Railway is known to be the best mode of land transport in terms of energy consumption and land use per passenger - km or ton - km transported; and also in terms of economic efficiency for freight transportation. It is also known to be superior to air transport in terms
energy consumption per passenger - km up to some specific distance of travel. Thus, it is of crucial importance to increase the market share of rail transport for economic and environmental sustainability. Customer satisfaction through better punctuality is one of the possible strategies towards this purpose. In reality, most of the railways operate according to a timetable, within which, all trains have predetermined departure times from, arrival times at and / or passing times without stopping through all the reference points (stations, sidings) in their routes. In daily operation, some of the trains may get delayed for various reasons. This creates a knock - on effect, spreading the delay to other trains. Thus, the timetable becomes invalid, and rescheduling of the traffic becomes necessary. Efficient rescheduling helps the railway system be more punctual. In practice, rescheduling is done by human operators (called dispatchers) by manual methods. Human brain has a limited computational ability. Given additionally the computationally complex nature of the problem, this puts an upper limit on the effectiveness of rescheduling solutions produced manually by humans. Making use of the computational power of today’s modern computers can provide significant improvement. In this study, an introduction for usage of mathematical models for scheduling the trains on a single - track railway line is given. Basic properties of the problem and the constraints that have to be taken into account are explained. Properties of the mathematical model which considers these constraints are mentioned. Some numerical tests performed on various sizes of problem instances are encouraging for using the proposed speed-up techniques.