A highly perishable drug spoils after three days. A hospital estimates that it is equally likely to need between one and nine units of the drug daily. Each time an order for the drug is placed, a fixed cost of

$200 is incurred as well as a purchase cost of $50 per unit. Orders are placed at the end of each day and arrive at the beginning of the following day. It costs no money to hold the drug in inventory, but a cost of $100 is incurred each time the hospital needs a unit of the drug and does not have any available. The following three policies are under consideration:

■ If the day’s ending inventory is less than 5 units, order enough to bring the next day’s beginning inventory up to 10 units.

■ If the day’s ending inventory is less than 3 units, order enough to bring the next day’s beginning inventory up to 7 units.

■ If the day’s ending inventory is less than 8 units, order enough to bring the next day’s beginning inventory up to 15 units.

Use simulation to compare these policies with regard to expected daily costs, expected number of units short per day, and expected number of units spoiling each day. Assume that the hospital begins day 1 with five new units of the drug on hand. (Hint: You will need to keep track of the age distribution of the units on hand at the beginning of each day. Assume that the hospital uses a FIFO [first in, first out] inventory policy. The trick is to get formulas that relate the age of each unit of the drug you have at the beginning of the day to the age of each unit you have at the end of the day.)

Modeling Problems