F116
Problem Set 2
Fall 2024
2. Inventory Management I (12 points)
As the owner of Wildstyle Music you would like to develop an inventory ordering policy which has at most a \( 10 \% \) probability of stocking out. Expected demand for professional mixing headphones is 2190 per year. The store is open 365 days per year. Every two weeks inventory is counted and a new order is placed. It takes 10 days for the headphones to be delivered. Standard deviation of demand for the headphones is 7 per week. There are currently 65 pairs of headphones in the store.
(a) (6 points) How many headphones should you order? (Hint: calculate the mean and standard deviation of the daily demand first.)
(b) (6 points) Suppose you placed the order in part (a) with the supplier yesterday, but today, you receive a call from your supplier saying that the order will be delayed by one day and will be sent out today instead of yesterday. After hanging up the phone, you check the inventory of strings and find that, fortunately, yesterday's demand was only 2 headphones. What is the probability that Wildstyle Music will run out of headphones before the order arrives?
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