Question

Cooper Company has an average demand of 50 units per day. Lead time from the supplier averages 20 days. The combined standard deviation of demand during lead time is 20 units. The item costs $75 and the inventory carrying cost is 24%. Answers to the next two questions are based on this information. How much is the annual inventory carrying cost of the safety stock because of this decision

Answer 1

The annual inventory carrying cost of the safety stock = $594

Step-by-step explanation:

Given that:

The average daily demand (d) = 50 units / day

The lead time (LT) = 20 days

The combined standard deviation of demand lead time = 20 units.

The item cost = $75

The inventory carrying cost = 24% of the item cost

i.e. (24/100) × 75 = $18 of the item cost

Let assume that the management of the company wants to offer a service level of 95%.

Then the z-value that relates to 95% confidence interval level = 1.65

So; the safety stock relating to the 95% service level =
`z * \sigma_(dlT)`

= 1.65 × 20

= 33 units

Now:

The annual inventory carrying cost of the safety stock = Safety stock × Inventory carrying cost.

= 33 × $18

= $594