Economic Production Quantity - Derivation of EPQ Formula

Derivation of EPQ Formula

Holding Cost per Year =

Where is the average inventory level, and F(1-x) is the average holding cost. Therefore multiplying these two results in the Holding cost per Year.

Ordering Cost per Year =

Where are the orders placed in a year, multiplied by K results in the Ordering Cost per Year.

We can notice from the equations above that the total ordering cost decreases as the production quantity increases. Inversely, the total holding cost increases as the production quantity increases. Therefore in order to get the optimal production quantity we need to set holding cost per year equal to ordering cost per year and solve for quantity (Q), which is the EPQ formula mentioned below. Ordering this quantity will result in the lowest total inventory cost per year.