## What Is Economic Order Quantity (EOQ)?

Economic order quantity (EOQ) is the ideal order quantity a company should purchase to minimize inventory costs such as holding costs, shortage costs, and order 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 inventory.
• The EOQ formula is best applied in situations where demand, ordering, and holding costs remain constant over time.

## Formula and Calculation of Economic Order Quantity (EOQ)

The formula for EOQ 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}﻿
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## What the Economic Order Quantity Can Tell You?

The goal of the EOQ formula is to identify the optimal number of product units to order. If achieved, a company can minimize its costs for buying, delivery, and storing units. The EOQ formula can be modified to determine different production levels or order intervals, 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. The formula can help a company control the amount of cash tied up in the inventory balance. For many companies, inventory is its largest asset other than its human resources, 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 determines a company's inventory reorder point. When inventory falls to a certain level, the EOQ formula, if applied to business processes, triggers the need to place an order for more units. By determining a reorder point, the business avoids running out of inventory and can continue to fill customer orders. If the company runs out of inventory, there is a shortage cost, which is the revenue lost because the company has insufficient inventory to fill an order. An inventory shortage may also mean the company loses the customer or the client will order less in the future.

## Example of How to Use EOQ

EOQ takes into account the timing of reordering, the cost incurred to place an order, and the cost to store merchandise. If a company is constantly placing small orders to maintain a specific inventory level, the ordering costs are higher, and there is a 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 assumes that consumer demand is constant. The calculation also assumes that both ordering and holding costs remain constant. This fact 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 realize for buying inventory in larger quantities.﻿﻿