Question: You have to decide how much ice cream to buy in order to meet demand at two retail stores. Demand is modeled as follows:
D1 = 100X + ?1, D2 = 120X + ?2
where X, ?1, and ?2 are independent normal variables with expected value and variance given by (28,16), (200,100), (300,150), respectively. Random variable X can be regarded as a common risk factor linked to temperature (the two retail stores are close enough that their sales levels are influenced by the same temperature value), whereas the other variables are specific factors, possibly related to competition in the zone of each store, as well as to pure random variability. Ice cream is stored at a central warehouse, which is close to the two retail stores, so that whatever is needed can be immediately transported by a van.
• Find how much ice cream you should order, in such a way that service level at the warehouse level will be 95%.
• Would this quantity increase or decrease in case of positive correlation between ?1 and ?2?