Mathematical model of transition of a production enterprise to a circular economy

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In the published article, a mathematical model of an enterprise is proposed, the production activity of which is described by two production functions. The main production function converts resources into the products of an enterprise, the additional production function turns resources into its waste, which are usually included in costs. Enterprises of a waste-free circular economy organize their own production so that the waste of an enterprise becomes new production factors and is completely converted into additional useful products. The process of transition in time of an enterprise of an ordinary economy to an enterprise of a waste-free circular economy is described using a special dimensionless transformation function, which varies from zero to one. Two variants of the peculiarities of changes in the economic indicators of an enterprise that arise during the transition to waste-free production are considered. In the first case, a one-factor manufacturing enterprise was investigated, which in its production activity uses only one resource, which integrates the volumes of factors of production consisting of fixed capital, production assets involved in the production of labor resources, used in the production of materials, applied technologies, of various kinds innovation. In the second case, a two-factor manufacturing enterprise has been investigated, which in its production activity uses two resources, the first of which is fixed capital and production assets, the second production factor includes labor resources involved in production. Regularities have been established for changes in the time of production, waste, profits and costs of an enterprise when introducing waste-free technologies for the case of one-factor production. A numerical analysis of the obtained economic and mathematical model shows that the maximum value of the enterprise's profit changes over time and corresponds to the level of the introduced circular technologies.

About the authors

Leonid A. Saraev

Samara National Research University

Author for correspondence.
ORCID iD: 0000-0003-3625-5921

Doctor of Physics and Mathematics, professor, head of the Department of Mathematics and Business Informatics

Russian Federation, 34, Moskovskoye shosse, Samara, 443086, Russian Federation.

Marina E. Тalikina

Samara National Research University

ORCID iD: 0000-0001-8149-082X

senior lecturer, Department of Mathematics and Business Informatics

Russian Federation, 34, Moskovskoye shosse, Samara, 443086, Russian Federation.


  1. Alexandrova V.D. Actual concept of circular economy. International Journal of Humanities and Natural Sciences, 2019, no. 5–1, pp. 87–93. DOI: (In Russ.)
  2. Ellen MacArthur Foundation: Towards a Circular Economy: Business Rationale For An Accelerated Transition. 2015. Available at:
  3. -Dec-2015.pdf.
  4. Gureva M.A. The theoretical basis of the concept of circular economy. Journal of international economic affairs, 2019, no. 3, pp. 2311–2336. DOI: (In Russ.)
  5. Val'ko D.V. Circular economy: a theoretical model and implementation effects. National interests: Priorities and Security, 2018, vol. 14, no. 8, pp. 1415–1429. DOI: (In Russ.)
  6. Valko D.V. Circular economy: definitions and diffusion of the concept in Russian research. Scientific Journal NRU ITMO. Series "Economics and Environmental Management", 2019, no. 2, p. 42–49. DOI: http://
  7. (In Russ.)
  8. Ratner S.V. Circular economy: theoretical foundations and practical applications in the field of regional economy and management. Innovations, 2018, no. 9 (239), pp. 29–37. Available at: https://
  9. (In Russ.)
  10. Jawahir I.S., Bradley R. Technological Elements of Circular Economy and the Principles of 6R-Based Closed-loop Material Flow in Sustainable Manufacturing. In: 13th Global Conference on Sustainable Manufacturing Decoupling Growth from Resource Use. Procedia CIRP 40, 2016, pp. 103–108. DOI: http://
  12. Kalmykova Y., Sadagopan M., Rosado L. Circular economy – From review of theories and practices to development of implementation tools. Resources, Conservation and Recycling, 2018, vol. 135, pp. 190–201. DOI:
  13. Kirchherr Julian et al. Conceptualizing the circular economy: An analysis of 114 definitions. Resources, Conservation and Recycling, 2017, vol. 127, pp. 221–232. DOI:
  14. Potting J., Hekkert M., Worrell E., Hanemaaijeret A. Circular Economy: Measuring Innovation in the Product Chain. The Hague: Netherlands Environmental Assessment Agency, 2017, 46 p. Available at:
  15. Batova N., Sachek P., Tochitskaya I. On the way to green growth: a window of opportunities for the circular economy. BEROC Green Economy Policy Paper Series, PP GE no. 1. Available at:
  16. upload/iblock/803/ge_1.pdf. (In Russ.)
  17. Füks R. Green revolution. Economic growth without damage to the environment. Moscow: Al'pina non-fikshn, 2016, 330 p. Available at: (In Russ.)
  18. D’Amato D., Korhonen J., Toppinen A. Circular, Green, and Bio Economy: How Do Companies in Land-Use Intensive Sectors Align with Sustainability Concepts? Ecological economics, 2019, no. 158, рр. 116–133. DOI: ecolecon.2018.12.026.
  19. Ghisellini P., Cialani C. and Ulgiati S. Review on circular economy: The expected transition to a balanced interplay of environmental and economic systems. Journal of Cleaner Production, 2014, vol. 114, no. 7, pp. 11–32. DOI:
  20. Heshmati A. (2016) A Review of the Circular Economy and its Implementation. IZA Discussion Paper No. 9611. Available at:
  21. Nosko P.A. Trends in the circular economy development in the European Union. Russian Journal of Resources, Conservation and Recycling, 2019, no. 1, vol. 6. DOI: (In Russ.)
  22. Ratner S.V. European experience in transition to circular economy. Economic Analysis: Theory and Practice, 2020, vol. 19, issue 4 (499), pp. 598–617. DOI: (In Russ.)
  23. Sysoev S. Review of municipal waste collection and treatment systems in Sweden and Finland. BEROC Green Economy Policy Paper Series, PP no. 16. Available at:
  24. d131a530b903ac2531797a4f4c04e81.pdf. (In Russ.)
  25. Bastein T. et al. (2013) Opportunities for a Circular Economy in the Netherlands. TNO, Report commissioned by the Netherlands Ministry of Infrastructure and the Environment. Available at:
  27. Alexandrova V.D. The actuality of transition to the model of circular economy in Russia. International Journal of Humanities and Natural Sciences, 2017, no. 11, pp. 106–110. Available at:
  28. item.asp?id=30725246. (In Russ.)
  29. Batova N., Tochitskaya I. Readiness of Belarusian enterprises to implement the principles of circular economy: traditional vs circular. BEROC Green Economy Policy Paper Series, PP no. 14. Available at: (In Russ.)
  30. Grigoryan A.A., Borodavkina N.Yu. The Baltics on their way towards a circular economy. Baltic Region, 2017, vol. 9, no. 3, pp. 7–22. DOI:
  31. Guryeva M.A. The theoretical forecast scenarios of the circular economy development in Russia. Journal of Economics, Entrepreneurship and Law, 2020, vol. 10, no. 8, pp. 2151–2178. DOI:
  32. 18334/epp.10.8.110689. (In Russ.)
  33. Kamenik L.L. Modernization of Russian economy. Recycling of resources – a new vector business development. Journal of Economy and entrepreneurship, 2015, no. 3 (56), pp. 177–184. Available at: (In Russ.)
  34. Kudryavtseva O.V., Mitenkova E.N., Solodova M.A. Circular economy: prospects for sustainable development in Russia. Economic Revival of Russia, 2019, no. 3 (61), pp. 115–126. Available at: (In Russ.)
  35. Molchanova S.M. Circular economy tools. Uchet i kontrol', 2020, no. 2 (52), pp. 24–30. Available at: (In Russ.)
  36. Pakhomova N.V., Richter K.K., Vetrova M.A. Transition to circular economy and closed-loop supply chains as driver of sustainable development. St. Petersburg University Journal of Economic Studies, 2017, vol. 33, issue 2, pp. 244–268. DOI:
  37. Pakhomova N.V., Richter K.K., Vetrova M.A. Circular economy as challenge to the fourth industrial revolution. Innovations, 2017, no. 7 (225), pp. 66–70. Available at:
  38. innovacii-n7-2017/cirkulyarnaya-ekonomika-kak-vyzov-chetvertoj-promyshlennoj-revolyucii; (In Russ.)
  39. Starostin A.L., Filippova T.V. Experience of the development of the closed-loop economy model in Russia and China. In: Barysheva G.A., Borisova L.M. (Eds.) Economy of Russia in the XXI century: collection of scientific papers of the XII All-Russian research and practical conference «Economic Sciences and Applied Research»: in 2 vols. Tomsk: Tomskii politekhnicheskii universitet, 2015, pp. 458–467. Available at:; (In Russ.)
  40. Tochitskaya I., Shershunovich E. FREE Policy Brief: Towards a More Circular Economy: Progress Assessment of Belarus. Free Network. Policy Brief Series. URL:
  41. iblock/bc4/bc472a61d034288bf36c261a83ee9aa9.pdf. (original in English)
  42. Chang N.V. Economic and policy instrument analyses in support of the scrap tire recycling program in Taiwan. Journal of Environmental Management, 2006, no. 86 (3), pp. 435–450. DOI:
  43. 1016/j.jenvman.2006.12.026.
  44. Su B., Heshmati A., Geng Y., Yu X. A review of the circular economy in China: Moving from rhetoric to implementation. Journal of Cleaner Production, 2013, pp. 215–227. DOI:
  45. j.jclepro.2012.11.020.
  46. Prasolov A.V. Mathematical methods of economic dynamics. Saint-Petersburg: Lan', 2015, 352 p. Available at: (In Russ.)
  47. Ilyina E.A. Saraev L.A. Predicting the dynamics of the maximum and optimal profits of innovative enterprises. Journal of Physics: Conference Series, 2021, vol. 1784, p. 012002. DOI:

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