USING THE DECOMPOSITION METHOD TO SIMULATE A DIVERSIFIED ECONOMIC SYSTEM

Abstract

The article focuses on the issues of constructing a dynamic model of a diversified economic system based on conservation laws (the method of dynamic Leontief equations) and methods for their solution.

When developing an economic and mathematical apparatus for the analysis, planning and forecasting of diversified production, a system of models is created based on the representation of production as a complex hierarchical system. The upper level of the system of models is formed by macroeconomic systems that make it possible to identify changes in free indicators and provide valuable information about the rates and proportions of development of diversified production. The model of interbranch balance assumes that each industry produces only one product and each product is produced by only one industry or one technological method. But if consider the production of any particular type of product, then the possibility of obtaining this product in several technological ways is revealed. There are many different options for the production of products in order to meet the final demand for certain types of products. Naturally, different options require unequal costs and bring unequal economic effect. Therefore, an optimization problem arises - the problem of choosing the best, most optimal production option. The problem of optimizing large systems is revealed by the problem of creating methods for solving problems of mathematical programming of large dimensions. To solve such problems, this article uses the decomposition method.

As a result of the implementation of the decomposition method, the initial system is decomposed into subsystems, for each of which it is necessary to solve a subproblem of a lower dimension. These subsystems are interconnected. A general solution cannot be obtained by isolation solving such subproblems. The paper builds a model of a multi-sectoral economic system and an algorithm for finding the optimal parameters, and it is found that, provided that the coordinating task is non-degenerate, the value of the objective function decreases at each iteration. If there are only a finite number of possible bases and provided that none of the bases is used twice, the use of the decomposition method leads to an optimal solution in a finite number of iterations.