Calculate the safety stock of a warehouse

After finishing his Masters degree, Patrick goes back to New Zealand to work as an inventory manager for a Pepsico distributor that serves Eastern New Zealand. Remembering the Operations Analytics class he took at UTD, he decides to control the inventory with a periodic review, base-stock (T, S) policy. The daily demand is normally distributed with mean 320 cases and standard deviation 75 cases.
(a) Patrick decides to review the inventory daily. Assuming it takes 8 days for the cola to be delivered from Europe, what is the base stock to assure that the service level is 99%? What is the safety stock amount associated with this service level?
(b) Suppose that the customers permit a grace period of 2 days. In other words, a customer demand on day t can be satisfied on day t + 1 or t + 2. How would you modify the base stock-is the new base stock level higher or lower compared to part (a)? Why?
(c) Patrick convinces the distributor to serve Western New Zealand as well. He estimates the demand for Western New Zealand to be normally distributed with mean 140 cases and standard deviation 35 cases. Assume that the lead-time for Western New Zealand is also 8 days and calculate the safety stock for a separate warehouse that serves Western New Zealand. Suppose that the correlation coefficient between the two demands is 0.6, and calculate the safety stock of a warehouse that serves both regions (lead-time is 8 days). Which alternative has the lowest total safety stock?

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