On the development and implementation of mathematical models for crisis management centers based on performance evaluation and state matrices

The article presents the development and practical testing of two complementary mathematical models aimed at evaluating and enhancing the operational efficiency of the Crisis Management Centers of EMERCOM of Russia. The first model is based on the use of state matrices that reflect the dynamics of key system parameters – the readiness of forces and assets, the state of information support, the level of interaction between operational units, and the quality of situational forecasting – at discrete points in time. This allows for tracking system changes over time. The second model is implemented through an integrated performance indicator, which aggregates the normalized values of ten key operational parameters, including response time metrics, readiness indicators, and personnel metrics. The aggregation is performed considering expert-assigned weighting coefficients, allowing for the consideration of the relative importance of each parameter for overall efficiency. Both models provide a tool for the quantitative assessment of the current state of a Crisis Management Center, the objective identification of weaknesses in operational activities, and the precise tracking of the results of implementing managerial and technical improvements. A pilot implementation of the models in regional Crisis Management Centers demonstrated high practical effectiveness: the overall operational efficiency increased by 22.85%. Simultaneously, a significant reduction in decision-making time under conditions of uncertainty was achieved, as confirmed by the decrease in all time-related indicators, such as the time for developing a forecast, forming a response team, and disseminating information to the public. The scientific novelty of the work lies in the synthesis of a matrix-based apparatus for dynamics analysis with the methodology of integrated performance evaluation. The proposed approach lays the foundation for further automation of data collection processes, near-real-time monitoring, and the development of decision support systems in emergency situations.