, J.; Du, Q.; Chen, Q.; Ye, Z.; Bai, L.; Li, Y. Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows. Mathematics 2025, 13, 1210. https://doi.org/10.3390/math13071210
Zhou J, Du Q, Chen Q, Ye Z, Bai L, Li Y. Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows. Mathematics. 2025; 13(7):1210. https://doi.org/10.3390/math13071210
Chicago/Turabian StyleZhou, Jiajie, Qiang Du, Qian Chen, Zhongnan Ye, Libiao Bai, and Yi Li. 2025. "Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows" Mathematics 13, no. 7: 1210. https://doi.org/10.3390/math13071210
APA StyleZhou, J., Du, Q., Chen, Q., Ye, Z., Bai, L., & Li, Y. (2025). Low-Carbon Transport for Prefabricated Buildings: Optimizing Capacitated Truck–Trailer Routing Problem with Time Windows. Mathematics, 13(7), 1210. https://doi.org/10.3390/math13071210