Research of the optimal control problem of inventory of a discrete product in the stochastic regeneration model

The paper considers the optimal control problem of inventory of a discrete product in a regeneration scheme with a Poisson flow of customer requirements. In the system, deferred demand is allowed, the volume of which is limited by a given value. The control parameter is the level of the stock, at which achievement it is necessary to make an order for replenishment. The indicator of management effectiveness is the average specific profit received in one regeneration period. The optimal control problem is solved on the basis of the statement about the extremum of a fractional-linear integral functional on the set of discrete probability distributions.