# Economic Order Quantity – Formula, Example, and Explanation

In any business, production costs are the foundation of the pricing strategy, profit margins, and market positioning. The most important costs incurred in any manufacturing operation are material, labor, and factory overhead.

Material is often existing as a cushion between production and consumption of the goods. In any inventory, you will find material in various shapes and sizes. The materials are waiting for processing, semi-processed material, finished goods at the site, in transit, at the warehouse, in retail outlets. In all these forms, there must be a legit economic justification for the inventories or material.

Each unit carried is costing something to the business, and all costs have to be incurred in the financial statements. Therefore, material planning is used to determine material levels and procurement.

The most critical factors managed by material planning are:

• The quantity of material
• Time to purchase material

To answer these two questions of how much and when is dealt by two conflicting costs that are:

• Cost of carrying inventory

The cost of carrying the variable costs that vary with the change in the amount ordered is included. The most common costs are interest, tax, warehousing, or storage. The cost of inadequate carrying, on the other hand, is also an important consideration for the calculation of order quantity.

One most popular and common methods of calculating the quantity to be ordered are Economic Order Quantity (EOQ). In this article, EOQ, its formula, calculation, importance, and limitations will be discussed.

## What is EOQ?

Economic Order Quantity is defined as,

It is the ideal or optimal quantity of inventory that can be ordered at a time to minimize the annual costs of inventory.

This quantity and production-scheduling model was developed by Ford W. Harris in 1913. Over the time of one century, there have been further developments and refinements in the model to make it more relevant

Suppose a business firm purchases materials once or twice a year, but the order sizes are big. In that case, they are incurring too much cost for carrying the inventory. It increases the annual inventory cost.

Conversely, if the business firm buys smaller quantities in too many orders during a year, the ordering cost goes up. Ultimately, it will also increase annual inventory costs.

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Therefore, an optimal quantity of inventory to be ordered at a time requires balancing two factors of the equation.

• Cost of carrying or possessing material
• Cost of ordering or acquiring material

## Assumption Of EOQ

The Economic Order Quantity model works on certain assumptions.

1. In EOQ, it is assumed that the demand for the material is always the same. The constant demand implies that the seasonal fluctuations and consumer behavior will not affect the demand over the year.
2. The second assumption is related to constant holding and ordering costs. According to the assumption, ordering costs and carrying cost is always same. The change in transportation costs, interest rates, warehouse rent do not impact the ordering and holding costs of the material.
3. The final assumption is the absence of any discounts. The EOQ model doesn’t encompass the rebates or trade discounts offered to the business.

## Formula

The differential calculus has been employed to devise a formula for the calculation of EOQ. The formula is as follow:

Following costs are components of the Economic Order Quantity.

Ordering Cost

Ordering cost represents the cost of one order. It is calculated by dividing the annual demand by the number of orders annually.

Number Of Orders = D/ Q

The annual ordering costs are found by multiplying the number of orders by the fixed cost of each order.

Annual Ordering Cost = (D/Q) x S

Holding Cost

Holding costs of inventory if often expressed as cost per unit multiplied by interest rate. The holding costs can be direct costs of financing the inventory purchase or the opportunity cost of not investing the money somewhere else.

The formula of Holding cost is expressed as,

Holding cost = H = iC

Since the inventory demand is assumed to be constant in EOQ, the annual holding cost is calculated using the formula.

Annual Holding Cost = (Q/2) X H

Total Cost And Economic Order Quantity

By adding the holding cost and ordering cost gives the annual total cost of the inventory. For calculation of the EOQ, that is, optimal quantity, the first derivative of the total cost with respect to Q is taken.

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Annual Total Cost = [(D/Q) X S] + [(Q/2) X H]

Now,

## How To Calculate EOQ?

Let’s calculate the EOQ by example.

Suppose a company has an annual demand of 2500 units. The total cost to place one order is \$1200. The per-unit cost is \$250. According to the calculations, the carrying costs of the company are 12% of the per-unit cost.

It is required to find the Economic Order Quantity.

If we arrange the data, it will look like this,

EOQ = 408 units per order.

## Why Is Economic Order Quantity Model Important?

The economic order quantity model is an important consideration because it helps to find the optimal number of units per order. The firms can minimize their material acquisition costs by applying the EOQ model.

There can be modifications in the EOQ formula to find other production levels or order intervals. According to the economies of scale, the larger quantities of orders result in decreased per-unit cost of ordering.

The EOQ is also used by companies as a cash flow tool. By the calculations, a business firm can control the amount of cash tied up to acquire the inventory. Besides, the companies are in a better position to manage their inventories more efficiently. In the absence of this technique, the companies might end up sticking too much cash into large amounts of inventories. Otherwise, the smaller orders will result in an unwanted surge in the annual ordering costs.

The investors can also calculate the EOQ for the assessment of a firm’s efficiency in managing its inventory.

There are certain benefits the firms can reap by using the EOQ as a cost-scheduling and production-scheduling model. Some of them are mentioned here.

## Inventory Costs Are Minimized

Using the EOQ model, the companies are saving them from the unnecessary warehousing costs resulting in the case of extra stocks of inventory. Other factors can be the reason behind the surge in inventory costs.

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For instance, damaged products, unsold inventory, the pattern of ordering affects costs. But suppose you’re business deals in low-velocity products. In that case, EOQ can be a beneficial tool to help you find an optimal level of order quantity.

## Optimized Inventory Means Minimum Stockouts

EOQ is the most efficient model that tells you how to minimize inventory stockouts without holding unnecessary inventory for longer periods. The essence of the EOQ model is the quantity a firm needs re-ordering and how often to re-order.

Every business is different. Different industries have different requirements. For some businesses ordering smaller amounts more often can be a cost-effective solution. For others, the case might be the complete opposite. You can optimize your inventory management by EOQ.

## Overall Efficiency of Handling Inventory Is Improved

The carrying costs and ordering costs are the two most important considerations in EOQ. When a company is using EOQ, its overall efficiency of handling the inventory is increased. You can smartly calculate the EOQ by taking into consideration of all important cost variables.

## Limitations Of EOQ

The limitations of the EOQ model are based on the assumptions made in the formula derivation. The EOQ assumes consumer demand, ordering costs, and holding costs to be constant. These assumptions affect the efficiency of the model.

The unpredictable and uncertain events that every business might face are totally ignored. The change in transportation fares, consumer demands, economic recession or boom, or seasonal fluctuations is some events that affect the demand and costs of ordering as well as holding inventory. Any purchase discounts are also not taken into account for the calculation of EOQ.

## Final Words

EOQ might not be a 100% accurate tool to calculate the optimal order quantity, but it helps the business improve its inventory management. Despite its limitations, EOQ is a powerful production-scheduling technique to make inventory-related decision-making more smooth.

However, one thing should be understood that EOQ is just one of the many inventory management techniques used by businesses. The EOQ will be higher if the business’s set-up costs increase or there is a demand surge. However, the EOQ will be lower when the cost of holding inventory is high.