Simulation model of the training program for citizens in employment centers

The relevance of the study is due to the need to improve the efficiency of vocational training programs in the context of limited data and resources. Modern employment centers are faced with the task of quickly and accurately identifying the risks of early participant attrition, which requires the use of adapted analytical tools. The article proposes a Markov model of the educational process that allows, based on a minimum set of input data, to predict the trajectories of students and identify key points for management intervention. Empirical testing of the model was carried out on the data of the Lipetsk Employment Center (2024), which made it possible to assess the probabilities of successful program completion, the risks of dropouts, the average duration of involvement and sensitivity to various types of interventions. A sensitive analysis showed that investments in retaining active students provide a greater increase in efficiency compared to attempts to engage passive participants. The results obtained are of practical value for professional retraining systems and can be used to increase the ROI of programs by optimizing curatorial strategies and attendance rules. The introduction of such models contributes to a more rational distribution of resources, reduction of losses and the formation of personalized trajectories, which is especially important in the context of a dynamically changing labor market.

1. Durbin E.P. Manpower Programs as Markov Chains. Santa Monica: Rand Corporation; 1968. 28 p.

2. Rosenbaum D.I., Jayanetti K. Worklife and Unemployment: A New Consideration. Journal of Forensic Economics. 2021;29(2):177–190. https://doi.org/10.5085/JFE-473

3. Card D., Sullivan D. Measuring the Effect of Subsidized Training Programs on Movements in and out of Employment. Econometrica. 1988;56(3):497–530. https://doi.org/10.2307/1911698

4. Ziderman A., Driver C. A Markov Chain Model of the Benefits of Participating in Government Training Schemes. The Manchester School of Economic and Social Studies. 1973;41(4):401–417. https://doi.org/10.1111/j.1467-9957.1973.tb00091.x

5. Matetskii K.S., Kharin Yu.S. O riske prognozirovaniya odnorodnykh konechnykh tsepei Markova s neizvestnymi parametrami. Vestnik BGU. Seriya 1: Fizika. Matematika. Informatika. 2010;(3):66–71. (In Russ.).

6. Chase G. Utilizing the Universal Squash Rating System and Markov Chains to Accurately Predict Outcomes of Squash Matches. Vestnik KRSU. 2023;23(10):136–149. https://doi.org/10.36979/1694-500X-2023-23-10-136-149

7. Karpova A.V. The Process of Informational Impact on Decision-Making in the Economy Through Markov Chains Model. Ekonomika i predprinimatel'stvo. 2017;(9–1):835–837. (In Russ.).

8. Panarina D.V. The Device of Explosive Chains of Markov in Economy. Ekonomika i predprinimatel'stvo. 2015;(11–2):79–82. (In Russ.).

9. Popov A.M., Ermakov E.I., Pakhomov S.A. Vlozhennye tsepi Markova v ekonomike. In: Aktual'nye problemy ekonomiki, upravleniya, prava: Materialy mezhvuzovskoi konferentsii, 11 December 2010, Moscow, Russia. Moscow: Institute of Economics and Business; 2010. P. 187–189. (In Russ.).

10. Ngai S.S.-Yu., Cheung Ch.-K., Ng Yu.-H., et al. Unraveling the School‑to‑Work Transition of Non‑Engaged Youth: A Continuous‑Time Markov Chain Analysis. Children and Youth Services Review. 2025;172. https://doi.org/10.1016/j.childyouth.2025.108253