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One of the important subjects related
to railways is the train scheduling problem, specially that of passenger trains which is
plotted by a mother graph. The mother graph is a time-distance diagram which contains information such as the trains departure and arrival times at the stations on the way, necessary stops at the stations, and the points at which the trains would
meet other trains coming from the opposite direction. Usually, this graph is done
manually by well-experienced staffs. In
this paper, a mixed zero-one programming is presented to obtain an optimum mother graph for single line track routes. Then, regarding the model structure and assumptions of the model, we have made an effort to solve the problem in real dimensions. We have, in order to solve the
problem, suggested several techniques such as constraints generation, valid inequalities, and size reduction to the
problem. A heuristic method, also, which finds a good upper bound is proposed. Using all the above methods, we have reported good computational results on the problem. The computations are done for
several randomly generated data using Cplex 5.0 on a PC with Pentium 233 processor.