Christian runs a small chocolate shop. He manages his chocolate raw material using a periodic review system. Daily demand has a mean of 100 pounds and standard deviation of 10 pounds. The annual holding cost is $10 per pound. He maintains 98% service level (so z = 2). The lead-time to get more chocolate is 10 days and he reviews his raw material inventory monthly(assume 30 days per month).
a. What is the chocolate raw material safety stock Christian needs to hold? What is the expected inventory level for the chocolate raw material?
b. A management consultant has told Christian that, by installing an IT system, the review period could be cut from one month to one week. How much would Christian be willing to pay for this IT system? (Hint: to simplify the problem, you can assume that the price Christian wants to pay is the saving he can achieve from using this IT system for a year.)