Analysis and practical application of resource distribution models

Russia, despite external constraints, continues to implement various social, scientific, defence and other programs that require a significant number of diverse resources. From their rational distribution depends on the efficiency of enterprises and the effectiveness of projects. The article is devoted to the optimization of resources using the apparatus of mathematical modelling. In this paper, we give a brief overview of mathematical methods for optimizing resources. Particular attention is paid to models studied by the Lagrange method and to the methods of game theory. In the paper, two optimization problems are considered — maximization of the result under conditions of limited resources and rational allocation of resources with a fixed output volume. The paper notes that existing models do not take into account the state of the external environment, which has a significant impact on the result. The variant of resource allocation, accepted by us as optimal under certain conditions, can be completely unsuitable when the state of the external environment changes after a certain period of time. The optimal allocation of resources can be considered only in a certain state of the external environment. To solve the optimization problem in conditions of complete and incomplete uncertainty, it is necessary to take into account all possible environmental conditions for the project implementation period. To solve problems in conditions of complete or incomplete uncertainty, a mathematical toolkit is proposed based on the theory of games with nature. The work is of practical importance since it allows you to optimize your economic activities at different levels of management — from the enterprise to a large corporation.