Question

Using the basic eoq model, if the ordering cost doubles, the order quantity will be

Answer 1

Answer:

The formula for the basic Economic Order Quantity (EOQ) model is given as,

EOQ = √[(2*D*S)/H]

Where:

D = Annual demand per unit for the inventory items

S = Set-up or Ordering cost per purchase order  

H = Holding or Carrying cost per unit per year  

The formula for Optimal Ordering quantity is given by

No. of orders per year = (Annual demand per unit for the inventory items) / (EOQ) = D / EOQ

Step 1:  

Let the initial EOQ be denoted as “EOQ 1” and the initial no. of orders or the initial order quantity as “O.Q. 1”.

So,  

EOQ 1 = √[(2*D*S)/H] ….. (i)

And,

O.Q. 1 = D / EOQ 1 …… (ii)

Step 2:

The ordering cost is doubled i.e., 2 * S

Here let the final EOQ be denoted as “EOQ 2” and the no. of orders or the final order quantity as “O.Q. 2”.

Therefore,  

EOQ 2 = √[{2 * D * (2*S)} / H] = √2*√[(2*D*S)/H] = √2 * EOQ 1 ….. [from (i)]

and,  

O.Q. 2 = D / EOQ 2 = D / [√2 * EOQ 1] = [1/√2] * [D / EOQ 1] = [1/√2] * O.Q. 1 …. [from (ii)]

Thus, from the calculations in step 2 we can clearly see that, after the ordering cost is doubled the final order quantity becomes [1/√2] times the initial order quantity.