We will try to generalize the so-called newsboy model so that we can deal with unsatisfied demand or unsold quantity. Consider the time interval that consists of multiple ordering cycles. Assume that the probability density function of
demand is given for each cycle. Then our problem is to make the ordering plan with which we can maximize the
expected profit. In the classical newsboy model ordering quantity is always equal to the (planned) initial inventory level.
But if we take account of unsatisfied demand and unsold quantity, the (desired) ordering quantity must be determined
by a proper stochastic rule. Then, in stead of determining the ordering quantity of each cycle, we must plan the initial
inventory level so that the expected profit may be maximized. If unsold exists in present cycle, the ordering quantity of
next cycle becomes smaller than the planned inventory level. And if unsatisfied demand exists in the present cycle, the
ordering quantity of next cycle becomes larger than the planned inventory level.