On the Formulation of the Problem of Optimal Control of Production Parameters Using a Two-Level Model of the Production Process

Using a statistical approach, widespread in natural sciences, a two-level model to control the parameters of the flow line production system has been built. The state of the system is given by the amounts of sets of the objects of labour. The state of the subject of labour is given by a point in the phase space. The function of the distribution of objects of labour by the state is introduced and the kinetic equation for the distribution function is written. Now we have closed system of dynamical equations for parameters of flow production line. The null and the first moments of the distribution function of labour objects in terms of the state characterize the magnitude of inter-operational stocks and the rate of processing of labour objects from operations of the technological route and are the main parameters of the management of the production line. The limiting transition from the kinetic description of the state of objects of labour to the stream description of the processing of objects of labour is accomplished. Integration of the kinetic equation by the states of the objects of labour made it possible to construct a closed system of balance equations for the parameters of the production line. The task of optimal control of the flow parameters of the production line has been set. The balance equations for the moments of the distribution function of objects of labour by states determine the constraint equations in the control problem