Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Algorithm 1

The shortest path algorithm with vertices constrained in .

tep 1. Initialization.

Set , , ; , ;

, , .

tep 2. Label updating

For to

For each arc

If Then

End if

End for

End for

tep 3. Fetch the shortest paths

For each , do

Set the sink-vertex as the current vertex ;

For to 1

If vertex is not the source node

Find the preceding vertex of the current vertex , and update as the current vertex ;

End if

End for

Reverse the backward path and output the least cost path from to with at most intermedium vertices.

End for