## 2 Basic Concepts  
The significance of developing theoretical and methodological foundations for assessing the effectiveness of complex systems emerges from the need to modernize the management system of modern enterprises. Such changes are necessary due to the requirements of a rapidly changing external environment. The management concept, which orients an organization of any type towards the effectiveness of its activities, requires the constant improvement of the existing methods and tools to enhance the efficiency of modern enterprises. [PERSON] [54] was the first to propose measuring the efficiency of a complex system based on one input and one output indicator. In 1957, the author applied this model to the elements of the United States agricultural system, failing, however, to combine all the possible input and output indicators to calculate the effectiveness of the elements studied. This methodology was developed by [PERSON], [PERSON], and [PERSON] in 1978 [55]. They suggested using mathematical programming to solve this kind of problem. The DEA method was then formulated. Over the years, the method has been widely applied in various fields to calculate both the technical and economic efficiency of the functioning of enterprises as complex systems [56; 57; 58; 59]. At this time, the basic models of the DEA method were formulated [51]. These models have become widespread in research around the world with practical applications in various fields. Data envelopment analysis is a mathematical programming method for determining relatively useful actions of decision-making units and technical efficiency [53]. DEA helps enable the use of multiple inputs and outputs in a linear software model that calculates efficiency [53]. The system for which comparative efficiency is evaluated is called the decision-making unit (DMU) [58]. A DMU uses certain resources at the input and converts them into products of a specific type at the output. For example, it can be proposed that the DMUs under study are a CHPP. Here, it is worth clarifying the type of enterprise under consideration. This article does not consider thermal power plants designed to produce electricity for industrial purposes for external consumers but concerns thermal power plants designed for the production of heat for industrial purposes, that is, for district heating. The combined heat and power plants considered in this article have as their main production function, like boiler houses, the production of heat (hereinafter in the calculations of the supply of thermal energy to heat networks), which is supplied to the grid for consumers. Electricity generation is an auxiliary function of such combined heat and power plants. The electricity generated is produced in relatively small quantities and is only used for the specific needs of the combined heat and power plants. Therefore, the main objective of the decision maker in the control of the CHPP is to regulate the heat supplied to the network for consumers at different times of the year. Increasing the electricity production is often impractical for such CHPPs, as it requires the construction of additional infrastructure for the consumers of the generated electricity. Therefore, we do not consider the electricity generation of these CHPPs in this study, as this function of the CHPPs under study is not the main one. Electricity is consumed only by the CHPPs themselves for their own needs. Heat generation is the main function of such plants and satisfies the heating needs of consumers in urban agglomerates with difficult climatic conditions in cold periods. Therefore, we consider heat production as the main output of CHPPs, requiring adjustments in warm and cold seasons. As input, it uses the available thermal power of the equipment and the consumption of conventional fuel for the released fuel cell. And, as a result of the work, it has as output: the production of heat (hereinafter in the calculation of supply of thermal energy to heat networks).