Modeling a Multi-objective Train Scheduling Problem with the Intersection

The purpose of a train scheduling problem is to determine the arrival and departure times of each train in a station considering the travel time and safety constraints. In this paper, two railroad tracks crossing is to be considered. Two important objectives are as follows: 1) minimizing the total time of train delays at a particular time-limit and 2) decreasing the related cost. The trains have priority appearing in the model, as a weight coefficient. Because of the priority of the train and considering crossing, the complexity of the issue is going to be increased. After defining the problem and related issue in an explanatory way, this paper presents the mathematical model consisting of two objective functions. Finally, to show the validity of this model, an example is solved by the Lingo software using the branch-and-bound method.