(untitled) (Modern Problems of Metallurgy, 2025)
The work is devoted to the urgent task of deploying fire groups of air defense forces to cover the lines of air attacks. To solve the problem, modern methods of the theory of optimal set partitioning, mathematical modeling using differential equations and their systems, a specialized software package has been developed, which includes a mobile and browser application, is used. When developing the software package, modern programming languages and technologies were used, an overview and comparison with existing solutions in different countries was made. A retrospective analysis was carried out, criteria for the optimality of the solution being sought were developed, advantages and disadvantages of the approach were determined. The use of methods of the theory of optimal set partitioning allows you to analytically determine the criteria for the quality of the solution, conduct an analytical study of admissible solutions and determine the optimal one, and approbation of analytical results in practice and examples with practical input data increases the accuracy and relevance of the results obtained analytically. Nowadays, the issue of dynamic deployment of fire groups is very relevant for Ukraine. The decision to create and operate fire groups was made and implemented only from the beginning of the full-scale invasion of the aggressor country and became widely used during the massive use of attack drones by the aggressor country against civilian, military and energy facilities of Ukraine. The effectiveness of the use of fire groups has been proven in practice, but the method of their placement, as a rule, is heuristic, that is, not optimal.