Development of the model of minimax adaptive management of innovative processes at an enterprise with consideration of risks

Abstract

The authors consider a discrete dynamic system, containing an object – the innovative process (IP). Its dynamics is described by the vector linear discrete recurrent ratio and is influenced by controlled parameters (controls) and an uncontrolled parameter (the vector of risk or obstacle). In this case, risks in the system of IP management at an enterprise will imply the factors that influence negatively or disastrously the results processes, considered in it. To solve the set problem, a general model of IP management for organization of minimax adaptive management in the selected class of permissible strategies of adaptive management was formalized. It was proposed to use a deterministic approach for modeling and solution of the original problem in the form of dynamic problem of minimax IP management (optimization of the guaranteed result) at a given moment of time, with consideration of risks. To solve the problem of minimax IP management in the face of risks, the authors propose the method that is reduced to implementation of solutions of a finite number of problems of linear and convex mathematical programming, as well as a discrete optimization problem. Solution of the set problem of minimax IP management allows obtaining the optimal guaranteed (minimax) outcome. For effective implementation of the resulting mathematical apparatus in practice of work of enterprises, the detailed model of multicriteria optimization of IP management at an enterprise in the face of risks was developed, which describes dynamics of the studied process to the full. Generated optimization criteria and the system of phase constraints of the model take into consideration possibilities of production capacities, as well as meet the requirements for IP. The proposed method makes it possible to develop effective numerical procedures that enable us to implement computer modeling of dynamics of the considered problem, to formulate adaptive minimax IP management at an enterprise and to obtain the optimum guaranteed results. The presented results could be used for economic-mathematical modeling and solution of other problems of optimization of processes of data forecasting and management under conditions of information deficit and existence of risks. In addition, the developed tools of modeling can be the basis for development of appropriate software and hardware complexes for supporting effective managerial decision making in practice.