A Mathematical Model for Human Capital Reproduction in Enterprises under Artificial Intelligence Adoption

Source abstract

Introduction . An economic-mathematical model of human capital development is an essential tool for managing a human capital of the enterprise. Existing models do not take into account the complex dynamics of such factors as training intensity, competence depreciation, introduction of new technologies, and worker mobility. Consequently, there arises a need for an economic-mathematical model of labor resource reproduction that provides a comprehensive picture of their current state and future parameters. The objective of the study is to develop a dynamic economic-mathematical model of the reproduction of human capital of enterprises, taking into account the key factors of its transformation, and to empirically validate it using data from Russian enterprises. Materials and Methods. Based on a theoretical analysis of the factors affecting the reproduction of enterprise human capital, these factors have been formalized to construct a dynamic economic-mathematical model. Logistic models are employed to describe the dynamics of human capital development, wherein the rate of growth is determined simultaneously by the internal management decisions of the enterprise, structural losses due to competence obsolescence, and the external competitive environment. Given the difficulty of obtaining corporate data to validate the developed model, the authors utilized survey results from engineers at three machine-building enterprises ( n = 617). Following the processing of the survey data, estimates were derived for the coefficients α and β, which characterize the intensity of artificial intelligence (AI) adoption and implementation. Results. To model competitive dynamics for a group of enterprises within an industry, a system of interconnected ordinary differential equations (ODE) has been formulated. It is shown that calibrating the presented dynamic model at the enterprise level requires data that include HR metrics, such as the intensity of training and artificial intelligence adoption, as well as mobility and attractiveness parameters linked to remuneration and workforce flows. A numerical experiment based on the proposed dynamic economic-mathematical model was conducted to generate a five-year forecast of human capital dynamics for three machine-building enterprises ( N = 3). Three scenarios reflecting labor resource dynamics are presented: 1) without inter-firm interaction; 2) accounting for the impact of wage differentiation; and 3) accounting for varying levels of activity in corporate compensation policies. The results confirmed the presence of a saturation effect for Scenario 1, the pronounced impact of labor market competition on human capital dynamics for Scenario 2, and the significance of training intensity and AI technology usage — factors that can even partially offset the adverse effects of the competitive environment in Scenario 3. Discussion. The proposed model of human capital reproduction is based on a system of ODE, providing a holistic and internally consistent description of how this resource evolves within an enterprise under the influence of investments in employee training, adoption of AI technologies, and changes in the competitive environment. The results of model testing across three scenarios for three enterprises align with the findings of other studies. In particular, the saturation effect at the enterprise level in the medium term is confirmed, as well as the positive impact of wage growth, increased employee training, and adoption of AI on the development of human capital (specifically, for organizations with a low initial level of it). Conclusion. The authors propose an approach to modeling enterprise human capital reproduction amid the rise of AI technologies. The approach is based on the premise that employee competencies are formed and lost over time under the combined influence of training, technological renewal, and inter-firm mobility. This economic-mathematical model describes human capital dynamics as a nonlinear process of bounded growth relative to a fixed industry frontier, which provides comparability of enterprise parameters. A numerical experiment involving three enterprises has demonstrated the model practical interpretability and the importance of jointly accounting for the above factors.