An automotive warehouse stocks a brand of oil fillter. It is purchased by the warehouse for $15 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on 28% annual interest rate. The monthly demand for the oil filter follows a normal distribution with mean 280 and standard deviation 100. Replenishment lead time is 4 months. Assume that if a filter is demanded when the warehouse is out of stock then the demand is backordered. The target cycle service level is 95%. The company uses a continuous review (s, Q) policy.

a. Calculate the optimal order quantity and the reorder level. What are the average annual inventory holding cost and ordering cost.

b. Evaluate the cost of uncertainty for this company. That is, compare the average total annual cost you obtained above with the average annual cost that would be incurred if the demand has zero variance.