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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).

Economic order quantity is used in inventory control. We shall discuss the economic order quantity formula below as well as show examples of Calculating Economic Order Quantity.

Economic order quantity explained

Inventory control is a science in itself. The concept of economic order quantity comes from the fact that if a firm holds excessively high levels of stocks then it incurs additional costs such as:

• warehousing costs
• insurance costs
• deterioration of stocks costs
• cost of capital tied up in acquiring stocks (opportunity cost)

However, if the firm holds too low level of stock then it may run out of stock. This leads to loss of production and sales to customers which is also a bad problem. The firm may need to order emergency stock and put in extra money to fulfill orders.

Assumptions in the Economic Order Quantity (E.O.Q) model

• lead time is zero (lead time is the delay between order being placed and delivery)
• demand is constant

The assumptions of the Economic Order Quantity (E.O.Q) model means that the stock level falls at a constant rate and when the last unit of stock is used, the stock level is immediately restored by the order and delivery. The saw tooth model below illustrates the Economic Order Quantity (E.O.Q) model.

Economic Order Quantity Formula

Calculating Economic Order Quantity