The National Transport University Bulletin

Abstract

This article provides a description of the theoretical foundations of the organization of freight transportation on transport networks. The task of organizing freight transportation can be solved not only on the matrix, but also on the diagram of the road network. Solution methods in both cases have their advantages and disadvantages. The matrix method is quite simple and does not require a large number of calculations. As the size of the problem increases, the number of iterations increases approximately linearly depending on the number of suppliers (consumers) of the cargo. This method should be used in practical tasks, since it is easier to set partial bans on deliveries to individual consumers, and purely homogeneous cargoes, in general, do not exist. The network method allows you to take into account the bandwidth of individual sections of the network, while the transport problem in the matrix form takes into account only the bandwidth of the nodes of the transport network. The object of the study is the process of managing freight transportation on transport networks. The purpose of the work is to study the features of decision-making in the management of freight transportation on transport networks of one type of cargo without capacity limitations. Research methods – a method of successive improvement of the cargo transportation plan on transport networks of one type of cargo without capacity limitations. The formulated general mathematical model of the representation of freight transportation on transport networks assumes two most common methods of solving transport problem in network form: the method of reducing disagreements or conditionally optimal plans by A.L. Lurie and the method of sequential improvement of the plan of L.V. Kantorovich and M.K. Gavurin, which was considered in the problem formulated without taking into account the throughput of transport communications. The organization of cargo transportation on transport networks of one type of cargo without limitations of throughput includes the following steps: the first step is to draw up an initial plan, in which all the cargo must be sent and all the needs of consumers must be satisfied; the second step is the assignment of potentials to the vertices; the third step is the selection of the unloaded arc with the greatest violation of the optimality condition. Its value is positive, therefore, it is necessary to direct the cargo flow in the direction from a lower potential to a higher one. We find a closed circuit, which includes arcs with a flow and a selected arc with a violation, and this can be done in the only way. Moving along the contour from the lower potential of the arc with a violation to the higher one, we find the arc with the minimum oncoming cargo flow. We add this value to all passing streams and subtract it from all opposing streams. The second and third steps are alternately repeated until there are arcs with a violation of the optimality condition. When planning transportation on a transport network without capacity restrictions, the actual capacity of individual arcs is not taken into account, although it is possible that some of them will have a load that they cannot cope with. If congested areas appear, then the costs of diverting freight flows past them in a roundabout way will be small. Therefore, planning the transportation of one cargo on networks without bandwidth limitations is of great practical importance, and on networks with bandwidth limitations – only methodical. Indeed, it is difficult to imagine that one cargo could completely fill the carrying capacity of the arc.

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