Research Article
An Optimization Method for the Train Service Network Design Problem
Table 11
Travel path of each shipment.
(a) |
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| | 1 | - | 1-2 | 1-2-3 | 1-4 | 1-2-3-5 | 1-2-3-5-6 | 1-2-3-8-7 | 1-2-3-8 | 1-2-3-8-9 | 1-4-10 | 1-2-3-5-6-11 | | 2 | 2-1 | - | 2-3 | 2-3-4 | 2-3-5 | 2-3-5-6 | 2-3-8-7 | 2-3-8 | 2-3-8-9 | 2-3-4-10 | 2-3-5-6-11 | | 3 | 3-2-1 | 3-2 | - | 3-4 | 3-5 | 3-5-6 | 3-8-7 | 3-8 | 3-8-9 | 3-4-10 | 3-5-6-11 | | 4 | 4-1 | 4-3-2 | 4-3 | - | 4-3-5 | 4-3-5-6 | 4-3-8-7 | 4-3-8 | 4-10-9 | 4-10 | 4-3-5-6-11 | | 5 | 5-3-2-1 | 5-3-2 | 5-3 | 5-3-4 | - | 5-6 | 5-6-7 | 5-6-7-8 | 5-6-7-8-9 | 5-3-4-10 | 5-6-11 | | 6 | 6-5-3-2-1 | 6-5-3-2 | 6-5-3 | 6-5-3-4 | 6-5 | - | 6-7 | 6-7-8 | 6-7-8-9 | 6-7-8-9-10 | 6-11 | | 7 | 7-8-3-2-1 | 7-8-3-2 | 7-8-3 | 7-8-3-4 | 7-6-5 | 7-6 | - | 7-8 | 7-8-9 | 7-8-9-10 | 7-11 | | 8 | 8-3-2-1 | 8-3-2 | 8-3 | 8-3-4 | 8-7-6-5 | 8-7-6 | 8-7 | - | 8-9 | 8-9-10 | 8-14-13-11 | | 9 | 9-8-3-2-1 | 9-8-3-2 | 9-8-3 | 9-10-4 | 9-8-7-6-5 | 9-8-7-6 | 9-8-7 | 9-8 | - | 9-10 | 9-8-14-13-11 | | 10 | 10-4-1 | 10-4-3-2 | 10-4-3 | 10-4 | 10-4-3-5 | 10-9-8-7-6 | 10-9-8-7 | 10-9-8 | 10-9 | - | 10-9-8-14-13-11 | | 11 | 11-7-8-3-2-1 | 11-7-8-3-2 | 11-7-8-3 | 11-7-8-3-4 | 11-6-5 | 11-6 | 11-7 | 11-7-8 | 11-7-8-9 | 11-7-8-9-10 | - | | 12 | 12-13-14-8-3-2-1 | 12-13-14-8-3-2 | 12-13-14-8-3 | 12-13-14-8-3-4 | 12-11-6-5 | 12-11-6 | 12-11-7 | 12-13-14-8 | 12-13-14-15-9 | 12-13-14-15-9-10 | 12-11 | | 13 | 13-14-8-3-2-1 | 13-14-8-3-2 | 13-14-8-3 | 13-14-8-3-4 | 13-11-6-5 | 13-11-6 | 13-11-7 | 13-14-8 | 13-14-15-9 | 13-14-15-9-10 | 13-11 | | 14 | 14-8-3-2-1 | 14-8-3-2 | 14-8-3 | 14-8-3-4 | 14-13-11-6-5 | 14-13-11-6 | 14-8-7 | 14-8 | 14-15-9 | 14-15-9-10 | 14-13-11 | | 15 | 15-14-8-3-2-1 | 15-14-8-3-2 | 15-14-8-3 | 15-9-10-4 | 15-14-13-11-6-5 | 15-14-13-11-6 | 15-14-8-7 | 15-14-8 | 15-9 | 15-9-10 | 15-14-13-11 | | 16 | 16-15-14-8-3-2-1 | 16-15-14-8-3-2 | 16-15-14-8-3 | 16-15-9-10-4 | 16-15-14-13-11-6-5 | 16-15-14-13-11-6 | 16-15-14-8-7 | 16-15-14-8 | 16-15-9 | 16-15-9-10 | 16-15-14-13-11 | | 17 | 17-14-8-3-2-1 | 17-14-8-3-2 | 17-14-8-3 | 17-14-8-3-4 | 17-14-13-11-6-5 | 17-14-13-11-6 | 17-14-8-7 | 17-14-8 | 17-15-9 | 17-15-9-10 | 17-14-13-11 | | 18 | 18-12-13-14-8-3-2-1 | 18-12-13-14-8-3-2 | 18-12-13-14-8-3 | 18-12-13-14-8-3-4 | 18-12-11-6-5 | 18-12-11-6 | 18-12-11-7 | 18-12-13-14-8 | 18-12-13-14-15-9 | 18-12-13-14-15-9-10 | 18-12-11 | | 19 | 19-17-14-8-3-2-1 | 19-17-14-8-3-2 | 19-17-14-8-3 | 19-17-14-8-3-4 | 19-17-14-13-11-6-5 | 19-17-14-13-11-6 | 19-17-14-8-7 | 19-17-14-8 | 19-17-15-9 | 19-17-15-9-10 | 19-17-14-13-11 | | 20 | 20-17-14-8-3-2-1 | 20-17-14-8-3-2 | 20-17-14-8-3 | 20-17-14-8-3-4 | 20-17-14-13-11-6-5 | 20-17-14-13-11-6 | 20-17-14-8-7 | 20-17-14-8 | 20-17-15-9 | 20-17-15-9-10 | 20-17-14-13-11 | | 21 | 21-17-14-8-3-2-1 | 21-17-14-8-3-2 | 21-17-14-8-3 | 21-17-14-8-3-4 | 21-17-14-13-11-6-5 | 21-17-14-13-11-6 | 21-17-14-8-7 | 21-17-14-8 | 21-17-15-9 | 21-17-15-9-10 | 21-17-14-13-11 |
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(b) |
| | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| | 1 | 1-2-3-8-14-13-12 | 1-2-3-8-14-13 | 1-2-3-8-14 | 1-2-3-8-14-15 | 1-2-3-8-14-15-16 | 1-2-3-8-14-17 | 1-2-3-8-14-13-12-18 | 1-2-3-8-14-17-19 | 1-2-3-8-14-17-20 | 1-2-3-8-14-17-21 | | 2 | 2-3-8-14-13-12 | 2-3-8-14-13 | 2-3-8-14 | 2-3-8-14-15 | 2-3-8-14-15-16 | 2-3-8-14-17 | 2-3-8-14-13-12-18 | 2-3-8-14-17-19 | 2-3-8-14-17-20 | 2-3-8-14-17-21 | | 3 | 3-8-14-13-12 | 3-8-14-13 | 3-8-14 | 3-8-14-15 | 3-8-14-15-16 | 3-8-14-17 | 3-8-14-13-12-18 | 3-8-14-17-19 | 3-8-14-17-20 | 3-8-14-17-21 | | 4 | 4-3-8-14-13-12 | 4-3-8-14-13 | 4-3-8-14 | 4-3-8-14-15 | 4-10-9-15-16 | 4-3-8-14-17 | 4-3-8-14-13-12-18 | 4-3-8-14-17-19 | 4-3-8-14-17-20 | 4-3-8-14-17-21 | | 5 | 5-6-11-12 | 5-6-11-13 | 5-6-11-13-14 | 5-6-11-13-14-15 | 5-6-11-13-14-15-16 | 5-6-11-13-14-17 | 5-6-11-12-18 | 5-6-11-13-14-17-19 | 5-6-11-13-14-17-20 | 5-6-11-13-14-17-21 | | 6 | 6-11-12 | 6-11-13 | 6-11-13-14 | 6-11-13-14-15 | 6-11-13-14-15-16 | 6-11-13-14-17 | 6-11-12-18 | 6-11-13-14-17-19 | 6-11-13-14-17-20 | 6-11-13-14-17-21 | | 7 | 7-11-12 | 7-11-13 | 7-8-14 | 7-8-14-15 | 7-8-14-15-16 | 7-8-14-17 | 7-11-12-18 | 7-8-14-17-19 | 7-8-14-17-20 | 7-11-13-14-17-21 | | 8 | 8-14-13-12 | 8-14-13 | 8-14 | 8-14-15 | 8-14-15-16 | 8-14-17 | 8-14-13-12-18 | 8-14-17-19 | 8-14-17-20 | 8-14-17-21 | | 9 | 9-8-14-13-12 | 9-8-14-13 | 9-15-14 | 9-15 | 9-15-16 | 9-15-17 | 9-8-14-13-12-18 | 9-15-17-19 | 9-15-17-20 | 9-8-14-17-21 | | 10 | 10-9-8-14-13-12 | 10-9-8-14-13 | 10-9-15-14 | 10-9-15 | 10-9-15-16 | 10-9-15-17 | 10-9-8-14-13-12-18 | 10-9-15-17-19 | 10-9-15-17-20 | 10-9-8-14-17-21 | | 11 | 11-12 | 11-13 | 11-13-14 | 11-13-14-15 | 11-13-14-15-16 | 11-13-14-17 | 11-12-18 | 11-13-14-17-19 | 11-13-14-17-20 | 11-13-14-17-21 | | 12 | - | 12-13 | 12-13-14 | 12-13-14-15 | 12-13-14-15-16 | 12-13-14-17 | 12-18 | 12-13-14-17-19 | 12-13-14-17-20 | 12-13-14-17-21 | | 13 | 13-12 | - | 13-14 | 13-14-15 | 13-14-15-16 | 13-14-17 | 13-12-18 | 13-14-17-19 | 13-14-17-20 | 13-14-17-21 | | 14 | 14-13-12 | 14-13 | - | 14-15 | 14-15-16 | 14-17 | 14-13-12-18 | 14-17-19 | 14-17-20 | 14-17-21 | | 15 | 15-14-13-12 | 15-14-13 | 15-14 | - | 15-16 | 15-17 | 15-14-13-12-18 | 15-17-19 | 15-17-20 | 15-17-21 | | 16 | 16-15-14-13-12 | 16-15-14-13 | 16-15-14 | 16-15 | - | 16-15-17 | 16-15-14-13-12-18 | 16-15-17-19 | 16-15-17-20 | 16-15-17-21 | | 17 | 17-14-13-12 | 17-14-13 | 17-14 | 17-15 | 17-15-16 | - | 17-19-18 | 17-19 | 17-20 | 17-21 | | 18 | 18-12 | 18-12-13 | 18-12-13-14 | 18-12-13-14-15 | 18-12-13-14-15-16 | 18-19-17 | - | 18-19 | 18-19-20 | 18-19-17-21 | | 19 | 19-17-14-13-12 | 19-17-14-13 | 19-17-14 | 19-17-15 | 19-17-15-16 | 19-17 | 19-18 | - | 19-20 | 19-17-21 | | 20 | 20-17-14-13-12 | 20-17-14-13 | 20-17-14 | 20-17-15 | 20-17-15-16 | 20-17 | 20-19-18 | 20-19 | - | 20-21 | | 21 | 21-17-14-13-12 | 21-17-14-13 | 21-17-14 | 21-17-15 | 21-17-15-16 | 21-17 | 21-17-19-18 | 21-17-19 | 21-20 | - |
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