A mail-order firm has two regional warehouses. Weekly demand at
the first warehouse is normally distributed with a mean of 16,000
units and a standard deviation of 5,000 units. Weekly demand at the
second warehouse is normally distributed with a mean of 2,400 and a
standard deviation of 1,400. The company purchases each unit of
product at $10. Annual holding cost of one unit of product is 25%
of its value. Each order incurs an ordering cost of $1,000
(primarily from fixed transportation costs), and lead time is 4
weeks. The company wants the probability of stocking out during the
lead time at each warehouse to be no more than 5%. Assume 50
working weeks in a year.
Assuming that these two warehouses operate independently.
1. What is the amount of safety stock in the first
warehouse?
2. What is the amount of safety stock in the second
warehouse?
3. Assuming that the firm has centralized all inventories
in a single warehouse and that the required probability
of stocking out during the lead time is still no more than 5%.
The demand in the central warehouse will be normally distributed
with a mean of _ , and a standard deviation of _?