Question

A manager reorders lubricant when the amount on hand reaches 422 pounds. Average daily usage is 45 pounds, which is normally distributed with a standard deviation of three pounds per day. Lead time is nine days. What is the risk of a stockout?

Answer 1

Answer:

2.94% (about 3%)

Explanation:

Average daily usage = 45 pounds

Lead time = 9 days

If we calculate the Reorder point using the above we get:

Reorder point = Lead time x Average daily usage = 45 x 9 = 405 pounds

However, the manager was reordering lubricant when the amount on hand reaches 422 pounds

Hence the safety stock = 422 - 405 = 17 units

Reorder point is calculated as: Lead time*demand per unit time=45*9=405

In the course of the lead time, we have a standard deviation calculated as:

Daily standard deviation x (Lead time)^0.5

= 3 x (9^0.5) = 3 x 3 = 9

Hence the risk of stock out = (422 - 405)/9 x Standard Deviation = 1.89 x S.D

Using the normal distribution curve, with the z-value of 1.89, this means that the probability of stock out = 0.0294 = 2.94%

Approximately 3%.

Answer 2

Answer: The risk of stock out = 2.94%

Explanation:

Reorder point is calculated as: Lead time*demand per unit time=45*9=405

While the amount on-hand reaches 422 pounds, the manager was reordering lubricant.

During the lead time, Standard Deviation of Demand =Daily S.D*(Lead time)^0.5=3*(9^0.5)=9

Risk of Stock Out=(422-405)/9 S.D=1.89 S.D

From Normal distribution curve 1.89 S.D=0.0294=2.94%

Therefore, the risk of stock out=2.94%