Some results concerning optimum inventory policies

The aim of the paper is to find optimum policies in some $n$-stage and infinite-stage inventory models. The following cases are considered: 1) the delivery lag is a random variable with two values 0 and 1; 2) the inventories have a high rate of obsolence and can be used only for one period; 3) there are two kinds of shipments, one a routine shipment with a one-period delivery lag and the other a priority shipment without any lag but at a higher price. If all the costs are directly proportional to the amount of the commodity and the unsatisfied demands can be backlogged and satisfied when the commodity becomes available, the optimum policies are those with constant levels. If in the case I the ordering cost is a convex function, the optimum policy is a $(s,S)$ policy.