Magazine Luiza is a Brazilian retail chain for consumer electronics. The company currently has 100 stores distributed across Brazil. It also operates an online channel. It is considering introduction of a new printer and must decide whether to offer it at retail stores or the online channel. Weekly demand for the printer at each store has been forecast to be normally distributed with a mean of 100 and a standard deviation of 80. The company has also forecast that the demand at the online channel would be the sum of demand across all 100 stores. The supplier will take 4 weeks to fulfill a replenishment order, whether placed separately by each store or by the online DC. Magazine Luiza is targeting a CSL of 95 percent and monitors its inventory continuously.
How much safety inventory will Magazine Luiza carry if the printer is carried at all 100 stores?
How much safety inventory will magazine Luiza carry if the printer is carried online and demand across stores is independent?
How much safety inventory will Magazine Luisa carry if the printer is carried online and the demand across stores has a correlation of ρ = 0.3?