### What Is Economic Order Quantity – EOQ?

Economic order quantity (EOQ) is the ideal order quantity a company should purchase for its inventory given a set cost of production, a certain demand rate, and other variables. This is done to minimize inventory holding costs and order-related costs.

The equation for EOQ also takes into account inventory holding costs such as storage, ordering costs and shortage costs. This production-scheduling model was developed in 1913 by Ford W. Harris and has been refined over time. The formula assumes that demand, ordering, and holding costs all remain constant.

### Key Takeaways

- The EOQ is a company's optimal order quantity that minimizes its total costs related to ordering, receiving and holding the inventory.
- The EOQ formula is best used in situations where demand, ordering, and holding costs remain constant over time.

### The Formula for Economic Order Quantity Is

- $\begin{aligned} &Q = \sqrt{ \frac{2DS}{H} }\\ &\textbf{where:}\\ &Q=\text{EOQ units}\\ &D=\text{Demand in units (typically on an annual basis)}\\ &S=\text{Order cost (per purchase order)}\\ &H=\text{Holding costs (per unit, per year)}\\ \end{aligned}$

#### Economic Order Quantity (EOQ)

### What Does the Economic Order Quantity Tell You?

The goal of the EOQ formula is to identify the optimal number of product units to order so that a company can minimize its costs related to buying, taking delivery of and storing the units. The economic order quantity (EOQ) formula can be modified to determine different production levels or order interval lengths, and corporations with large supply chains and high variable costs use an algorithm in their computer software to determine EOQ.

EOQ is an important cash flow tool for management to minimize the cost of inventory and the amount of cash tied up in the inventory balance. For many companies, inventory is the largest asset owned by the company, and these businesses must carry sufficient inventory to meet the needs of customers. If EOQ can help minimize the level of inventory, the cash savings can be used for some other business purpose or investment.

The EOQ formula can be used to calculate a company's inventory reorder point, which is a specific level of inventory that triggers the need to place an order for more units. By determining a reorder point, the business avoids running out of inventory and is able to fill all customer orders. If the company runs out of inventory, there is a shortage cost, which is the revenue lost because the company does not fill an order. Having an inventory shortage may also mean the company loses the customer or the client orders less in the future.

### Example of Using EOQ

EOQ takes into account the timing of reordering, the cost incurred to place an order and costs to store merchandise. If the company is constantly placing small orders to maintain a specific inventory level, the ordering costs are higher, along with the need for additional storage space.

Assume, for example, a retail clothing shop carries a line of men’s jeans and the shop sells 1,000 pairs of jeans each year. It costs the company $5 per year to hold a pair of jeans in inventory, and the fixed cost to place an order is $2.

The EOQ formula is the square root of (2 x 1,000 pairs x $2 order cost) / ($5 holding cost) or 28.3 with rounding. The ideal order size to minimize costs and meet customer demand is slightly more than 28 pairs of jeans. A more complex portion of the EOQ formula provides the reorder point.

### Limitations of Using EOQ

The EOQ formula inputs make an assumption that consumer demand is constant. The calculation also assumes that both ordering and holding costs remain constant, which makes it difficult or impossible for the formula to account for business events such as changing consumer demand, seasonal changes in inventory costs, lost sales revenue due to inventory shortages, or purchase discounts a company might get for buying inventory in larger quantities.