The problem of optimization of investment projects related to the development of modern production systems is considered. The tasks of managing of operation and development of production systems considering external resources – the synthesis and analysis of optimal credit strategies – are posed and solved. An analysis of analogs – solutions of the variational problem of optimal development, the disadvantage of which is the difficulty of obtaining information about the state of production and the external environment, was carried out. The new solution is based on the resource approach, when external resources are taken into account in the cost of production resources. A generalized model of optimal development is used, in which the planned period of the investment project is divided into intervals. At the beginning of each interval, the optimal development strategy is adjusted taking into account the clarification of information about the future state of the active environment: actions of competitors, consumers, world markets. To determine the optimal amount and optimal distribution of credits between subsystems, the maxima of the criterion – the parameterized function of the system's efficiency – are determined at each interval. A new model has been developed based on the model of optimal development, which takes into account the use of external resources, such as loans. The method of including an external resource in the development function and the production function is considered. Examples of modeling are given.


optimal aggregation; production function; development function; external resource; simulation modeling

Avrunin O. et al.: Classification of CT-brain slices based on local histograms. Proc. of SPIE 9816, 2015, 98161J. DOI: https://doi.org/10.1117/12.2229040

Azarova A.: Information Technologies and Neural Network Means for Building the Complex Goal Program „Improving the Management of Intellectual Capital”. Lecture Notes on Data Engineering and Communications Technologies 77, 2022, 534–547. DOI: https://doi.org/10.1007/978-3-030-82014-5_36

Bellman R. E. et al.: Certain problems of mathematical control theory. Publishing House of Foreign Literature, Moscow 1963.

Bellman R. E., Kalaba R. E.: Dynamic programming and modern control theory. Academic, New York 1965.

Bertsekas D. P.: Dynamic programming and Optical Control. Athena Scientific, 2017.

Borovska T, Hryshyn D.: Comparative Analysis of Methods for Optimizing Production Systems based on Hamiltonian and the Method of Optimal Aggregation. IEEE 16th International Conference on Computer Sciences and Information Technologies (CSIT), 1, 2021, 345–348 [http://doi.org/10.1109/CSIT52700.2021.9648626]. DOI: https://doi.org/10.1109/CSIT52700.2021.9648626

Borovska T. et al.: Searchless Intelligent System of Modern Production Control. IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT), Zbarazh, Ukraine, 2020, 291–296 [http://doi.org/10.1109/CSIT49958.2020.9321842].

Borovska T.: Generalized model of optimal development, based on the integration of production and development subsystems. XII International Scientific and Technical Conference „Computer science and information technologies” CSIT’2017, Lviv, Ukraine, 2017, 446–449, 17353622 [http://doi.org/10.1109/STC-CSIT.2017.8098826]. DOI: https://doi.org/10.1109/STC-CSIT.2017.8098826

Borovska T. et al.: Intelligent System of Modern Production Control Based on the Methodology of Optimal Aggregation, 2021, 291–296 [http://doi.org/10.1109/CSIT49958.2020.9321842]. DOI: https://doi.org/10.1109/CSIT49958.2020.9321842

Borovska T. et al: Adaptive production control system based on optimal aggregation methods. Proc. of SPIE 10808, 2018, 108086O [http://doi.org/10.1117/12.2501520]. DOI: https://doi.org/10.1117/12.2501520

Borovska T. et al.: Mathematical models of production systems development based on optimal aggregation methodology. Proc. of SPIE 10445, 2017, 104452P [http://doi.org/10.1117/12.2281222]. DOI: https://doi.org/10.1117/12.2281222

Chertovskoy V., Tsehanovsky V.: Optimal model of manufacturing control system. Journal of Physics Conference Series 1864(1), 2021, 012096 [http://doi.org/10.1088/1742-6596/1864/1/012096]. DOI: https://doi.org/10.1088/1742-6596/1864/1/012096

Das S. et al.: A production inventory model with partial trade credit policy and reliability. Alexandria Engineering Journal 60(1), 2021, 1325–1338 [http://doi.org/10.1016/j.aej.2020.10.054]. DOI: https://doi.org/10.1016/j.aej.2020.10.054

Denardo E. V.: Dynamic Programming: Models and applications. Dover Publications 2003.

Fagin R., Kumar R., Sivakumar D.: Efficient similarity search and classification via rank aggregation. ACM SIGMOD International Conference on Management of Data, SIGMOD 2003 [http://doi.org/10.1145/872794.872795]. DOI: https://doi.org/10.1145/872757.872795

Forrester J.: Fundamentals of cybernetics of the enterprise (Industrial dynamics). Progress, Мoscow 1971.

Koulouris A. et al.: Applications of process and digital twin models for production simulation and scheduling in the manufacturing of food ingredients and products. Food and Bioproducts Processing 126, 2021, 317–333. DOI: https://doi.org/10.1016/j.fbp.2021.01.016

Leggatt T. W.: The evolution of Industrial Systems. Croom Helm, London 1985.

Leontiev V.: Theoretical assumptions and nonobservable facts. Economy, ideology, politics 9, 1972, 15.

Mesarovic M., Takahara Y.: General systems theory: mathematical foundations. Academic Press, New York, San Francisco, London 1975.

Mukha Ap. A.: Control of the process of complex engineering systems and processes development. Characteristic features of FMEA-analysis application. Mathematical machine and systems 2, 2012, 168–176.

Murayama T., Devis P.: Optimal aggregation of noisy observations. Journal of Physics: Conference Series 233(1), 2003, 301–312 [http://doi.org/10.1145/872794.872795]. DOI: https://doi.org/10.1145/872794.872795

Opoitsev V. I.: Equilibrium and stability in models of collective behavior. Mir, Moscow 1977.

Raymo M. et al.: A New Method for Food Production Analysis and Optimization Applied to Citrus Industry. Computer Aided Chemical Engineering 48, 2020, 2005–2010. DOI: https://doi.org/10.1016/B978-0-12-823377-1.50335-9

Romanyuk N. et al.: Microfacet distribution function for physically based bidirectional reflectance distribution functions. Proc. of SPIE 8698, 2012, 86980L [http://doi.org/10.1117/12.2019338]. DOI: https://doi.org/10.1117/12.2019338

Romanyuk O. et al.: Method of anti-aliasing with the use of the new pixel model. Proc. of SPIE 9816, 2015, 981617 [http://doi.org/10.1117/12.2229013]. DOI: https://doi.org/10.1117/12.2229013

Romanyuk S. et al.: New method to control color intensity for antialiasing. International Siberian Conference Control and Comm. – SIBCON, 2015 [http://doi.org/10.1109/SIBCON.2015.7147194]. DOI: https://doi.org/10.1109/SIBCON.2015.7147194

Rüttimann B., Stockli M.: Going beyond triviality: The Toyota production system-lean manufacturing beyond Muda and Kaizen. J. Serv. Sci. Manag. 9, 2016, 140–149 [http://doi.org/10.4236/jssm.2016.92018]. DOI: https://doi.org/10.4236/jssm.2016.92018

Rüttimann B.: Introduction to Modern Manufacturing Theory. Springer International Publishing AG 2018 [http://doi.org/10.1007/978-3-319-58601-4]. DOI: https://doi.org/10.1007/978-3-319-58601-4

Skrynkovskyy R. et al.: Improvement of the express diagnostics of the production activity of the enterprise taking into account the method of determining the optimal production programs in the operational management system. Technology Audit and Production Reserves 6(44), 2018, 4–10 [http://doi.org/10.15587/2312-8372.2018.147968]. DOI: https://doi.org/10.15587/2312-8372.2018.147968

Skrynkovskyy R. et al.: Improvement of the model of the innovative development of the production system of industrial enterprises. Reports on Research Projects 1/4(45), 2019, 53. DOI: https://doi.org/10.15587/2312-8372.2019.159227

Taylor C.: Dynamic programming and the curses of dimensionality. Applications of dynamic programming to agricultural decision problems. CRC Press, 2019. DOI: https://doi.org/10.1201/9780429040917

Tsybakov B.: Optimal Rates of Aggregation, Statistical Learning Theory and Stochastic Optimization. In: Saint-Flour E. D. et al.: Statistical learning theory and stochastic optimization: École d'eté de probabilités de Saint-Flour XXXI – 2001. 2004, 54–69.

Weijia D., Ginger Z., Jungmin L.: Optimal Aggregation of Consumer Ratings. NBER Working Paper No. 18567, 12–23.

Xinxin L.: Self-Selection and Information Role of Online Product Reviews. Information Systems Research 19(4), 2012, 56–64.


Published : 2022-12-30

Hryshyn, D., Borovska, T., & Kalizhanova, A. (2022). ELABORATION AND RESEARCH OF A MODEL OF OPTIMAL PRODUCTION AND DEVELOPMENT OF INDUSTRIAL SYSTEMS TAKING INTO ACCOUNT THE USE OF THE EXTERNAL RESOURCES. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 12(4), 60-66. https://doi.org/10.35784/iapgos.3248

Dmytro Hryshyn  dmitriygrishin2@gmail.com
Vinnytsia National Technical University  Ukraine
Taisa Borovska 
Vinnytsia National Technical University  Ukraine
Aliya Kalizhanova 
University of Power Engineering and Telecommunications; Institute of Information and Computational Technologies MES CS RK  Kazakhstan