Prediction and minimax estimation of the production system in the presence of risks

The solution of the problem of forecasting the state of complex socio-economic systems is possible only on the basis of appropriate dynamic economic and mathematical models that describe their main parameters, the presence of control actions and risks. In this paper, it is proposed to use a deterministic minimax approach for modeling and solving the problem of estimating the predicted states of a production system in the presence of risks. To make managerial decisions at a manufacturing enterprise aimed at improving the efficiency of its functioning, it is necessary to have high-quality information support, the basis of which is the solution of the corresponding problem of predicting the states of its basic parameters. In this article, to describe the functioning of a production system, it is proposed to use a discrete-time controlled dynamical system in the presence of risks. It is assumed that the values of the control action (admissible control scenarios) are realized from a finite set of admissible elements of the corresponding finite-dimensional vector space, and the realizations of the values of the phase vector of the model and the risk vector are limited by the given compact polyhedrons in the corresponding finite-dimensional vector spaces. Application of the developed discrete-time controlled dynamical model that describes the output products of an enterprise in the presence of risks, and the developed methodology for the formation and minimax estimation of the predictive set of its phase states in a given period of time, allow us to develop appropriate numerical algorithms that can be used in the development and creation of computer intelligent information systems that provide support for making effective management decisions at manufacturing enterprises. The main results of this work is the development of a new economic-mathematical model that describes the dynamics of the output products of an enterprise in the presence of risks and the creation on its basis of a methodology for constructing and minimax estimation of the predictive set of its phase states in the form of implementing a finite number of one-step operations that allow their algorithmization. The results obtained in this work can serve as a basis for developing methods for optimizing the management of enterprise production processes and creating computer intelligent information systems to support managerial decision-making.