The mathematical models used as an instrument of management by an enterprise are examined in the article. A review is conducted of mathematical models, investigating influence of different factors on the level of production with the use of productive functions. The models of business processes are examined. Advantages and lacks of the indicated models are analysed. Supposition is done that by the actual and effective instrument of management an imitation design that is confirmed by the examples of already existent system-dynamic models of home and foreign researchers can become a modern enterprise. On the basis of analysis of existent theoretical models the applied possibilities of the use of design are demonstrated taking into account the difficult and dynamic structure of co-operation of productive components.

Keywords: modeling, mathematical model, enterprise management, enterprise management tool, efficiency, simulation, economic system