A music store sells a bestselling compact disk The daily dem

A music store sells a best-selling compact disk. The daily demand (in number of units) for the disk is approximately normally distributed with a mean of 200 disks and standard deviation of 20 disks. The cost of keeping the disks in the store is $.04 per disk per day. It costs the store $100 to place a new order. There is a 4-day lead time for delivery. Assuming that the store wants to limit the probability of running out of disks during lead time to no more than .02, determine the store’s optimal inventory policy.

Solution

Let X be the daily demand for the disk

X is normal with (200, 20)

Storage cost =0.04 per disk per day

Ordering cost = 100

Lead time = 4 days

P(Z<=z)=0.02

z=2.33

x = 200+2.33(20)

= 200+46.6 = 246.6