In this paper, the single track railway scheduling problem with 2
stations and Q segments of the track is considered. Two subsets of
trains N01
and N02
are given, where trains from N01
go from the station
1 to the station 2, and trains from N02
go in the opposite direction. The
speed of trains over each segment is the same. A polynomial time reduction
from the problem under consideration to a special case of the
single machine equal-processing-time scheduling problem with setup
times is presented. For this special case with different objective function
under different constraints polynomial time solution algorithms
are presented.