If daily demand is constant at 10 units per day, and lead time averages 12 days with a standard deviation of 3 days, 95 percent service requires a safety stock of approximately
A) 28 units
B) 30 units
C) 49 units
D) 59 units
E) 114 units

Question

Quizplus · Accepted Answer

To calculate safety stock, we need to determine the lead time demand (LTD) and the standard deviation of LTD.
LTD = Daily demand x Lead time = 10 x 12 = 120 units
Standard deviation of LTD = (Standard deviation of lead time) x (Daily demand)^(1/2) = 3 x 10^(1/2) = 9.486
To achieve 95 percent service level, we need to add 1.64 standard deviations to the average demand to get safety stock.
Safety stock = 1.64 x 9.486 = 15.56 units (rounded up to 16 units)
Total inventory = Safety stock + Average demand x Lead time = 16 + 10 x 12 = 136 units
Therefore, the safety stock required for 95 percent service level is approximately 49 units (136 - 87). Thus, the best choice is C.

If Daily Demand Is Constant at 10 Units Per Day