Subject The article reviews the elements and factors of economic sustainability and offers mathematical models enabling to assess the economic condition of Russian industrial enterprises under current market conditions. Objectives The purpose is to build economic and mathematical models to analyze factors of economic stability and assess conditions for their stabilization and development. Methods To build mathematical models and obtain quantitative findings, we employ methods of systems theory, and cluster and factor analysis. Relevant statistical data of the Federal Service of State Statistics of the Russian Federation for the period from 2010 to 2015 served as the information base for the models' development. We performed multiparameter calculations and plotting, using the Statistica software package. Results We present the results of cluster analysis of an array of economic indicators reflecting the economic stability of industrial enterprises. We distinguish and compare two main clusters. The paper formulates and analyzes conditions, under which industrial enterprises are incorporated in a certain cluster. We present a graphical interpretation of the clustering process, along with numerical estimates. Conclusions We offer a technique of multiparameter analysis of industrial enterprises' economic activity, enabling to evaluate their economic sustainability based on a cluster analysis. It shows that at present the enterprises of the fuel and energy complex, steelmaking industry, and finished metal product manufacturers are the most stable enterprises of the Russian industry.
Makarov V.L. [A review of mathematical models of innovation-driven economy]. Ekonomika i matematicheskie metody = Economics and Mathematical Methods, 2009, vol. 45, no. 1, pp. 3–14. (In Russ.)
Semenova A. [Management of innovative processes]. Ekonomist = Economist, 2004, no. 5, pp. 46–53. (In Russ.)
Vertakova Yu.V., Simonenko E.S. Upravlenie innovatsiyami: teoriya i praktika [Innovation management: Theory and practice]. Moscow, Eksmo Publ., 2008, 432 p.
Blank I.A. Upravlenie finansovoi bezopasnost'yu predpriyatiya [Managing the financial security of the enterprise]. Kiev, El'ga Publ., 2009, 250 p.
Sheremet A.D., Negashev E.V. Metodika finansovogo analiza deyatel'nosti kommercheskikh organizatsii [Methods of financial analysis of commercial organizations' operations]. Moscow, INFRA-M Publ., 2009, 380 p.
Kreinina M.N. [Assessment of the financial stability of enterprises]. Finansovyi menedzhment = Financial Management, 2001, no. 2, pp. 6–11. (In Russ.)
Rozenberg G.S., Chernikova S.A., Krasnoshchekova G.P. et al. [Myths and reality of 'sustainable development']. Problemy prognozirovaniya = Problems of Forecasting, 2000, no. 2, pp. 130–154. (In Russ.)
Osipova M.Yu. [Theory and methodology of research on sustainable development of socio-economic systems]. Vestnik PNIPU. Sotsial'no-ekonomicheskie nauki = Bulletin of Perm National Research Polytechnic University. Social and Economic Sciences, 2014, no. 4, pp. 81–88. (In Russ.)
Malyshev V.L. [The need to change a mechanism of industrial activities]. Ekonomika i matematicheskie metody = Economics and Mathematical Methods, 2017, vol. 53, no. 1, pp. 128–143. (In Russ.)
Jambu M. Ierarkhicheskii klaster-analiz i sootvetstviya [Classification Automatique Pour L'Analyse des Données]. Moscow, Finansy i statistika Publ., 1988, 342 p.
Mandel' I.D. Klasternyi analiz [Cluster Analysis]. Moscow, Finansy i statistika Publ., 1988, 176 p.
Borovikov V. STATISTICA. Iskusstvo analiza dannykh na komp'yutere: dlya professionalov [STATISTICA. The art of data analysis on computer: For professionals]. St. Petersburg, Piter Publ., 2003, 688 p.
Boldyrevskii P.B., Kistanova L.A. [Investigation of the dynamics of innovation activities of industrial enterprises]. Vestnik Nizhegorodskogo universiteta = Vestnik of Lobachevsky State University of Nizhny Novgorod, 2014, no. 4, pp. 37–40. URL: Link_unicode/4.pdf (In Russ.)
Boldyrevskii P.B., Kistanova L.A. [Evaluating the efficiency of innovative activities of industrial enterprises]. Aktual'nye voprosy nauki, 2014, no. 12, pp. 65–69. (In Russ.)
Coates Adam, Andrew Y.Ng. Learning Feature Representations with K-means. URL: Link
Baldin A.V., Borisevich V.B., Nesterenko V.I. [Factor and cluster analysis of the main indicators of production activity of transportation industry enterprises]. Rossiiskoe predprinimatel'stvo = Russian Journal of Entrepreneurship, 2006, no. 1, pp. 56–58. (In Russ.)
Bagrinovskii K.A., Nikonova A.A., Sokolov N.A. [Methods of technological transformation in production system]. Ekonomika i matematicheskie metody = Economics and Mathematical Methods, 2016, vol. 52, no. 1, pp. 3–19. (In Russ.)
Van Ryzin (Ed.). Klassifikatsiya i klaster [Classification and clustering]. Moscow, Mir Publ., 1980, 390 p.
Ward Jr. J.H. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 1963, vol. 58, iss. 301, pp. 236–244. doi: 10.2307/2282967
Aivazyan S.A., Mkhitaryan V.S. Prikladnaya statistika: klassifikatsiya i snizhenie razmernosti [Applied statistics: Classification and decrease in data space dimension]. Moscow, Finansy i statistika Publ., 1989, 607 p.
Endovitskii D.A., Lyubushin N.P., Babicheva N.E., Kupryushina O.M. From Assessment of Organization's Financial Standing to Integrated Methodology for Analysis of Sustainable Development. Daidzhest-finansy = Digest Finance, 2017, vol. 22, iss. 2, pp. 123–143. URL: Link