Economic and Mathematical Modeling of Human Resource Management in a Hybrid Environment Based on the Competency-Based Approach

Objective. The purpose of the article is to develop an optimization-based economic and mathematical model for the formation and development of employee competencies tailored to work in a hybrid environment. The model is designed not only to assess the degree of personnel compliance with job-specific requirements, but also to ensure the achievement of the maximum level of organizational efficiency aligned with the overall development goals of the enterprise. Method. The methodological foundation of the study is based on general scientific and specialized methods that ensure a comprehensive analysis of human resource management processes in a hybrid environment and the development of an economic and mathematical model relevant to the conditions of digital transformation and resource constraints. A system-based approach was applied to formalize the interrelations between employee competencies, organizational efficiency, training costs, and the risks of failing to achieve target parameters. This approach made it possible to integrate behavioral, economic, and managerial variables into a coherent model that reflects the complex dynamics of hybrid work organization. Mathematical modeling methods formed the basis for building an optimization model for managing the development of employee competencies. In particular, the tools of quadratic programming were used, enabling consideration of enterprise resource limitations in achieving target competency levels. The Analytic Hierarchy Process (AHP) was used to determine the weighting coefficients of competencies based on their strategic significance for the enterprise. This allowed for the formalization of expert evaluations in ranking competencies by development priority. Exponential modeling was applied to describe the dynamics of the risk of unmet competencies as a function of their development level. Considering the nonlinear decline of risks enabled adequate modeling of the learning effect and growing employee confidence. Comparative analysis methods were employed to examine alternative personnel development strategies in traditional versus hybrid work formats. This allowed for the identification of significant differences in cost structures and the time dynamics of competency acquisition. A scenario-based approach was used to explore variations in the organizational environment, such as increasing uncertainty, expansion of digital technologies, or escalation of social risks. This made it possible to adapt the model to potential external shocks. The integration of the above-mentioned methods enabled the development of a quantitatively substantiated model for HR decision-making in a hybrid environment, combining the enterprise’s strategic objectives with its actual resource capabilities and the individual needs of its personnel. The results. The article presents the conceptualization and formalization of the process of managing personnel development at an industrial enterprise in a hybrid work environment through the lens of the competency-based approach. An economic and mathematical model is developed to evaluate and optimize the development of key employee competencies, taking into account the weight of each competency, the risks of underdevelopment, and the enterprise's resource constraints. The model is based on an integrated indicator of organizational efficiency, which depends on the level of competency development and the magnitude of risk reduction. The proposed model includes the definition of growth functions for efficiency and risk mitigation depending on the level of competency development, with exponential modeling used to reflect the decreasing probability of loss as a result of enhanced professional training. A method for calculating risk sensitivity parameters (α-parameters) is developed, based on the structure of competencies, the expected consequences of their underachievement, and stakeholder priorities. The model enables the optimal allocation of the personnel development budget, taking into account preset constraints, priorities, and minimum acceptable competency levels. Model-based simulations yield results that demonstrate the practical applicability of the system in making strategic HR decisions. In particular, a clear dependence is established between the level of organizational efficiency and the combination of competency development strategies under various funding scenarios. The results also confirm the hypothesis of the existence of threshold values for certain competencies, whose development has a disproportionate impact on overall efficiency in hybrid work formats. The study substantiates the need to develop individualized employee development trajectories in accordance with the enterprise’s positional structure and the expected level of digital integration. It is found that adaptability, digital literacy, and emotional intelligence are critical competencies in the hybrid ISSN1680-0044 Наукові праці ДонНТУ. Серія: «Економічна» №1 (31), 2025 66 environment. Based on this, alternative management scenarios are formulated to ensure stable productivity with minimal HR-related risks. The results of the study form a new methodological platform for strategic human resource development in hybrid work environments. The model can be implemented as a component of HR analytics and integrated into digital decision-support systems. This opens up avenues for further research involving fuzzy logic, scenario-based forecasting, and dynamic modeling of competency potential under conditions of increased uncertainty. Scientific novelty. Unlike existing studies that examine personnel management from a competency-based perspective in a fragmented manner or explore the effects of the hybrid work environment without formalization, this paper proposes a comprehensive economic and mathematical model that enables quantitative assessment of organizational efficiency based on the development level of key employee competencies, taking into account resource constraints and human capital risks. The proposed approach is grounded in the integration of expert evaluation of competency importance, exponential modeling of the risks of underachievement, and optimization of the personnel development budget. This provides a systematic linkage between enterprise HR strategies and strategic performance in the context of hybrid organizational structures. In contrast to traditional models where competencies are treated as static or linearly measured parameters, the developed model incorporates the nonlinear nature of efficiency gains, threshold effects of specific competencies, and the dynamic sensitivity of risk. A distinctive feature of this study is the method introduced for determining risk sensitivity coefficients (α-parameters), which reflect the relationship between the depth of competency development, its weight in the organizational structure, and its strategic criticality. Thus, the study lays the groundwork for scientifically justified decision-making in human resource management under conditions of digital orientation, limited resources, and hybrid organizational formats, representing a significant contribution to the advancement of the modern HRM paradigm. The practical significance. The practical significance of the research lies in the development of approaches to integrating the principles of The practical significance of the study lies in the development of a toolkit for making managerial decisions regarding personnel development in industrial enterprises operating in a hybrid work environment, based on a formalized assessment of employee competencies. The proposed economic and mathematical model enables the rational allocation of resources for the development of key competencies, taking into account their weighted significance, the risks of underachievement, and the expected return in terms of organizational effectiveness. The model can be integrated into strategic HR planning systems, digital HR analytics platforms, and managerial decision-support tools. It provides opportunities to design individualized employee development trajectories in accordance with the enterprise’s positional structure, justify budgets for training and upskilling, and minimize the risks of inefficient investment in human capital. The research findings are aimed at the practical improvement of personnel management policies under real conditions of digital transformation, organizational turbulence, and adaptation to hybrid work models. This supports executives and HR professionals in making strategically sound decisions directed toward sustainable productivity growth, the developm