On track procession assignment problem at the railway network sections

We consider the problem of assigning a “track procession,” i.e., the time for railway network maintenance, when train movements are forbidden. The railway network is presented in the form of an undirected multigraph. Movements along this multigraph are carried out with a set of conflict-free subslots, where each “subslot” is a five-tuple of the arrival and departure vertices, number of the edge used for movement, and arrival and departure times. In this work, we construct a mathematical model for carrying out transportations plan with accounting for constraints on time when trains are for departure as well as constraints on arrival time. An optimization problem on time selection for track processions assignment and trains schedule corresponds to a mixed integer linear programming problem with a criteria of the minimization of total time spend by trains in run. An applied implementation of the proposed approach was performed using ILOG CPLEX software. We present the results of a numerical experiment.