An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $2 each. It is estimated that the cost of order processing and receipt is $120 per order. The company uses an inventory carrying charge based on a 15% annual interest rate. The monthly demand for the filter follows a normal distribution with mean 80 and standard deviation 20. Order lead time is assumed to be 4 months. The target cycle service level is 99%. Determine the following quantities:
a. The safety stock, order quantity and the reorder level.
b. The average annual cost of holding cost and fixed order cost.
c. Evaluate the cost of uncertainty for this process. That is, compare the average annual cost you obtained in part (b) with the annual cost that would be incurred if the demand had zero variance.