Urgency of the research. To overcome the image of one of the most energy-intensive countries in Europe, to reduce gas consumption in Ukraine, the need for compensation from the state budget the difference in tariffs for communal heatgenerating and heat supply companies may decrease if the cost of services, to take into account and eliminate heat loss. The priority of the Government of Ukraine has been the introduction of new mechanisms to promote energy efficiency on the consumer side (in particular, the payment of the loan, which the inhabitants of the house take for its thermo-or to go to alternative heating, etc.), while according to experts 80% of heat loss it occurs in areas generating and transporting. Tasks relating to the modernization and reorientation of the country's heating systems in order to reduce consumption of natural gas are those that actually increase national, primarily the energy security of Ukraine and are highly relevant and important state. Target setting. Creating application of economic and mathematical tools for decision support in the process of modernization and renewal of generating capacity of thermal generation, construction of replacement facilities using modern technologies to achieve European standards for emissions of pollutants and the use of other fuels, renovation of trunk and distribution heat networks allow perform analysis of alternative management actions and will boost the development of energy-efficient, technically reliable and safe operation of heating systems of society with minimal economic burden on end users. Actual scientific researches and issues analysis. Scientific, methodological and applied aspects of economic and mathematical modelling of power system development processes are devoted to the study Y. Bakhshan, S. Motadayen Aval, F. Kamel and A. Hajhossini, J. Okrajni, K. Mutwil and M. Cieśla, B. Yakovlev, A. Sapuhina, V. Kurochkina and S. Novikov, S. Orlovsky, V. Volkov and O. Timofeenko, B. Polovnikova and V. Huzeeva, V. Klimenko and Y. Orlov, D. Chernikov, A. Aleksakhina and A. Boblovskogo, A. Bujak, O. Havrysya, K. Mahkotilo and other domestic and foreign scientists. Uninvestigated parts of general matters defining. However, until now no one has proposed to apply the models and methods of the theory of planning and network management, as well as still have not developed a science-based system of economic and mathematical models of decision support with respect to the modernization of communal heat power. The research objective. The main objective of this work is to systematize and review of scientific works of foreign and domestic scientists, containing analogues and prototypes, which are the basis for further improvement of the concept of rational functioning of the market of energy materials and products based on the creation of a complex of economic and mathematical models of resource management and costs in the process of modernization of communal heat energy in Ukraine. The statement of basic materials. The paper systematically analyses and scientific works of foreign and domestic scientists, containing analogues and prototypes, serve as the basis for further improvement of the functioning of the concept of sustainable market for energy materials and products based on the creation of a complex of economic-mathematical models of management of resources and costs in the process of modernization municipal power system in Ukraine. It is proved that the idea of adapting the methods of graph theory, as well as deterministic and probabilistic network models taking into account the time, cost and resources for planning and management practice, modernization, reconstruction and replacement of process equipment heating stations and thermal networks enterprises of power in Ukraine, characterized by scientific novelty and is a tool inform decisions heat generating and heat supply companies, investment companies, the legislative bodies regarding the technically reliable and safe functioning of the energy supply company systems. Conclusions. The use of modern information technology and network of economic and mathematical models and methods to simultaneously consider all the economic and physical conditions and to determine the best option in the process of modernization of communal thermal power will become one of the components forming a system of support for the introduction of new management systems to the innovative development of the energy sector of Ukraine , will provide decision-making in favour of the power supply systems, which are the most beneficial to the safety position, the reliability (continuity), the quality of energy supply and the provision of affordable and attractive for the environmental consequences of energy services.