Research by Nataliia Mahas: Mathematical Support for Anti-Crisis Management and Economic Security
Nataliia Vasylivna Mahas, a researcher at the Interregional Academy of Personnel Management (IAPM), PhD in Economics and Associate Professor, has co-authored the research article “Mathematical and Analytical Support for the Functioning of the Anti-Crisis Management System in the Context of Ensuring Economic Security.”
The study was published in 2026 in Mathematical Modeling and Computing, a scientific journal indexed in the Scopus bibliographic database.
In addition to Nataliia Mahas, the article was co-authored by N. Struchok, O. Molnar, O. Denysov, M. Tarnavskyi, and R. Darmits. The paper was published by the scientific journal of Lviv Polytechnic National University. It presents a mathematical and analytical approach to the functioning of an anti-crisis management system aimed at maintaining an enterprise’s economic security under the simultaneous impact of financial, operational, market, and credit shocks.
Anti-Crisis Management as the Focus of the Study
Modern enterprises may face several groups of risks simultaneously, affecting their financial condition, operations, supply chains, market position, and ability to respond to adverse changes. Therefore, the authors consider anti-crisis management not merely as a set of individual response measures, but as a system that requires quantitative assessment of an enterprise’s condition and evidence-based management decisions.
The study proposes an approach that combines several mathematical and analytical tools. These include indicator normalization, entropy-based determination of local weights, the Analytic Hierarchy Process for coordinating the weights of functional components, a multiplicative economic security index, and a dynamic model of an enterprise’s condition. Particular attention is given to optimizing the structure of anti-crisis measures using the Conditional Value-at-Risk (CVaR) criterion.
This approach makes it possible to move beyond assessing an enterprise’s financial condition at a particular point in time and examine its potential dynamics under the influence of different factors. The model takes into account the inertia of an enterprise’s internal condition, interactions between functional components, crisis-related pressures, limitations on the anti-crisis budget, and the risk of adverse scenarios.
Economic Security of an Enterprise in a Dynamic Model
Economic security is one of the central concepts of the study. The researchers consider it as an indicator whose condition may change depending on the internal characteristics of an enterprise and external influences.
The proposed model takes into account not only the current value of the relevant index but also the trajectory of its changes over time. This is important for anti-crisis management because a management decision should be associated not only with the current condition of an enterprise but also with the potential consequences of allocating resources among different areas.
Within the study, the authors developed a model dataset comprising 10 hypothetical industrial enterprises and 16 indicators. To test the proposed approach, 5,000 scenario runs were conducted using a reproducible random disturbance generator. This made it possible to analyze the behavior of the model under different initial enterprise characteristics and crisis-development conditions.
The simulation results showed that an identical allocation of anti-crisis resources among enterprises with different vulnerability structures does not produce the same outcomes. By contrast, optimized resource allocation within the proposed model reduced the CVaR indicator and the probability of economic security falling below a critical threshold. At the same time, the authors emphasize that the effect depends on the initial vulnerability profile of a particular enterprise.
Mathematical Tools for Anti-Crisis Decision-Making
A distinctive feature of the study is the combination of several methods within a unified model. Indicator normalization ensures comparability, the entropy-based method is used to determine local weights, while the Analytic Hierarchy Process is applied to coordinate the weights of individual functional components.
Another element is the multiplicative economic security index, which provides a comprehensive representation of an enterprise’s condition. The dynamic model, in turn, makes it possible to track changes in this condition under the influence of internal and external factors.
The authors also consider the potential use of the model to identify priorities in areas such as maintaining liquidity, operational recovery, supply diversification, adaptation to market changes, as well as analytical and coordination support for management decisions.
Results of Scenario Modeling
One of the quantitative results of the study is an analysis of changes in key indicators under different levels of anti-crisis budget intensity. For an enterprise with an average initial condition, increasing the normalized anti-crisis budget intensity from 0.08 to 0.18 within the proposed model increased the expected final economic security index from 0.427 to 0.593.
At the same time, the CVaR indicator decreased from 0.941 to 0.407. These results characterize the behavior of the proposed model and the model dataset rather than representing a universal pattern applicable to all enterprises. The researchers specifically emphasize that the effect depends on the initial vulnerability structure of an enterprise.
The scenario component therefore allows the model to be used not only to assess the current condition but also to compare possible economic security trajectories under different conditions. This expands the possibilities for quantitative support of management decisions in situations of uncertainty.
Practical Significance of the Research
The approach proposed by the researchers provides a quantitative basis for identifying priorities among anti-crisis measures. Instead of distributing available resources evenly, the model makes it possible to take into account the specific vulnerability profile of an enterprise and the potential consequences of different resource allocation strategies.
The method may be useful for analyzing management decisions related to liquidity, operational recovery, supply-chain diversification, and adaptation to changes in the market environment. At the same time, the proposed model is research-oriented, and its results require adaptation to the real-world data of a particular enterprise.
The publication by Nataliia Mahas, co-authored with researchers from other Ukrainian higher education institutions, demonstrates interinstitutional cooperation in studying economic security, anti-crisis management, and the application of mathematical methods in economic analysis.
The new article continues research focused on economic security and enterprise management mechanisms under conditions of instability. It also contributes to IAPM’s academic output in economics, management, and the application of modern analytical tools. The findings may serve as a basis for further research into economic security models, anti-crisis management, and resource optimization.
The full article is available on the website: https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-13-number-3-2026/mathematical-and-analytical-support-functioning
Bibliographic information
Mahas N., Struchok N., Molnar O., Denysov O., Tarnavskyi M., Darmits R. Mathematical and Analytical Support for the Functioning of the Anti-Crisis Management System in the Context of Ensuring Economic Security. Mathematical Modeling and Computing. 2026. Vol. 13, No. 3. Pp. 856–866. DOI: 10.23939/mmc2026.03.856.
