Разработка алгоритма решения задачи распределения времени обучения по направлениям подготовки
Работая с нашим сайтом, вы даете свое согласие на использование файлов cookie. Это необходимо для нормального функционирования сайта, показа целевой рекламы и анализа трафика. Статистика использования сайта отправляется в «Яндекс» и «Google»
Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

Development of an algorithm for solving the problem of distributing training time in training areas

Reznikov D.A.  

UDC 51-77
DOI: 10.26102/2310-6018/2024.45.2.008

  • Abstract
  • List of references
  • About authors

During their service in the penal system, employees continuously improve their knowledge, skills, and abilities through official training. This article discusses the problem of allocating training time to different areas in order to maximize the value of minimal average grades in those areas. A solution algorithm has been developed. The first step involves determining the maximum possible increase in the minimal average score for one area as well as the amount of time required for this increase. If the resultant score value is lower than the average score in other areas, the second step identifies the maximum possible increases for multiple areas and the corresponding amount of time needed. The article also determines the type of relationship between the increase in average grades for training areas and the time spent on training through the approximation of statistical data. This allows for the analytical solution of the problem. The analysis of the potential use of power and exponential functions for approximation, which allows for the approximate solution of a problem through numerical methods, is also conducted. The resulting values of the coefficient of determination confirm the high accuracy of the approximation. Graphs of the dependency are presented. Two examples of analytical solutions to the problem are provided, illustrating the use of the proposed method. In the first example, all employees have the same initial average training grades in all areas, and in the second example, average grades differ.

1. Otsuka J. The Role of Mathematics in Evolutionary Theory. Cambridge: Cambridge University Press; 2020. 74 p.

2. Belov M.V., Novikov D.A. Modeli tekhnologii. Moscow: LENAND; 2019. 160 p. (In Russ.).

3. Stroganov V.Yu., Tsvetkov Yu.B. Optimization methodology of curriculum digital model based on learning-forgetting functions. In: Tsifrovye tekhnologii v inzhenernom obrazovanii: novye trendy i opyt vnedreniya, 28-29 November 2019, Moscow, Russia. Moscow: Bauman Moscow State Technical University; 2020. P. 108–112. (In Russ.).

4. Rawle F., Bowen T., Murck B., Hong R.J. Curriculum mapping across the disciplines: differences, approaches, and strategies. Collected Essays on Learning and Teaching. 2017;10:75–88. https://doi.org/10.22329/celt.v10i0.4765.

5. Novikov D.A. Zakonomernosti iterativnogo naucheniya. Moscow: Trapeznikov Institute of Control Sciences of Russian Academy of Sciences; 1998. 96 p. (In Russ.).

6. Belov M.V., Novikov D.A. Models of experience. Problemy upravleniya = Control Sciences. 2021;(1):43–60. (In Russ.). http://doi.org/10.25728/pu.2021.1.5.

7. Belov M.V., Novikov D.A., Rogatkin A.D. Learning curves estimates. Upravlenie bol'shimi sistemami: sbornik trudov = Large-Scale Systems Control. 2019;(82):6–27. (In Russ.). http://doi.org/10.25728/ubs.2019.82.1.

8. Anzanello M.J., Fogliatto F.S. Learning Curve Models and Applications: Literature Review and Research Directions. International Journal of Industrial Ergonomics. 2011;41(5):573–583. http://doi.org/10.1016/j.ergon.2011.05.001.

9. Henderson B.D. The Application and Misapplication of the Experience Curve. Journal of Business Strategy. 1984;4(3):3–9. https://doi.org/10.1108/eb039027.

10. Ezerskii V.V. Izbrannye razdely vysshei matematiki. Vypusk 7. Metody approksimatsii funktsii. Omsk: Siberian State Universitey of Physical Culture and Sports; 2011. 52 p. (In Russ.).

Reznikov Dmitriy Alexandrovich

Voronezh institute of the Russian Federal Penitentiary Service

Voronezh, Russian Federation

Keywords: average grade, average grade increment, learning time, learning curve, approximation, least squares method

For citation: Reznikov D.A. Development of an algorithm for solving the problem of distributing training time in training areas. Modeling, Optimization and Information Technology. 2024;12(2). Available from: https://moitvivt.ru/ru/journal/pdf?id=1540 DOI: 10.26102/2310-6018/2024.45.2.008 (In Russ).


Full text in PDF

Received 22.03.2024

Revised 09.04.2024

Accepted 19.04.2024

Published 24.04.2024