Two-station single-track railway scheduling problem with trains of equal speed

•A single track railway scheduling for 2 stations and several segments is considered.•Often this situation concerns the case of maintenance of one track of a double track line.•A reduction to the single machine scheduling problems with setup-times is presented.•Polynomial time solution algorithms were developed.•Can serve as a basis to develop efficient algorithms for decision support systems. 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.