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Deriving Economic Order Quantity Formula

The Economic Order Quantity calculation below derives the formula for Economic Order Quantity. Simple calculus is used. First, we rewrite T in the form that is easily differentiable.

At minimum value, dt/dQ is zero therefore:

Remember Q is Economic Order Quantity and we have arrived at the Economic Order Quantity formula.

< H3 align=center>Economic Order Quantity Formula

In this section, we are going to derive the Economic Order Quantity formula which you can use as a template for other Economic Order Quantity calculation.

Deriving the economic order formula

From the diagram in the Economic Order Quantity section, let's:

• C = cost of carrying a unit of stock for one year
• O = cost of placing an order for stock
• D = annual demand in units
• Q = Economic Order Quantity

In calculating the Economic Order Quantity and deriving the Economic Order Quantity formula, we observe that the level of stock falls from Q to zero at a steady rate. The average level of stock held over a period of time is therefore: Q/2.

If D units are required over the year and Q units are ordered each time then the firm will need to replace D/Q orders each year. Therefore:

The total inventory cost (holding cost and ordering cost) per year, T is then:

Now we can find the order size, Q, which minimized the total inventory cost (the Economic Order Quantity).