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# Economic Order Quantity (EOQ)

Economic Order quantity is used to determine the most efficient order size for a company. Ordering inventory cost a company money in several ways, there is a carrying cost for holding inventory, and there is a fixed cost per order. By determining the most efficient order size, a firm can satisfy demand for their product while minimizing the costs associated with ordering and carrying inventory.

### Economic Order Quantity (EOQ) Definition

Economic Order Quantity is the optimal order size to minimize all inventory costs.

### Variables

C=Carrying cost per unit per year
F=Fixed cost per order
D=Demand in units per year

### Economic Order Quantity (EOQ) Formula ### Economic Order Quantity Model (EOQ)

Managing inventory is an important task for every business that holds it.  There are many costs that occur because of inventory that need to be minimized, while still providing enough inventory to operate without losing customer business.  The EOQ Economic Order Quantity model is used to minimize these inventory related costs.  You will find the EOQ Economic Order Quantity formula above, as well as the EOQ Economic Order Quantity calculator.

Inventory can be expensive, and money is a precious commodity to any business.  Using a large amount of capital to carry inventory comes at a cost of opportunity for the business.  This capital could have been used in other ways to improve business, such as marketing or leasehold improvements, so it is important that this cost be minimized.

The cost of carrying inventory can be calculated by multiplying the cost of carrying a unit of inventory by the average number of units carried, usually for a year.  If inventory is used at a steady pace, and restocked when empty, then the average number of units held would be the order size divided by 2.

C=Carrying cost per unit of inventory
Q=Inventory order size (quantity) We can see by the equation above that the carrying cost of inventory can be reduced by reducing the size of Q.  This is usually achieved by reducing the amount of capital invested in inventory, as well as the space and expense required to store it.  However, every time inventory is ordered, a transaction and shipping cost usually occurs.  This is important since typically reducing the size of inventory held by a company will usually mean an increase in the frequency of orders.   If this increase in ordering cost is larger than the savings from the reduced inventory size, then the total cost of inventory is increased.

We can determine the ordering cost by calculating the number of orders in a year, and multiply this by the cost of each order.  To determine the number of orders we simply divide the total demand (D) of units per year by Q, the size of each inventory order.

D=Total demand (units)
Q=Inventory order size (quantity) We then multiply this amount by the fixed cost per order (F), to determine the ordering cost. The total inventory cost for a year for a business is simply the sum of the carrying cost and the ordering cost.  The total inventory cost formula is below, and the total inventory cost calculator can be found on this website.

C=Carrying cost per unit of inventory
Q=Inventory order size (quantity)
D=Total demand (units)
F=Fixed cost per order This total inventory cost value can be expressed graphically, and will have a minimum value.  Using calculus to determine the minimum point, where the slope equals zero, will provide us with the optimal order quantity to reduce total inventory cost over the year.  This is known as the Economic Order Quantity.