Economic order quantity EOQ

Home - inventory management

This web site is designed to help navigate you through the mountain loads of information about inventory management.

ECONOMIC ORDER QUANTITY

The economic order quantity (EOQ) refers to the optimal order size that will result in the lowest total of order and carrying costs for an item of inventory given its expected usage, carrying costs and ordering cost. By calculating an economic order quantity, the firm attempts to determine the order size that will minimize the total inventory costs.

Total inventory cost = Ordering cost + Carrying cost
Total ordering costs = Number of orders x Cost per order
= $ U / Q X F

Where
U = Annual usage
Q = Quantity ordered
F = Fixed cost per order
The total carrying costs = Average level of inventory x Price per unit x Carrying cost (percentage)

Total carrying costs
= $ Q / 2 x P x C
= $ QPC over 2

Where
Q = Quantity ordered
P = Purchase price per unit
C = Carrying cost as %

As the lead-time (i.e., time required for procurement of material) is assumed to be zero an order for replenishment is made when the inventory level reduces to zero.
The level of inventory will be equal to the order quantity (Q units) to start with. It progressively declines (though in a discrete manner) to level O by the end of period 1. At that point an order for replenishment will be made for Q units. In view of zero lead-time, the inventory level jumps to Q and a similar procedure occurs in the subsequent periods. As a result of this the average level of inventory will remain at (Q/2) units, the simple average of the two end points Q and Zero.

From the above discussion the average level of inventory is known to be (Q/2) units.
From the previous discussion, we know that as order quantity (Q) increases the total ordering costs will decrease while the total carrying costs will increase. The economic order quantity, denoted by Q*, is that value at which the total cost of both ordering and carrying will be minimized. It should be noted that total costs associated with inventory
T= $ UF / Q + $QPC / 2

Where the first expression of the equation represents the total ordering costs and the second expression the total carrying costs.

The total cost curve reaches its minimum at the point of intersection between the ordering costs curve and the carrying costs line. The value of Q corresponding to it will be the economic order quantity Q*. We can calculate the EOQ formula.

Behavior of costs associated with inventory for changes in order quantity. For order quantity Q to become EOQ the total ordering costs at Q should be equal to the total carrying costs.

Using the notation, it amounts to stating:
UF/Q + QPC / 2 (i.e.) 2UF = Q²PC or Q² = 2UF / PC units
To disguish EOQ from other order quantities, we can say:
2 UF*
EOQ = Q* PC

In the above formula, when `U' is considered as the annual usage of material, the value of Q* indicates the size of the order to be placed for the material, which minimizes the total inventory-related costs. When `U' is considered as the annual demand Q* denotes the size of production run.

Suppose a firm expects a total demand for its product over the planning period to be 10,000 units, while the ordering cost per order is $100 and the carrying cost per unit is $2. Substituting these values, EOQ = 2 x10, 000 x100 = 1000 units. 2

Thus, if the firm orders in 1000-unit lot size, it will minimize its total inventory costs.

Inflation affects the EOQ: model in two major ways. First, while the EOQ model can be modified to assume constant price increases, many times major price increases occur only once or twice a year and are announced ahead of time.
Read more about Inflation point information

Site pages | Other business articles | Terms Of Use | Resources

The Economic Order Quantity