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?

Inputs Expected demand per day, D Standard deviation of demand, D Order quantity, Q Reorder point, ROP Replenishment lead time in days, L Unit costs, C Inventory holding costs, h (enter as \%) Distribution of demand during lead time Mean demand during lead time, DL SD of demand during lead time, L Outputs Current safety inventory Cycle service level, CSL Cost of holding one unit for one year, H Implied cost of understocking with backlogging