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A Theorem on the Recycling Paradox

Part of the Lecture Notes in Management and Industrial Engineering book series (LNMIE)


Significant differences in the scale of metallurgical slag processing in different countries has led us to observe and formulate a paradox for a company that is engaged in recycling in the framework of a market economy. The theorem about the existence of the paradox of waste processing is formulated and proven. A mathematical model based on the original logarithmic one-factor production function of the enterprise is used. An analysis of the interaction of factors made it possible to determine the optimal conditions for the processing of production waste. The elasticity of the production function, the price of waste and the price of the product ratio predetermine the profitability for the company of processing either its own waste or those involved in the processing of waste from other enterprises on an agency basis. Based on the research results, options for building efficient circular industrial ecosystems are proposed. The institutional alternative is a market recycling company or an enterprise as part of a vertically integrated structure. An example is given from the practice of a large metallurgical plant.


  • Industrial waste
  • Recycling
  • Production function
  • Sustainability
  • Maximization of profits

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  1. Kabirifar, K., Kamyar, M., et al.: Construction and demolition waste management contributing factors coupled with reduce, reuse, and recycle strategies for effective waste management: a review. J. Clean. Prod. 263, 121265 (2020)

    CrossRef  Google Scholar 

  2. Van Beukering, P., Kuik, O., Oosterhuis, F.: Chapter 31—the economics of recycling. Editor(s): Ernst Worrell, Markus A. Reuter, Handbook of Recycling, Elsevier, 479–489 (2014)

    Google Scholar 

  3. Guo, J., Bao, Y., Wang, M.: Steel slag in China: treatment, recycling, and management. Waste Manage. 78, 318–330 (2018)

    CrossRef  Google Scholar 

  4. Goncalves, D.R., Fontes, W.C., Mendes, J.C., Silva, G.J., Peixoto, R.A.: Evaluation of the economic feasibility of a processing plant for steelmaking slag. Waste Manag. Res. 34(2), 107–112 (2016)

    Google Scholar 

  5. Ryumina, E.V.: Why businesses are unwilling and unable to protect the environment: a quantitative analysis]. Ekonomicheskaya nauka sovremennoj Rossii. 3, 6–74 (2009). [In Russian]

    Google Scholar 

  6. The Circular Gap Report 2019.

  7. Nerlove, M.: Estimation and identification of Cobb-Douglas production functions. Rand McNally, Chicago (1965)

    Google Scholar 

  8. Smirnov, R.G., Wang, K.: In search of a new economic model determined by logistic growth. E. J. Appl. Math. 31, 339–368 (2020)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Cherevatskyi, D. Yu.: Compositum mixtum of a one-factor production function. Ekonomika promyslovosti 4(92), 118–128 (2020) [In Ukrainian]

    Google Scholar 

  10. Cherevatskyi, D., Atabyekov, O.I.: Production function of a coal mine and economic efficiency of its operation. Econ. Visn. Donbas. 4(30), 56–62 (2012)

    Google Scholar 

  11. Nazyuta, L., Smotrov, A.V., Gubanova, A.V., Kornev, G.V.: The structure of formation and recycling of technological waste at full-cycle metallurgical enterprises. Energotekhnol. Resursosberezhenie 4, 44–54 (2011). [In Russian]

    Google Scholar 

  12. The port of Mariupol resumed transshipment of blast furnace slag.

  13. The MIISW n 2011 processed 2.66 million tons of slag and received more than 288,000 tonnes of recyclable materials.

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Correspondence to R. G. Smirnov .

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Cherevatskyi, D.Y., Smirnov, R.G., Lyakh, O.V., Soldak, M.O. (2023). A Theorem on the Recycling Paradox. In: Koval, V., Kazancoglu, Y., Lakatos, ES. (eds) Circular Business Management in Sustainability. ISCMEE 2022. Lecture Notes in Management and Industrial Engineering. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23462-0

  • Online ISBN: 978-3-031-23463-7

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