What Is the EOQ Formula & How Is It Calculated?

The Economic Order Quantity (EOQ) is a strategic inventory management calculation that helps businesses determine the optimal order size for their inventory to minimize associated costs. It provides a framework for businesses to manage stock levels efficiently, ensuring enough products to meet demand without excessive expenses. The primary objective of applying the EOQ model is to strike a balance between the costs of ordering inventory and the costs of holding inventory. By identifying this ideal quantity, companies can enhance their operational efficiency and financial health.

Understanding the EOQ Concept

The core principle behind the Economic Order Quantity (EOQ) revolves around balancing two primary types of inventory costs: ordering costs and holding costs. Ordering costs are expenses incurred each time a business places an order for new inventory. These can include administrative labor, processing, communication, and transportation setup fees. For example, the internal processing of a single purchase order might cost a business anywhere from $50 to $200.

Holding costs, also known as carrying costs, are the expenses associated with storing and maintaining inventory over a period. These costs encompass warehouse rent, utilities, insurance, obsolescence, spoilage, and the opportunity cost of capital tied up in inventory. This opportunity cost is often estimated to be between 5% and 15% of the inventory’s value annually. The EOQ model aims to find the specific order quantity where the sum of these two opposing cost categories is at its lowest point.

The EOQ Formula and Its Components

The standard Economic Order Quantity (EOQ) formula is expressed as: EOQ = √((2DS) / H). This formula serves as a foundational tool for inventory optimization, integrating three key variables. Understanding each component is essential for accurate calculation.

The variable ‘D’ represents the annual demand for the product in units. This figure is typically derived from historical sales data, market forecasts, and production plans, reflecting the total quantity of units a business expects to sell or use over a 12-month period.

‘S’ denotes the ordering cost per order, which is the fixed expense incurred each time a new inventory order is placed. Examples include administrative labor costs, the expense of inspecting goods upon receipt, and any fixed shipping or handling fees charged per order.

Finally, ‘H’ stands for the holding cost per unit per year. This represents the cost of keeping one unit of inventory in storage for an entire year. It is often calculated as a percentage of the inventory item’s purchase price, with common estimates ranging from 15% to 30% of the unit’s value annually. This percentage covers expenses such as warehousing costs, insurance premiums, and the opportunity cost of the capital invested in the inventory.

Calculating Economic Order Quantity

Calculating the Economic Order Quantity involves a straightforward application of the formula using specific numerical values for annual demand, ordering cost per order, and holding cost per unit per year. For instance, consider a business that sells 10,000 units of a particular product annually, so D = 10,000 units. The cost associated with placing each order is determined to be $100, making S = $100. The holding cost for one unit for one year is calculated as $5 per unit, meaning H = $5.

To find the EOQ, these values are substituted into the formula: EOQ = √((2 D S) / H). This becomes EOQ = √((2 10,000 100) / 5). The calculation proceeds as follows: (2 10,000 100) equals 2,000,000. Dividing 2,000,000 by 5 yields 400,000.

The final step involves taking the square root of 400,000, which results in 632.45. Therefore, the calculated Economic Order Quantity for this product is approximately 632 units. This means that, under the given cost structure and demand, the most cost-effective approach for the business is to place orders for around 632 units each time to minimize the combined costs of ordering and holding inventory.

Underlying Assumptions of the EOQ Model

The Economic Order Quantity model operates under several simplifying assumptions. One fundamental assumption is that the annual demand for the product is known, constant, and evenly distributed throughout the year, implying a steady consumption rate. Similarly, the costs associated with ordering and holding inventory are assumed to be fixed and known.

Another assumption is that the lead time, the time between placing an order and receiving inventory, is either zero or constant and known. The model also assumes that there are no quantity discounts available from suppliers, meaning the per-unit purchase price remains the same regardless of order size.