Joe has a mail order business where he sells skateboards directly to consumers. Joe currently uses 4 warehouses and always ships to customers from their nearest warehouse. Each warehouse experiences demand that is independent and normally distributed with a mean weekly demand of 5,000 skateboards and a standard deviation of 1,000. Joe replenishes the warehouses weekly to ensure each warehouse maintains a 99% Type 2 Service Level.
a. How much total safety stock should Joe carry across the 4 warehouses?
b. What would Joe’s inventory reduction be if he consolidated to 1 single distribution warehouse?