A single product inventory system with a storage capacity of 2 units is replenished weekly using the following policy: if there are 0 or 1 units in stock, order up to the storage capacity; else, do not order. Weekly demands are iid rv’s with pmf P(D = k) = 0.1 + 0.1k, k = 0, 1, 2, 3. Any unmet demand is lost. Assume zero order replenishment time. For any week, the ordering cost is 3n, where n is the number of units ordered during the week. The weekly storage cost is 1.5m, where m is the number of units on hand at the beginning of the week (before ordering).
a) Calculate the long-run expected average total cost (LREAC) of ordering and storage for this policy.
b) An alternative ordering policy is considered: if there are zero units in stock, order 2 units; else, do not order. Compare this policy to the original one on the basis of LREAC.