The paper is devoted to the development and research of new mathematical models of the functioning and development of modern production systems. The development is based on the methodology of optimal aggregation and the solution of a variational problem of optimal development applying the maximum principle method. The following modules have been developed: operators of optimal aggregation of the “production, development”, “innovation” structures. The simulation model of the active external environment has been modified: “producers, products, consumers”. The decomposition of the development process has been made into intervals where correction of the optimal development strategy is performed. The analysis of the existing integral criteria of optimality of the “accumulated output” type has been made. The criterion of the generalized stability of the optimally aggregated production system on the given classes of environment is selected and implemented in the software environment. Examples of modelling are given.
Production control system, enabling to distribute resources or loads between subsystems quickly and optimally is suggested. The methodology of optimal aggregation allows us to replace the multidimensional optimization problem by a system of one-dimensional optimization problems, which removes the dimensionality problem. The solution of optimization problem is the optimal equivalent function of the production system. A technique of parametrization of this function is developed. Optimum control is represented as a function of resources prices, production products, parameters of production functions. A decision support system has been developed and software modules have been tested.
Development of mathematical models for the analysis and synthesis of optimal management of an enterprise, with the account of the requirements of efficiency and survivability criteria, was performed. A single resource approach was used to develop models for an enterprise operation in nominal and non-nominal conditions – in the event of subsystems failures. The survivability functions are developed – the dependences of the enterprise efficiency losses on the cost of the failure configuration. The tasks of the enterprise optimization are identified: – minimization of survivability functions on the set of failure configurations due to the search for rational structures of the subsystems, and – maximization of the efficiency function in nominal and non-nominal operation modes. The method of optimal aggregation was used. The results of research on models are presented.