Rudkovskyi O. Models and means of applied mathematical modeling of resource-efficient rail freight operations.

The dissertation is devoted to the creation of models of resource modeling of railway rolling stock, based on further development of the life cycle cost criterion, as well as the method of numerical realization of the proposed mathematical models of one class of goods during their transportation by rail typification and unification. The paper systematizes and highlights the features of the organization of rail transport, taking into account the rolling stock and the characteristics of the goods that are in terms of logistics of transport operations. Based on this, the approach to resource modeling of railway RS based on the application of the concept of life cycle cost is substantiated and appropriate mathematical models (MM) of options for resource renewal (modernization) of rolling stock based on the life cycle cost criterion (LCC-criterion) are developed. A mathematical description of the states of the class of bulk, bulk, lump and granular cargoes transported by the respective non-traction rolling stock is performed. The description is strictly formalized in the form of differential equations in partial derivatives (or their systems). Mathematical models of the investigated class of cargoes and rolling stock in which they are transported (temporarily stored) are offered. The abstraction of these mathematical models, resulting in generalized continuous mathematical models, allowed to develop an approach to mathematical modeling of the states of the studied class of cargo (and the corresponding non-traction rolling stock) based on the principle of typification and unification. The constructive method of numerical realization of mathematical models class of bulk, loose, lump and granular loads (and involved in the process of transportation of non-traction rolling stock) is proposed, which is reduced to discretization of continuous generalized mathematical models according to implicit difference scheme with weights and further solution of discrete level system. by the iterative Seidel procedure. The method provides unconditional convergence of the obtained system of discrete equations. The results of theoretical research are the basis for the construction of software tools focused on solving applied problems of mathematical modeling of the state of the studied class of goods in the operations of the transport cycle of the railway. The effectiveness of the developed mathematical models and software is illustrated by model examples in the course of solving test task. The results of the work are implemented in production and in the educational process.