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 direc-
tion. 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.
E.R. Gafarov, A. Dolgui, A.A.Lazarev (2015). Two-Station Single-Track Railway Scheduling Problem With Trains of Equal Speed. Computers & Industrial Engineering, 85, 260—267. (journal impact factor 2018: 3.6). Q1