The strong aggravation of military and political instability in the world, the introduction by the United States of America and other Western countries of a huge number of various and unjustified sanctions against Russia created very difficult conditions for doing business in our country's industrial enterprises. In this regard, the issues of forming a methodology for the strategic and operational management of industrial enterprises, which need to ensure survival and further development, despite the harmful effects of Western states and the most difficult problems with resource support for production, as well as sales of products outside the Russian Federation, are of particular importance. The article discusses the main directions of development of scientific thought in the field of strategic and operational management of industrial enterprises, including in modern conditions, characterized not only by the military-political aggravation of the situation in the world, but also in many respects related to these processes, the emergence of economic crises in the largest regions of America and Europe. The authors propose a new aggregated algorithm for managing industrial enterprises, both at the strategic and operational levels, based on mathematical models and methods, taking into account the characteristics of modern industry markets. It is also noted that the modern world economy is subject to cyclical phenomena due to the very nature of capitalist relations, and not only from the desire of the Western world to destroy Russia and its powerful industrial potential. The article also presents a number of mathematical models developed by the authors for assessing the production efficiency of industrial enterprises both for the options for the functioning of manufacturing companies in a stable environment and increased demand for enterprise products, and for their working conditions during periods of crisis. The most relevant today are the models of choosing strategic decisions in the context of the global crisis. Thus, the paper proposes a methodology for the preparation of managerial decision - making by the management of industrial enterprises, which ensures the minimization of costs for the production and sale of finished products, as well as the feasibility of technical re - equipment by enterprises in various periods of the functioning of the world economy. It is also reported how the proposed methodology for the strategic and operational management of industrial enterprises in the quite recent past allowed Russian manufacturing companies to achieve fairly high performance and competitiveness at the international level.