МАТЕМАТИЧНА МОДЕЛЬ РЕСУРСНОЇ ОПТИМІЗАЦІЇ ЦІЛЬОВОЇ ПРОГРАМИ ЗАСТОСУВАННЯ СИЛ І ЗАСОБІВ ЗАПОБІГАННЯ ТА ЛІКВІДАЦІЇ НАСЛІДКІВ НАДЗВИЧАЙНИХ СИТУАЦІЙ

Abstract

An analysis of recent research and publications has shown that during emergencies, it is necessary to calculate the forces and means that can be used to eliminate them. The problem of optimizing resources during the elimination of the consequences of emergencies remains relevant today not only for Ukraine but also for the whole world. To solve these problems, mathematical models are developed depending on the state of threat sources and protection resources. In the control complex the problems of distribution of protection resources according to forecasting results are formulated. The article considers mathematical models of resource optimization to eliminate the consequences of emergencies depending on the state of sources of threats and resources of protection. The construction of these mathematical models depends on the characteristics of the area of the degree of escalation of the armed conflict in the South-East of Ukraine. After determining the amount of resources of forces and means to prevent and eliminate the consequences of emergencies, a scenario of their application is developed and the use of program-targeted approach is envisaged. This approach allows to solve the problem of resource optimization, which is considered as a process of applying resources for operations - a system of measures of the program at the stages of planning. In this case, the set of operations of the program is given by its mathematical model - a network graph, which reflects the operational composition of the program and its logical structure. As a result, there are two interpretations of the main task of resource optimization of the process (direct and inverse), which maximize the efficiency of the process through the rational use of resources. Formal formulation of problems requires the use of nonlinear programming methods to solve them. The method of indefinite Lagrange factors is used in the article. Formalization of the research problem allows to apply methods of mathematical programming and to receive its decision in the form of algorithms and mathematical models. The article highlights the scientific result, which has an applied value - a mathematical model and algorithms for solving problems of optimal resource management in preventing and eliminating the consequences of emergencies. The essence of the developed model and algorithm is to calculate the optimal allocation of resources by objects based on the assessment of threats and regulatory costs of resources and the development of the optimal program (scenario) of resource use. Based on the methods of mathematical programming, algorithms are developed, which in the presence of initial data allow to solve the problems of optimal control in the implementation of measures to prevent emergencies, eliminate their consequences, as well as optimize the program-scenario of forces during these measures. The use of these models allows to improve the quality of decision-making in relation to the creation of rational use of forces and means during the elimination of the consequences of emergencies.