Home Depot sells the LawnBoy T650 lawn mowers at 64 stores in the Western US. Weekly demand for the T650 at each of the stores is identical and given by: X ~ Normal (60, 40). Assume that the demands at the 64 stores are independent of each other. The manufacturer’s lead time for supplying the mowers is 4 weeks. Home Depot has a stated policy of 96% cycle service level for mowers.
a. How much safety stock is required at each store?
b. The chain is considering centralizing the inventory of the T650 to a distribution center that will serve all 64 stores. How much safety stock would be required at the DC to provide the same cycle service level of 96%?
c. If the cost of each mower is $500, and Home Depot uses a 20% holding cost rate, what is the annual savings for the chain in inventory holding costs as a result of the centralization?