Question

Post Card Depot, an large retailer of post cards, orders 4,660,332 post cards per year from its manufacturer. Post Card Depot plans on ordering post card 23 times over the next year. Post Card Depot receives the same number of post cards each time it orders. The carrying cost is $0.09 per post card per year. The ordering cost is $362 per order. What is the annual total inventory management costs of post card inventory?

Answer 1

Solution :-

In usual notations, we are given,

Annual Demand ( D) = 4660332 units

Ordering Cost ( C_o) = $362 per order

Carrying Cost per post card per year (C_h)= $0.09 per unit per year

No. of orders = 23

Now, the Annual Total Inventory Management Cost = Ordering Cost + Inventory Carrying Cost

Ordering Cost = No. of orders * Ordering Cost per order

Here, Ordering cost = $ (23 * 362) = $ 8326

Again, Total Inventory Carrying Cost = Q/2 * C_h

Here, Q = per order size

Therefore , Q = Annual Demand / No. of orders placed

= 4660332 / 23 = 202623.1304 units

Hence, Inventory Carrying Cost = $ {(202623.1304 / 2) * 0.09} = $ 9118.04

Since, Annual Total Inventory Management Cost = Ordering Cost + Inventory Carrying Cost

Therefore, Annual Total Inventory Management Cost = $ ( 8326 + 9118.04) = $ 17444.04

Now, we can get the total annual inventory management cost by applying Economic order quantity model also.

What is EOQ ?

Economic order quantity is the size of the order representing standard quality of materials & it is the one for which the aggregate of the costs of procuring the inventory & the costs of holding the inventory is minimum. It is represented as Q^*.

Therefore , as per EOQ formula, the economic order quantity (Q^*) is given by :-

Q^* = (2DC_o / C_h) ^1/2

Here , Q^* = {( 2 * 4660332 * 362) / 0.09} ^1/2

= 193622.7824

Therefore, As per EOQ model, no.of orders = D / Q^* = 4660332 / 193622.7824 = 24

in EOQ model,

Annual Inventory Management Cost = (D / Q^* ) * C_o + (Q^*/2) * C_h

Hence, Annual Inventory Management Cost as per EOQ model : -

$ {(4660332 / 193622.7824) * 362 + (193622.7824 / 2) * 0.09} = $ (8688 + 8713.025) = $ 17401.025

Annual Total Inventory Management Cost as per EOQ model = $ 17401.025