In this paper, we tried to extend the classical newsboy problem. There are many ways with which the
classical newsboy model is generalized and extended. Our trial was carried out so that we may deal with
the amount of demands that are not satisfied and with the amount of quantities that are not sold.
Assume that we are given a time interval that consists of n successive ordering periods. Moreover suppose
that we are given some data concerning buying or selling price. And certain parameters are given
which describe our choice of inventory policies. Under such conditions our problem is to make a plan with
which we may determine amount of ordering quantity or initial inventory level. According to the classical
newsboy problem there is no reason why we must distinguish ordering quantity from initial inventory level.
But when we must consider the unsold quantity or unsatisfied demand, ordering quantity is not always
equal to initial inventory level.
Assume the initial inventory level of each period is planned. If unsold quantity exists, the proper portion
of unsold quantity is to be stored as extra increase of inventory. And ordering quantity of next period becomes
the initial inventory level of next period minus unsold quantity of present period. If unsatisfied demand
must be took into consideration, penalty must be paid. And some portion of this unsatisfied demand
becomes extra increase of demand of next period. Then ordering quantity of next period becomes inventory
level of next period plus this extra increase of demand.
Let xi be demand level and li be initial inventory level of the ith period. Then, under the condition that
xi, li, i = 1,2 ,. . .,n, are given, the (total) profit can be calculated. xi must be regarded as a realized value of a
random variate which obeys some stochastic rules. Then in stead of determining the amount of ordering
quantity, we plan the initial inventory level of each period. In other words, our problem is to determine