Suppose the 100 retail stores of a supermarket chain have identical weekly demand for a product (mean 200, standard deviation 120). There is zero correlation between the retailers' demands. The lead time to replenish each retail store is 4 weeks. A cycle service level of 95% is desired.
a. If each retail store maintains its own dedicated warehouse, how much safety stock is needed at each store?
b. What is the total safety stock across all stores?
c. It is now proposed to have a central DC servicing all 100 retailers. The lead time to replenish the DC is the same (4 weeks). How much safety stock is needed at the DC to maintain the same cycle service level?
d. If annual inventory holding cost is $50/unit/year, how much money was saved as a result of the decrease in the safety stock?