The owner of a hardware store is surprised to find that he is completely out of stock of ‘‘Safe-t-lock,’’ an extremely popular hardened-steel safety lock for bicycles. Fortunately, he became aware of this situation before anybody asked for one of the locks; otherwise he would have lost $2 in profits for each unit demanded but not available. He decides to use his pickup truck and immediately obtain some of the locks from a nearby warehouse. Although the demand for locks is uncertain, the probability distribution for demand is known; it is the same in each month and is given by:

The storage capacity is 400 units, and the carrying cost is $1 per unit per month, charged to the month’s average inventory [i.e., (initial + ending)/2]. Assume that the withdrawal rate is uniform over the month. The lock is replenished monthly, at the beginning of the month, in lots of one hundred. What is the replenishment strategy that minimizes the expected costs (storage and shortage costs) over a planning horizon of four months? No specific inventory level is required for the end of the planning horizon.