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 Q^{2}Ch = D CO
∴ Q^{2}= √(2DO/h)
Q^{2}Ch = 2D CO
Q^{2} = 2DCo/Ch
Here Q = √(2DCo/Ch)
Here EOQ= √(2DCo/Ch)