РОЗРОБКА МАТЕМАТИЧНОЇ МОДЕЛІ ОПТИМАЛЬНОГО ВИРОБНИЦТВА ТА РОЗВИТКУ ВИРОБНИЧИХ СИСТЕМ З ДЕКОМПОЗИЦІЄЮ ПЛАНОВОГО ПРОЦЕСУ РОЗВИТКУ НА ІНТЕРВАЛИ

Abstract

The problem of developing effective models of optimal development and functioning of modern production systems functioning in an active environment is considered. Analyzing analogues showed that there are no adequate models for "production-development" industries that operate in an active environment – competitors, intermediaries, suppliers and consumers. The basic analogue c the solution to the variation problem of development and production has a limited area of adequacy – productions with a static environment. In the basic analogue, the optimal development strategy is created for the entire planning period, which is usually 2-10 years. For such a long-term period, it is impossible to predict the state of product, finance, and technology markets. The above confirms that this work is relevant. This work uses a generalized model of optimal development based on the methodology of optimal aggregation. Using the methodology of optimal aggregation allows us to move from a multidimensional problem of nonlinear programming to a system of one-dimensional optimization problems. At the same time, the computational complexity increases linearly, which allows us to use this methodology for production systems with a large number and nonlinearity of connections between elements. The work modifies the basic model of optimal development with the division of the development process into intervals. At the beginning of each interval, the optimal development strategy is adjusted taking into account the clarification of information about the future state of the active environment: the actions of competitors, consumers, suppliers, intermediaries, world markets. To determine the optimal value and the optimal distribution of resources between subsystems, the maxima of the – criterion the parameterized function of the system efficiency – are determined at each interval. Examples of modeling and testing models are given.