A Proposal and Analysis of New Realistic Sets of Benchmark Instances for Vehicle Routing Problems with Asymmetric Costs
Abstract
:1. Introduction
2. Literature Review
2.1. VRP with Asymmetric Costs
2.2. VRP and Map APIs
3. New Sets of Benchmark Instances for the ACVRP
3.1. Existing Benchmark Instances
3.2. New Benchmark Instances
3.2.1. Territory
3.2.2. Depot Locations
3.2.3. Customer Locations
3.2.4. Vehicle Capacities
3.2.5. Weight and Volume Per Delivery
3.2.6. Dimension and Distance from Depot
3.2.7. Cost Matrix
3.2.8. Solution Methods and Results
4. Analysis on Air Distance, Road Distance and Road Time
4.1. Closeness Deceived by Air Distance
4.2. Assymetric Costs
4.3. Air Distance to Road Distance and Road Time Multiplier
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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To | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Distance between Coordinates | Map API Used | ||||||||||||||||||
(a) Air Distance (Meters) | (b) Road Distance (Meters) | (c) Road Time (Seconds) | |||||||||||||||||
A | B | C | D | E | F | A | B | C | D | E | F | A | B | C | D | E | F | ||
From | A | 0 | 2348 | 2494 | 1261 | 3,72 | 2206 | 0 | 3109 | 5904 | 2528 | 680 | 6331 | 0 | 619 | 1311 | 396 | 228 | 1364 |
B | 2348 | 0 | 4467 | 1861 | 2004 | 4151 | 3151 | 0 | 8478 | 4348 | 2429 | 8905 | 560 | 0 | 1755 | 679 | 397 | 1808 | |
C | 2494 | 4467 | 0 | 3749 | 2665 | 317 | 4247 | 6836 | 0 | 5904 | 4407 | 427 | 619 | 1101 | 0 | 881 | 709 | 53 | |
D | 1261 | 1861 | 3749 | 0 | 1207 | 3466 | 2223 | 4221 | 6928 | 0 | 1792 | 7354 | 648 | 917 | 1543 | 0 | 520 | 1596 | |
E | 372 | 2004 | 2665 | 1207 | 0 | 2362 | 722 | 2429 | 6049 | 1919 | 0 | 6476 | 152 | 430 | 1351 | 265 | 0 | 1404 | |
F | 2206 | 4151 | 317 | 3466 | 2362 | 0 | 4674 | 7263 | 427 | 6331 | 4834 | 0 | 692 | 1177 | 74 | 942 | 782 | 0 |
City | Depot | Customer Location | Range within | Dimension | Name | Avg Time (DV1M5, Sec) * | BKS (DV1M5) ** |
---|---|---|---|---|---|---|---|
Seoul (S) | UDC (L) | Residential Complex (A) | 2.5 km (S) | 100 | SLAS100 | 10 | 76,358 |
5 km (M) | 250 | SLAM250 | 58 | 182,120 | |||
10 km (L) | 500 | SLAL500 | 149 | 594,420 | |||
Restaurant Business (F) | 2.5 km (S) | 100 | SLFS100 | 11 | 39,488 | ||
5 km (M) | 250 | SLFM250 | 66 | 135,313 | |||
10 km (L) | 500 | SLFL500 | 149 | 425,651 | |||
Convenience Store (C) | 2.5 km (S) | 50 | SLCS50 | 6 | 47,043 | ||
5 km (M) | 75 | SLCM75 | 7 | 75,004 | |||
10 km (L) | 100 | SLCL100 | 11 | 180,753 | |||
Postal Hub (P) | Residential Complex (A) | 2.5 km (S) | 100 | SPAS100 | 11 | 115,582 | |
5 km (M) | 250 | SPAM250 | 57 | 251,667 | |||
10 km (L) | 500 | SPAL500 | 139 | 729,496 | |||
Restaurant Business (F) | 2.5 km (S) | 100 | SPFS100 | 11 | 47,119 | ||
5 km (M) | 250 | SPFM250 | 62 | 168,662 | |||
10 km (L) | 500 | SPFL500 | 146 | 480,624 | |||
Convenience Store (C) | 2.5 km (S) | 50 | SPCS50 | 6 | 71,011 | ||
5 km (M) | 75 | SPCM75 | 7 | 142,406 | |||
10 km (L) | 100 | SPCL100 | 11 | 245,746 | |||
Large-sized Mall (S) | Residential Complex (A) | 2.5 km (S) | 100 | SSAS100 | 11 | 73,950 | |
5 km (M) | 250 | SSAM250 | 37 | 230,226 | |||
10 km (L) | 500 | SSAL500 | 135 | 561,442 | |||
Restaurant Business (F) | 2.5 km (S) | 100 | SSFS100 | 11 | 62,644 | ||
5 km (M) | 250 | SSFM250 | 62 | 180,621 | |||
10 km (L) | 500 | SSFL500 | 143 | 492,579 | |||
Convenience Store (C) | 2.5 km (S) | 50 | SSCS50 | 6 | 40,758 | ||
5 km (M) | 75 | SSCM75 | 7 | 109,477 | |||
10 km (L) | 100 | SSCL100 | 8 | 194,559 | |||
Busan (B) | UDC(L) | Residential Complex (A) | 20 km (S) | 100 | BLAS100 | 11 | 197,486 |
30 km (M) | 250 | BLAM250 | 71 | 612,256 | |||
40 km (L) | 500 | BLAL500 | 172 | 1,142,420 | |||
Restaurant Business (F) | 20 km (S) | 100 | BLFS100 | 10 | 199,864 | ||
30 km (M) | 250 | BLFM250 | 71 | 524,744 | |||
40 km (L) | 500 | BLFL500 | 178 | 938,741 | |||
Convenience Store (C) | 20 km (S) | 50 | BLCS50 | 5 | 180,941 | ||
30 km (M) | 75 | BLCM75 | 9 | 269,538 | |||
40 km (L) | 100 | BLCL100 | 10 | 322,354 | |||
Postal Hub (P) | Residential Complex (A) | 15 km (S) | 100 | BPAS100 | 11 | 190,075 | |
20 km (M) | 250 | BPAM250 | 44 | 467,338 | |||
25 km (L) | 500 | BPAL500 | 191 | 904,537 | |||
Restaurant Business (F) | 15 km (S) | 100 | BPFS100 | 11 | 193,485 | ||
20 km (M) | 250 | BPFM250 | 70 | 430,466 | |||
25 km (L) | 500 | BPFL500 | 168 | 694,761 | |||
Convenience Store (C) | 15 km (S) | 50 | BPCS50 | 5 | 158,240 | ||
20 km (M) | 75 | BPCM75 | 9 | 252,686 | |||
25 km (L) | 100 | BPCL100 | 11 | 289,195 | |||
Large-sized Mall (S) | Residential Complex (A) | 5 km (S) | 100 | BSAS100 | 10 | 100,103 | |
10 km (M) | 250 | BSAM250 | 42 | 266,803 | |||
15 km (L) | 500 | BSAL500 | 161 | 609,610 | |||
Restaurant Business (F) | 5 km (S) | 100 | BSFS100 | 11 | 86,652 | ||
10 km (M) | 250 | BSFM250 | 55 | 257,710 | |||
15 km (L) | 500 | BSFL500 | 142 | 471,597 | |||
Convenience Store (C) | 5 km (S) | 50 | BSCS50 | 5 | 89,989 | ||
10 km (M) | 75 | BSCM75 | 9 | 136,604 | |||
15 km (L) | 100 | BSCL100 | 11 | 217,444 |
Cost | Vehicle | Capacity | Multiple | Name |
---|---|---|---|---|
Distance (D) | 1-ton trucks (V1) | 5 cubic meters | 5 times (M5) | DV1M5 |
10 times (M10) | DV1M10 | |||
20 times (M20) | DV1M20 | |||
2.5-ton trucks (V2) | 12.5 cubic meters | 5 times (M5) | DV2M5 | |
10 times (M10) | DV2M10 | |||
20 times (M20) | DV2M20 | |||
Time (T) | 1-ton trucks (V1) | 5 cubic meters | 5 times (M5) | TV1M5 |
10 times (M10) | TV1M10 | |||
20 times (M20) | TV1M20 | |||
2.5-ton trucks (V2) | 12.5 cubic meters | 5 times (M5) | TV2M5 | |
10 times (M10) | TV2M10 | |||
20 times (M20) | TV2M20 |
Benchmark | Number | Dimensions | Depot and Customer Nodes | Road Distance | Road Time | Reported BKS *** |
---|---|---|---|---|---|---|
Fischetti | 32 * | 34~74 | Real data of pharmaceutical product delivery | O | X | O |
De Smet | 10 ** | 50~2750 | Administrative districts | O | O | X |
Rodríguez | 2700 | 50~500 | Random, grid, and radial | O | X | X |
Proposed instances | 648 | 50~500 | Real data of UDCs, postal hubs, large malls, residential complexes, restaurants, and convenience stores | O | O | O |
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Lee, K.; Chae, J. A Proposal and Analysis of New Realistic Sets of Benchmark Instances for Vehicle Routing Problems with Asymmetric Costs. Appl. Sci. 2021, 11, 4790. https://doi.org/10.3390/app11114790
Lee K, Chae J. A Proposal and Analysis of New Realistic Sets of Benchmark Instances for Vehicle Routing Problems with Asymmetric Costs. Applied Sciences. 2021; 11(11):4790. https://doi.org/10.3390/app11114790
Chicago/Turabian StyleLee, Keyju, and Junjae Chae. 2021. "A Proposal and Analysis of New Realistic Sets of Benchmark Instances for Vehicle Routing Problems with Asymmetric Costs" Applied Sciences 11, no. 11: 4790. https://doi.org/10.3390/app11114790