A company currently has two warehouses. Each warehouse services half the company’s demand, and the annual demand serviced by each warehouse is normally distributed with mean 10,000 and standard...

A company currently has two warehouses. Each warehouse services half the company’s demand, and the annual demand serviced by each warehouse is normally distributed with mean 10,000 and standard deviation 1000. The lead time for meeting demand is 1/10 year. The company wants to meet 95% of all demand on time. Assume that each warehouse uses the EOQ formula to determine its order quantity and that this leads to Q =2000 for each warehouse.

a. How much safety stock must be held at each warehouse?

b. Show that if the company had only one warehouse, it would hold less safety stock than it does when it has two warehouses.

c. A young MBA argues, “By having one central warehouse, I can reduce the total amount of safety stock needed to meet 95% of all customer demands on time. Therefore, we can save money by having only one central warehouse instead of several branch warehouses.” How might this argument be rebutted?