Journal of Advanced Transportation

Research Article

An Exact Solution Approach for the Bus Line Planning Problem with Integrated Passenger Routing

Table 2

Optimal solutions for 3 to 14 lines with at most 8 nodes per line.
3 lines4 lines5 lines
Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 12Line 1: 1, 2, 3, 6, 8, 10, 14, and 13
Line 2: 5, 4, 6, 15, 7, 10, 14, and 13Line 2: 1, 2, 5, 4, 6, 8, 10, and 11Line 2: 1, 2, 3, 6, 15, 7, 10, and 11
Line 3: 2, 4, 12, 11, 10, 8, 15, and 9Line 3: 10, 7, 15, 6, 3, 2, 4, and 12Line 3: 1, 2, 5, 4, 6, 8, 10, and 11
 Line 4: 9, 15, 8, 10, 14, 13, 11, and 12Line 4: 2, 4, 12, 11, 10, 7, 15, and 9
  Line 5: 7, 15, 8, 6, 4, 12, 11, and 13
6 lines7 lines8 lines
Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13
Line 2: 1, 2, 3, 6, 15, 7, 10, and 14Line 2: 1, 2, 3, 6, 15, 7, 10, and 14Line 2: 1, 2, 3, 6, 15, 7, 10, and 14
Line 3: 1, 2, 5, 4, 6, 8, 10, and 14Line 3: 1, 2, 5, 4, 6, 8, 10, and 14Line 3: 1, 2, 5, 4, 6, 8, 10, and 14
Line 4: 3, 2, 5, 4, 6, 8, 15, and 7Line 4: 3, 2, 5, 4, 6, 8, 15, and 7Line 4: 3, 2, 5, 4, 6, 15, 7, and 10
Line 5: 5, 4, 12, 11, 10, 7, 15, and 9Line 5: 5, 4, 12, 11, 10, 7, 15, and 9Line 5: 5, 4, 12, 11, 10, 7, 15, and 9
Line 6: 1, 2, 4, 12, 11, 13, 14, and 10Line 6: 9, 15, 6, 3, 2, 4, 12, and 11Line 6: 9, 15, 6, 3, 2, 4, 12, and 11
 Line 7: 1, 2, 4, 12, 11, 13, 14, and 10Line 7: 1, 2, 4, 12, 11, 13, 14, and 10
  Line 8: 12, 4, 6, 8, 15, 7, 10, and 13
9 lines10 lines11 lines
Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13
Line 2: 1, 2, 3, 6, 15, 7, 10, and 13Line 2: 1, 2, 3, 6, 15, 7, 10, and 8Line 2: 1, 2, 3, 6, 15, 7, 10, and 8
Line 3: 1, 2, 3, 6, 15, and 9Line 3: 1, 2, 3, 6, 15, and 9Line 3: 1, 2, 3, 6, 15, and 9
Line 4: 12, 4, 2, 3, 6, 8, 10, and 14Line 4: 12, 4, 2, 3, 6, 8, 10, and 14Line 4: 12, 4, 2, 3, 6, 8, 10, and 14
Line 5: 1, 2, 5, 4, 6, 8, 10, and 11Line 5: 5, 4, 6, 8, 10, 11, 13, and 14Line 5: 5, 4, 6, 8, 10, 11, 13, and 14
Line 6: 3, 2, 5, 4, 6, 8, 15, and 7Line 6: 1, 2, 5, 4, 6, 15, 7, and 10Line 6: 1, 2, 5, 4, 6, 15, 7, and 10
Line 7: 5, 4, 12, 11, 10, 7, 15, and 9Line 7: 5, 4, 12, 11, 10, 7, 15, and 9Line 7: 5, 4, 12, 11, 10, 7, 15, and 9
Line 8: 9, 15, 8, 6, 4, 12, 11, and 10Line 8: 3, 2, 5, 4, 6, 8, 15, and 9Line 8: 3, 2, 5, 4, 6, 15, and 9
Line 9: 1, 2, 4, 12, 11, 13, 14, and 10Line 9: 12, 4, 6, 8, 15, 7, 10, and 14Line 9: 9, 15, 8, 6, 4, 12, 11, and 10
 Line 10: 1, 2, 4, 12, 11, 13, 10, and 7Line 10: 12, 4, 6, 8, 15, 7, 10, and 14
  Line 11: 1, 2, 4, 12, 11, 13, 10, and 7
12 lines13 lines14 lines
Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13Line 1: 1, 2, 3, 6, 8, 10, 11, and 13
Line 2: 1, 2, 3, 6, 15, 7, 10, and 8Line 2: 1, 2, 3, 6, 15, 7, 10, and 8Line 2: 1, 2, 3, 6, 15, 7, 10, and 8
Line 3: 1, 2, 3, 6, 15, and 9Line 3: 1, 2, 3, 6, 15, and 9Line 3: 1, 2, 3, 6, 15, and 9
Line 4: 1, 2, 3, 6, 8, 10, 14, and 13Line 4: 1, 2, 3, 6, 8, 10, 14, and 13Line 4: 1, 2, 3, 6, 8, 10, 14, and 13
Line 5: 2, 5, 4, 6, 8, 10, 11, and 13Line 5: 1, 2, 5, 4, 6, 8, 10, and 11Line 5: 1, 2, 5, 4, 6, 8, 10, and 11
Line 6: 1, 2, 5, 4, 6, 15, 7, and 10Line 6: 1, 2, 5, 4, 6, 15, 7, and 10Line 6: 1, 2, 5, 4, 6, 15, 7, and 10
Line 7: 5, 4, 12, 11, 10, 7, 15, and 9Line 7: 5, 4, 12, 11, 10, 7, 15, and 9Line 7: 5, 4, 12, 11, 10, 7, 15, and 9
Line 8: 3, 2, 5, 4, 6, 15, and 9Line 8: 3, 2, 5, 4, 6, 15, and 9Line 8: 3, 2, 5, 4, 6, 15, and 9
Line 9: 9, 15, 8, 6, 4, 12, 11, and 10Line 9: 9, 15, 8, 6, 4, 12, 11, and 10Line 9: 7, 10, 11, 12, 4, 6, 15, and 9
Line 10: 12, 4, 6, 15, 7, 10, 14, and 13Line 10: 2, 5, 4, 6, 8, 10, 14, and 13Line 10: 2, 5, 4, 6, 8, 10, 14, and 13
Line 11: 1, 2, 4, 12, 11, 13, 14, and 10Line 11: 1, 2, 4, 12, 11, 13, 14, and 10Line 11: 1, 2, 4, 12, 11, 13, 10, and 7
Line 12: 7, 15, 8, 6, 3, 2, 4, and 12Line 12: 7, 15, 8, 6, 3, 2, 4, and 12Line 12: 9, 15, 8, 6, 3, 2, 4, and 12
 Line 13: 12, 4, 6, 15, 7, 10, 14, and 13Line 13: 7, 15, 6, 4, 12, 11, 13, and 14
  Line 14: 12, 4, 6, 8, 15, 7, 10, and 14