Context. Effective solution of a number of application problems related to transportation, as a rule, depends on the solution of two problems: the correct formation of the composition of the column of technique and the successful choice of the route of its movement. Each of the problems is optimization, the methods of solving which are currently being worked out. Theoretical studies of each of the individual problems and their practical applications indicate their interdependence, which has not yet been fully studied. Practical applications necessitate the development of a suitable scientific and methodological apparatus.Objective. The purpose of this work is development of a method for solving a complex optimization problem of forming a column of vehicles and choosing the route of its movement on a non-stationary road network.Method. The mathematical model of solving the optimization problem of complex formation of the composition of the column of machinery and the choice of its route of motion is proposed. A heterogeneous set was used to describe the array from which the vehicles were selected. A graph was used to describe the road network. As a criterion for the optimality of the complex problem is the minimization of time spent on moving. The peculiarity of the model is to take into account the possibility of dynamically changing the time weights of edges of the graph when implementing the movement of a column of machinery along the chosen route. Based on the use of this model, a method is proposed, which provides a comprehensive choice of the composition of the column of equipment and optimal routes of its movement on a non-stationary road network.Results. The article proposes an algorithm that provides the solution of the optimization problem of complex formation of the composition of machinery column and the choice of its route of motion in terms of time-fixed edges that describe the network of roads. The features of application of the proposed algorithm are given. Using the developed software, the choice of technique from an existing inhomogeneous array and the choice of a route on a graph with a non-stationary time weight of edges was investigated. The example shows the imperfection of decisions regarding the complex formation of the column composition and the choice of its optimal route of travel on a non-stationary network of roads obtained using classical methods.Conclusions. Not taking into account the impact of a possible change in traffic conditions, as evidenced by a change in the time weights of the edges of the graph describing the road network, on the composition of the column of machinery can lead to suboptimality of the obtained solutions using classical methods of forming the composition of the column and finding the shortest route in the graph. The method proposed in this study can be used to obtain the optimum composition of the column and the route, taking into account the change in road conditions during the movement of the column. The obtained results extend the possibilities of the theory of discrete optimization and the theory of graphs.