Mathematical Derivation of EOQ

Let cost per order is represented via Co. it is the cost incurred every instance one order is placed.

Let the economic quantity purchase every instance be represented via Q

Let holding cost per unit be represented via Ch

Let total demand be represented via D

The net holding cost = ½ QCh

The net Ordering cost =    C/O:  Note that C/O provides you the number of order in the period

Then net cost = ½ Qch + D/Q CO or simply the net holding up cost plus the net ordering costs

EOQ is at the point where holding cost is equal to ordering costs

That is ½ Ch = D/Q CO

½ Q²Ch = D CO                     

∴  Q²= √(2DO/h)  

   Q²Ch = 2D CO            

   Q² = 2DCo/Ch 

Here Q = √(2DCo/Ch)

Here EOQ= √(2DCo/Ch)