Product A’s inventory is controlled by a continuous review policy. Let us consider that the replenishment lead-time is 7 days. The weekly demand is normally distributed with mean 250 and standard deviation 64.55. Let us consider the optimal order quantity is 250 units.

1) If we set Re-order point R = 282. Calculate the service level?

2) Calculate the average inventory level?

3) How many stock-out cycles are expected per year? (Assume 350 days per year) and type 1 service level

4) What should the safety stock for a service level of 98%?

5) Suppose there two categories of customers X and Y. We promise a higher level of service to the X customers (e.g., 95% of demand is satisfied from stock); for Y

customers, the service level would be lower, e.g., 85% of demand satisfied from stock. Describe in words how to manage the inventory to serve the two demand categories?

6) Modify your answer to Part A if it is known that the demand is uniformly distributed in [138.2, 361.8] that is it has the same mean and standard deviation.