  The paper considers the optimal control problem of inventory of a discrete
product in 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. The significant content of the work
is the derivation of analytical representations for the mathematical
expectation of the increment of the functional of profit obtained during the
regeneration period. The obtained analytical representations enable us to
explicitly determine the stationary cost indicator of control efficiency, which
was introduced in the first part of the research. Thus, it becomes possible to
numerically solve the optimal control problem of inventory in the model under
consideration.
