Company A is controlling its inventory for a specific product according to an (s,Q) policy. The product has weekly demand Normally distributed with mean 100 and variance 900. The inventory holding cost per unit SKU per year is $80. In case of stock out demand is backordered. The company is using a fixed order quantity of 1 week supply. The replenishment lead time is 4 weeks.

a. The company wants to reach a cycle service level of 98%. Calculate the reorder level and the safety stock. Calculate the average inventory holding costs.

b. Suppose that the company wants to decrease the replenishment lead time from 4 weeks to 2 weeks. Find the average total annual cost for cycle service levels 80%, 85%, 90%, 95%, 98%, 99% and 99.9%. Draw the graphs of service level v.s. total cost for both lead time of 4 weeks and lead time of 2 weeks. Discuss about what the graphs tells?