## 1 Introduction  
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. This forms a set of new approaches to understanding the quality of an organization's activities, and consequently its viability. This becomes possible if the main criterion is met: making decisions relevant to certain conditions in which the reproduction process of the objects in the system is carried out [1, 2, 3, 4, 5]. Therefore, this article will discuss in detail how, depending on the goal of the decision maker, the conditions for setting the task and the results of calculating performance indicators change. Many scientists [6, 7, 8, 9, 10] have addressed the problem of evaluating effectiveness. In [11], we presented a comparative analysis of all the methods of evaluating effectiveness. Among the methods analyzed was the data envelopment analysis (DEA) method, which is one of the most effective methods for evaluating the effectiveness of complex systems [12, 13, 14, 15]. Scientists from different countries have proposed various modifications of the basic models in order to improve the DEA method [16, 17, 18, 19]. Research in this direction is still ongoing. New publications with practical applications of the method in various fields are constantly appearing [20, 21, 22, 23, 24]. New DEA models are also emerging to solve the problems of evaluating the effectiveness of complex systems [25, 26, 27]. Most of the theoretical and methodological features have been described in various scientific articles and textbooks [28; 29; 30; 31]. In addition, scientists from different countries and scientific groups have presented various classifications of the methodology and its description. One of the method founders, [PERSON], created a website to highlight the development of the theoretical and practical foundations of the DEA method, as well as various innovations in the practical application of the method [32]. Furthermore, some scientists conducting research in this direction are seeking to popularize the method in scientific circles, having published textbooks, monographs, articles, and operating websites with basic information about the DEA method. There are several main theoretical sources of scientists from different countries on the models of the method and their application [33; 34; 35]. In addition, a conference dedicated to scientific research on the DEA method has been held [36]. All these sources contain various scientific works devoted to this method and the peculiarities of its application. Understanding the variety of the uses of the features, models, and modifications of basic models is somewhat complicated, with much time being required to study all the submitted works, each of which describes new scientific developments and additions to the method. In modern scientific works, the DEA method is primarily considered when solving a variety of practical technical and economic problems [36; 37; 38; 39; 40]. On the basis of the practical applications, various methodologies are identified with modified models of the DEA method being used. The latest developments in this direction are described in various scientific sources [41; 42; 43]. Recently, modifications of some models have also been presented to solve certain practical problems in various industries [44; 45; 46]. Despite the interest of certain scientific groups, the popularization of the method, publications, and new developments in this field, the DEA method is still in the formation stage. Therefore, this article, to some extent, fills a gap in the scientific literature on the analysis of the effectiveness and productivity of complex systems based on the DEA method. In addition, it describes a new algorithm for applying the method in the fuel and energy complex, where the DEA method has not previously been used.