Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.​ Thomas's fastest-moving inventory item has a demand of 6,100 units per year. The cost of each unit is ​$101​, and the inventory carrying cost is ​$8 per unit per year. The average ordering cost is ​$31 per order. It take about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and the are 250 working days per year.)A) What is the EOQ?B) What is the average inventory if the EOQ is used?C) What is the optimal number of orders per year?D) What is the optimal number of days in between any two orders?E) What is the annual cost of ordering and holding inventory?F) What is the total annual inventory cost, including cost of the 6,100 units?

Answer 1

Answer and Step-by-step explanation:

The computation is shown below:

a. The economic order quantity is

$= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

$= \sqrt{\frac{2\times \text{6,100}\times \text{\ 31}}{\text{\ 8}}}$

= 217 units

b. The average inventory used is

$= \frac{economic\ order\ quantity}{2}$

$= \frac{217}{2}$

= 108.5 units

c. The optimal order per year

$= \frac{annual\ demand}{economic\ order\ quantity}$

$= \frac{6,100}{217}$

= 28 orders

d. The optima number of days is

$= \frac{working\ days}{optimal\ number\ of\ orders}$

$= \frac{250}{28}$

= 8.9 days

e. The total annual inventory cost is

= Purchase cost + ordering cost + carrying cost

where,

Purchase cost is

$= \ 6,100 \times \ 101$

= $616,100

Ordering cost = Number of orders × ordering cost per order

= 28 orders × $31

= $868

Carrying cost = average inventory × carrying cost per unit

= 108.50 units × $8

= $868

So, the total would be  

= $616,100 + $868 + $868

= $617,836