In this paper, the single-track railway scheduling problem with two stations
and several segments of the track is considered. Two subsets of trains are
given, where trains from the first subset go from the first station to the
second station, and trains from the second subset 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. Different polynomial time algorithms are developed for special
cases with divers objective functions under various constraints. Moreover,
several theoretical results which can be ranked in a series of similar investigations
of NP-hardness of equal-processing-time single-machine scheduling
problems without precedence relations are obtained.