عنوان مقاله [English]
Train timetabling is one of the most important problems in the railway scheduling field. It concerns with determining the trians’ arrival and departure times to/from each station so that some constraints are satisfied and some objectives are met. The objective in this thesis is to minimize the summation of dwell times of all trains. The timetables which are offered in this thesis are periodic. It means that each event repeats after a period time. The events are arrivals and departures of trains to/ from stations. In this timetable, the praying constraint is considered as well so that after Azan time, the train has to dwell in the first station which has enough room for praying. So an integer programming model has been presented. Then some valid inequalities have been proposed and at the end the effect of these inequalities on the solving time has been studied.