Question 1:
A highly perishable drug spoils after three days. A hospital estimates that they are equally likely to need between 1 and 9 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 inventors 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:
Policy 1: If we end the day with fewer than 5 units, order enough to bring next week's beginning inventory up to 10 units.
Policy 2: If we end the day with fewer than 3 units order enough to bring next week's beginning inventory up to 7 units.
Policy 3: If we end the day with fewer than 8 units order enough to bring next week's beginning inventory up to 15 units.
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 we begin Day 1 with 5 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 week. Assume that the hospital uses a FIFO (First in, First out) inventory policy. The trick is to get formulas that relate the age of tack 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.
Question 2:
The B-School at State U currently has three parking lots each containing 155 spaces. Two hundred faculties have been assigned to each lot. On a peak day, an average of 70% of all Lot 1 parking sticker holders show up an average of 72% of all Lot 2 parking sticker holders show up, and an average of 74% of all Lot 3 parking sticker holders show up.
a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who shows up at each lot is independent of the number who shows up at the other two lots.
Can you come up with a solution to this problem (that does not involve creating more parking spaces!)?
b. Now suppose the number of people who show up at the three lots are correlated, (correlation .9). Does your solution work as well? Why or why not?