Purpose. Transport costs increase the cost of a product by one third, and in some cases, the delivery of cargo increases the cost of goods by an amount equivalent to the cost of the goods themselves. Therefore, reducing the share of transport costs is a priority for many businesses. One of the ways to achieve the goal of reducing transport costs is through the efficient use and distribution of rolling stock. A purpose is the research and development of a mathematical model for solving the problem of optimal distribution of vehicles, which takes into consideration the real necessities of cargo owners and possibilities of trucking companies at distribution of vehicles to the lines of transportations. Methodology. The research task is the efficient use of rolling stock for the delivery of goods between shippers and consignees in full according to the efficiency criterion – the minimum total carrying capacity of rolling stock. The object of modelling is the process of vehicle distribution. To solve this type of problem, the optimisation modelling method was used, which allows for the optimal assignment of consignees to shippers. Findings. This article provides the mathematical model of task of optimal distribution of vehicles, which solves the problem formulated as follows: according to the given direction of cargo delivery and volume of transportation along them and the determined number of trucks of different types, need to distribute the vehicles for ensure of delivery of cargo to each customer in full volumes and most effectively. Originality. Mathematical model allows to solve the problem of optimal distribution of vehicles in case of insufficient number of trucks in two different ways. In case of a possibility to the increasing of number of vehicles for performing of a given volume of transportations – due to the increasing of amount of vehicles. If there is no possibility to the increase of number of vehicles – due to reduction of volume transportations considering an equivalence of customers in case of under delivery of cargo. Practical value. Practical value is that a mathematical model allows takes into consideration the real necessities of cargo owners and possibilities of trucking companies at distribution of vehicles to the lines of transportations. On the basis of the created models there can be developed algorithms for the solving of tasks of optimal distribution of vehicles, each of that can be programed and realized by means of the computer technology and used for practical calculations.
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