In a continuous review inventory system the inventory level is watched continuously, and an order is placed when the inventory level gets down to a particular value, known as the reorder point, or ROP. The ROP is set so that there is at most an percent chance of stocking out while waiting for the order to arrive (during the lead time). The service level is 1 . There will be a stock out if the demand during the lead time (a random variable, call in D) is greater than the supply during the lead time, which is just the ROP. That is, = P{D > ROP}. The quantity 1 is known as the service level. Suppose that the demand during the lead time is normally distributed with mean 110 units and standard deviation 30 units, i.e., D ~ N(110,900), and that = 4% (so the service level is 96%).

a) What should the ROP be? b) Your answer to a) should be larger than the mean demand, 110. The difference between the ROP and the mean demand is known as the safety stock. What is the safety stock for a)? c) If, instead of a), the ROP is set to 140 units, what will the service level be?