Daily demand for aspirin at DoorRed Pharmacy is normally distributed, with a mean of 40 bottles and a standard deviation of 5. The replenishment lead time from the supplier is one day. The current inventory policy at DoorRed is to order 200 bottles when the quantity on hand drops below 45. Each bottle costs DoorRed $4, and the pharmacy uses an annual holding cost of 25 percent.
a. If all unfilled demand is assumed to be backlogged and carried over to the next cycle, what cost of understocking justifies the current policy?
b. If all unfilled demand is assumed to be lost, what cost of stocking out justifies the current policy?
c. DoorRed believes that all unfilled demand can be backlogged if customers are given a $1.50 discount on their next purchase (effectively making the cost of understocking $1.50). What inventory policy do you recommend for DoorRed?