In this paper, a single machine scheduling model is used to schedule trains in order to minimize the total weighted delay time. The railway studied, is composed of a part of two joined railways in Brazil, which belongs to VALE company and to Ferrovia Centro-Atlântica (FCA). This railway is a single-track line composed by single-tracks and it is shared by these railways (VALE and FCA). The trains travel in both directions on this single-track line. These railways have a bottleneck caused by a heavy traffic. Therefore, mathematical equations are developed to determine the shortest time interval admissible between two trains, ensuring that they will not overlap. These equations enable us to simplify the mathematical representation of the problem and define it as a single machine scheduling problem. Later, two single machine scheduling formulations are proposed and analyzed; one based on “Arc-Time-Indexed” variables and other, on “Binary” variables. Each formulation reflects a specific concept on how the variables and parameters are defined and require particular settings and definitions. Extensive computational experiments are performed considering various instances to capture several aspects of practical situations. Based on the results of experiments, these mathematical formulations are evaluated as decision-support tools.