Mathematical model for optimizing the formation of a fleet of reclamation machines

Purpose of the research. Reduction of energy consumption for works in land reclamation production through the development of mathematical model and methodology, which allow carrying out optimal formation of machinery park.

Materials and methods. The most effective (optimal) units of machinery were selected on the basis of the original methodology developed by means of mathematical modeling using elements of set theory, mathematical analysis and algebra. The application of set theory made it possible to make the transition from real components of the fleet to mathematical subjects for modeling and back. Elements of mathematical analysis made it possible to establish functional dependence between the model elements and graphically represent the algorithm of sequential selection of units of machinery meeting certain requirements. With the help of algebra tools, the model components included in the developed methodology were structured. The formula for calculating the optimality coefficients, which are used to determine the indexes of machinery efficiency, is proposed, which allows selecting the most efficient machinery when forming machine parks for land reclamation production.

Results and discussion. Thanks to the constructed universal mathematical model, an original method was developed, the purpose of which is to increase productivity and reduce energy consumption in land reclamation production by optimizing the formation of a fleet of machines. The novelty of this work consists in the approach to the construction of a mathematical model using elements of set theory, providing versatility of application of the methodology of optimal variant selection developed on its basis. The conducted research has been tested on real data, which allows us to talk about the practical orientation of the presented work.

Conclusions. The mathematical model has been developed and with its use, the original methodology, allowing carrying out optimum formation of a park of machines for ameliorative manufacture with condition of increase of productivity and minimization of power consumption for manufacture of works, has been offered. On the basis of mathematical model calculations and approbation of the methodology in application to practical problems, the developed method of optimization of machine park formation for land reclamation production can be proposed for use in problems of modern realities.

1. Abdrazakov F.K., Goryunov D.G. Optimisation of machine park formation and machinery distribution to production facilities. Stroitel’nye i rozhnye mashiny. 2002. N3. 12-14. EDN YKPMVH.

2. Chumakova S.V., Abdrazakova Y.R. Application of mathematical modeling to applied tasks. Modern intellectual transformation of socio-economic systems: Proceedings of the III International Scientific and Practical Conference, Saratov: SSAU. 2020. pp. 147-150.

3. Solov’ev D.A.; Chumakova S.V.; Goncharov R.D. Mathematical model of the analytical approach of the comparative analysis of the agricultural machinery productivity using the visualisation technology. Helix. 2021. N10 (5). 114.

4. Frenkel A.A.; Bar-Hillel I.. Foundations of Set Theory. Translated from English by Y.A. Gastev; edited by A.S. Esenin-Volpin. – 2nd ed. 2006-554 p.

5. Solovev D.A., Chumakova S.V., Goncharov R.D. Mathematical model of analytical approach of comparative analysis of productivity of agricultural machinery when using visualisation technology. Vavilov readings-2021. Dedicated to the 101st anniversary of the discovery of the law of homological series and the 134th anniversary of the birth of N.I. Vavilov. Saratov. 2022. 59.

6. Minu M. Mathematical Programming. Theory and algorithms. М. Nauka. 1990. 485 s.

7. Reckleitis G., Reivindran A., Ragsdell K. Optimization in engineering: in 2 books, Moscow: Mir. 1986. 485 s.

8. Rogachev D.А. Optimization of measures for the technical operation of irrigation systems by artificial intelligence methods. // Prirodoobustrojstvo. 2024;(4): 12-19.

9. Zhuravleva L.A., Aldiab Anas. Development of the material and technical base of the melioration complex on an innovative basis // Prirodoobustrojstvo. 2024. No. 2. P. 21-27.

10. Karimxodjayev N., Almatayev T., Odilov X. Main factors causing the deteriation of automobile partswhichare used in various natural-climate conditions. Universum: technical sciences. 2020. N5 (74). 68-71

11. Zagoruiko M.G. Reducing the energy intensity of irrigation during operation of multi-supportirrigation machines “Cascade” / M.G. Zagoruiko, D.A. Soloviev, N.F. Ryzhko, S.N. Ryzhko // Land Reclamation and Water Management. – No. 1. – 2024. – P. 39-42.

12. Abdrazakov F.K. Technologies and technical means for carrying out operational and repair work on irrigation canals / F.K. Abdrazakov, V.S. Egorov, R.N. Bakhtiev. – Saratov: Federal State Educational Institution of Higher Professional Education “Saratov State Agrarian University”, 2008. 152 p.