DEVELOPMENT AND ANALYSIS OF METHODS FOR SOLVING TYPICAL PROBLEMS OF RATIONAL DISTRIBUTION OF LIMITED RESOURCES

The object of research is the problem of rational distribution of limited resources between subsystems of a complex system that function independently. The relevance of the work is determined by the fundamental features of this problem, which take into account the possible variability of the parameters of the environment in which real systems operate. The work sets out tasks for the rational distribution of resources for multiplicative, additive and parametrically defined objective functions, as well as for cases where the parameters of the objective function are not clearly defined. Methods for solving these tasks have been developed. At the same time, it is shown how the desired result can be obtained analytically or numerically. To solve the problem of rational allocation of a one-dimensional resource with multiplicative and additive functions, the method of Lagrange multipliers is used. Under these conditions, the mathematical model of the problem allows it to be reduced to an easily solvable equation. The paper investigates a significantly more complex problem in which the production function for the elements of the system is represented as regression polynomials. In particular, a special case is considered in detail where the parameterised production function depends linearly on two arguments that determine a two-dimensional resource. It is further shown that even a more complex problem with a multidimensional resource can be reduced to an equation that can be solved numerically. Of greatest theoretical interest is the problem of resource allocation for cases where the parameters of the production function are defined imprecisely with (L-R)-type membership functions. The fundamental scientific novelty of the proposed approach to solving the problem consists in the development and use of a technology for reducing the initial fuzzy problem to a clear one by finding and using the membership function of the fuzzy criterion of the problem. At the same time, the unique adaptive properties of (L-R)-type numbers determine good opportunities for the practical use of the proposed methods.