If daily demand is constant at 10 units per day, and lead time averages 12 days with a standard deviation of 3 days, 95% 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

We can calculate the safety stock using the formula:

Safety Stock = z * σLT * sqrt(LT)

where z is the z-score at the desired service level (95% for this question), σLT is the standard deviation of lead time (3 days), and LT is the average lead time (12 days).

First, we need to find the z-score at the 95% service level. This corresponds to a probability of 0.95 or 1 - α/2, where α/2 is the cumulative probability in the tails of a standard normal distribution. Using a standard normal distribution table or a calculator, we find that the z-score for 95% service is approximately 1.96.

Plugging in the values, we get:

Safety Stock = 1.96 * 3 * sqrt(12) = 17.96

Rounding up to the nearest whole unit, the safety stock required is approximately 18 units. However, since demand is constant at 10 units per day, we need to have enough safety stock to cover the entire lead time demand, which is:

Lead Time Demand = daily demand * lead time = 10 * 12 = 120 units

Therefore, the total safety stock required is:

Total Safety Stock = Safety Stock * Lead Time Demand = 18 * 120 = 2160 units

However, since safety stock cannot be fractional, we need to round up to the nearest integer. The final answer is therefore:

Total Safety Stock = 49 units (rounded up from 48.46)

If Daily Demand Is Constant at 10 Units Per Day