Answer:
The answer is 150 gallons
Explanation:
First we will write out the relevant information in the question that will help us with our calculation:
Safety stock = 50 gallons
50 gallons = 9% stockout risk
??? gallons = 3% stockout risk
Next, you have to understand that the relationship between the safety stock and stockout risk is an inverse proportion. This means that the bigger the safetystock amount, the smaller the stockout risk, and vice versa. Therefore, there will be a lesser risk of running out of stock, as the safety stock amount increases.
Let g be the safety stock
Let r be the stockout risk
This relationship is represented as:
where k = a constant relating the safety stock and stockout risk.
Therefore :
where:
g₁ = 50 gallons
r₁ = 9%
r₂ = 3%
g₂ = ????
Therefore, making g₂ the subject of the formula:
Therefore, the saftey stock that would provide a stockout risk of 3% = 150 gallons.