The rapid response border commandant's office is a structural unit of the border detachment, designed to protect and strengthen the protection of a certain section of the state border, and must quickly redeploy its forces and assets. The success of the tasks assigned to the unit depends largely on the timeliness of arrival at the destination. Operational transportation of a significant amount of weapons, personnel and dissimilar cargoes on land is carried out using equipment. At the preparatory stage of the organization of transportation, the problem of forming the optimal composition of the convoy of equipment is solved. The existing road network provides a sufficiently large number of traffic routes between the starting and ending points. Moreover, this takes place even for insignificant distances between points of departure and destination. The specified conditions for multivariance in the selection. In addition, the choice of the route of movement depends on many auxiliary conditions: driver training, technical characteristics and reliability of vehicles, traffic safety, road and environmental conditions, distance and timing of transportation, and the like. Poor accounting of these factors in the aggregate may lead to the choice of an irrational route of movement, will not ensure the timely arrival of the unit at the destination, and may lead to the failure to fulfill certain tasks. Therefore, the task of choosing the optimal route of movement of the column of equipment is relevant. At the substantive level, the task looks like the justification of the mathematical model for choosing the optimal route for the column of equipment, if the criterion of optimality is minimizing the time it takes to move from the starting point to the destination. The authors formed a mathematical model of the given problem, proposed an algorithm for its solution for three cases: discrete-stochastic, discretely-determined and continuously-indefinite, and the corresponding software was developed. The choice of routes is carried out for three options, taking into account the fact that the change in the weights of the ribs can be carried out: at times when the column is at a certain vertex of the graph, and the update of the matrix of weights is carried out precisely at these moments. This is the case when a decision on the further route of movement is formed at the road branching points, taking into account the situation, the status of individual sections changes dynamically and data for which appears periodically; at times when the column is at a certain vertex of the graph, and for these moments, the matrix of weights that will occur when the column hits the vertex are known in advance. This is the case when a decision on the route of movement can be formed at the beginning of the movement, taking into account the known situation on the state of the roads, dynamically change, but data on which can be taken into account in advance; randomly depending on the speed of the column at a fixed point in time for which the column speed function is known.
A MATHEMATICAL MODEL OF SELECTING TRANSPORT FACILITIES FOR MULTIMODAL FREIGHT TRANSPORTATION