Resumen
The subject of the research in the article is the reverse flows of material resources within the circular processes of closed supply chains of the logistics system with feedback. The aim of this article is to develop a model of the formation of reverse material flows using the processes of circular economy, which will achieve maximum efficiency of the logistics system. To achieve this aim it is necessary to solve the following tasks: to determine the essence and study the evolution of the circular economy through changes in the frameworks that form it; develop a graphical model of a logistics system with feedback, which is based on the implementation of circular processes; develop a mathematical model of the logistics system with feedback and conduct experimental calculations confirming its adequacy. Methods of systems analysis, operations research, namely linear programming (distribution problem is solved by the simplex method) are used to solve the tasks set in the study. The following results were obtained: the essence of the circular model of the economy, the evolution of its economic frameworks and the processes that are part of them were studied; the graphical model of the logistics system with feedback was presented by means of circular processes; a mathematical model of the logistics system with feedback was created. Conclusions. The concept of a circular economy is based on the principles and objectives of the concept of sustainable development and emphasizes the need to close logistics systems, i.e. to create logistics systems with feedback. The tools for the implementation of its concept are closed supply chains, which include direct and reverse material flows. Closed circuits are created through the use of circular processes, which create logistics loops that provide feedback between the participants in the chain and allow you to organize the reverse flow of products, their components, raw materials and materials. The application of operations research methods allows to create a mathematical model of the task of optimizing return material flows and to distribute material resources by loops, so that the total cash flows of the logistics system reach the maximum value and ecodestructive impact on the environment by creating return flows of secondary material resources was minimal.