In a safety stock problem where both demand and lead time are variable, demand averages 200 units per day with a daily standard deviation of 25, and lead time averages 5 days with a standard deviation of 2 days. How much safety stock is required for a 90% service level?

517 safety stock is required for a 90% service level

Explanation:

In this question, we are tasked with calculating the amount of safety stock required for a 90% service level.

From the question, we can identify the following;

Demand d = 200 units per day

Daily standard deviation =  25

Lead time average  = 5 days

Standard deviation of lead time = 2 days

Amount of safety stock = 90%

The z-score for 90%(0.9)  confidence interval = 1.28

Mathematically;

Safety stock SS = z × (Daily standard deviation)^2(Lead Time) + (standard deviation of lead time)^2(demand)^2

Plugging the values into the equation above, we have;

Safety stock SS = √(25)^2(5) + (2)^2(200)^2

Safety stock SS = 1.28 × √3125 + 160,000

SS = 1.28 × √163,125 = 1.28 × 403.89 = 516.98 which is approximately 517