A hospital must order the drug Porapill from Daisy Drug Company. It costs $500 to place an order. Annual demand for the drug is normally distributed with mean 10,000 and standard deviation 3000, and it costs $5 to hold one unit in inventory for one year (a unit is a standard container for the drug). Orders arrive one month on the average after being placed - there is a standard deviation of 10 days. Assume all shortages are backlogged.
a. What (Q,R) policy should the company use if it wants to meet 95% of all customer demand from existing inventory?
b. Suppose the company could pay C dollars per year to get rid of the variability in its lead-time per order. What is the most it would be willing to pay to do this (and still have a 95% service level)?