Question

Problem 13-22 The injection molding department of a company uses an average of 30 gallons of special lubricant a day. The supply of the lubricant is replenished when the amount on hand is 170 gallons. It takes four days for an order to be delivered. Safety stock is 50 gallons, which provides a stockout risk of 9 percent. What amount of safety stock would provide a stockout risk of 3 percent

Answer 1

The answer is 150 gallons

Step-by-step 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:

`g = (k)/(r)`

where k = a constant relating the safety stock and stockout risk.

Therefore :

`g*r=k`

`g_1r_1=g_2r_2`

where:

g₁ = 50 gallons

r₁ = 9%

r₂ = 3%

g₂ = ????

Therefore, making g₂ the subject of the formula:

`g_2=(g_1*r_1)/(r_2)`

`g_2 = (50*9)/(3) = (450)/(3) = 150`

Therefore, the saftey stock that would provide a stockout risk of 3% = 150 gallons.