# Use This Formula to Calculate Economic Order Quantity (EOQ)

Post on Tuesday, August 7th, 2018 in Accounting For many businesses, inventory is the biggest asset.

These companies must have enough inventory to satisfy the demand of their customers or they will not be successful. EOQ, or economic order quantity, is a valuable tool that can help businesses monitor their inventory levels without overloading on unnecessary costs.

## What is Economic Order Quantity (EOQ)?

Economic Order Quantity represents the optimal amount of inventory a company should order each cycle to keep costs as low as possible.

These costs include:

Getting your Economic Order Quantity calculation right should be an integral part of any inventory management process because it makes sure that your business orders the appropriate amount of each item each time the inventory levels hit their reorder points. Inventory management experts use an EOQ formula to calculate the reorder quantity and ensure constant replenishment of stock.

Calculating the Economic Order Quantity assists retailers with making informed decisions, such as:

• How much inventory to order
• How many items to keep on hand
• How often to reorder inventory
• How to minimize inventory costs

## EOQ Model: How It Works

The economic order quantity model was created by 1913 by Ford W. Harris. However, R. H. Wilson, a consultant who applied it, and K. Andler are given credit for taking it to a more in-depth, analytical level. The model is based upon the following assumptions:

• Constant demand, which is equally distributed throughout a year
• Immediate replenishment and no out of stock issues
• Number of inventory items reduced to a fixed rate until they hit the reorder point
• The same number of new items arriving exactly after the inventory hits the reorder point
• Known purchase order lead time (time period between placement and delivery of the order)
• The same purchase cost per unit

Assuming all of the above, calculating inventory costs under the EOQ involves finding a balance between inventory carrying costs and order costs. Ordering a large amount at one time will increase inventory carrying costs. At the same time, ordering fewer items at frequent intervals will reduce carrying costs, but increase order costs. Calculating the EOQ keeps these costs at the lowest possible level. ## Economic Order Quantity Formula

Before we explain how to calculate EOQ, let’s see how and where this value can be applied.

Specifically, it is used to calculate the total order costs, according to the following formula:

Total Cost (TC) = P x D + C x Q / 2 + S x D / Q

Where:

• P × D = purchase price per unit × annual demand, i.e. total number of units that are purchased during a year
• C x Q = carrying costs per unit per year x quantity per order
• S x D = setup cost of each order × annual demand

To reach the optimal order quantity, the two parts of this formula (C x Q / 2 and  S x D / Q) should be equal.

As you can see, the key variable here is Q – quantity per order. And this is exactly the EOQ.

### So the EOQ equation, sometimes referred to as Wilson formula, will be as follows:

EOQ = √ (2 x S x D / C), where

• S = setup costs (per order, including shipping and handling)
• D = demand rate (quantity sold per year)
• C = carrying costs (per unit per year)

Now let’s consider an example:

• A clothing retailer sells 2,000 shirts annually (D = 2,000).
• Carrying costs per shirt are \$ 7 a year (C = 7).
• It costs the company \$ 2 to place each order (S = 2).

As a result, the EOQ is calculated as follows:

√ (2 x \$ 2 x 2,000 units / \$ 7) = 33.8 units (with rounding)

Therefore, to reduce inventory costs and satisfy demand, this business should always place an order for 33 or 34 shirts. Based on this, let’s calculate the total cost for our example.

Again, the formula is:

Total Cost (TC) = P x D + C x Q / 2 + S x D / Q, where

• P (purchase price) = \$ 10
• D (demand) = 2,000 units
• C (carrying costs) = \$ 7
• Q (EOQ) = 33.8 units
• S (setup costs) = \$ 2

As a result, the total cost will be:

\$ 10 x 2,000 units + \$ 7 x 33.8 units / 2 + \$ 2 x 2,000 units / 33.8 units = 20,000 + 118.3 + 118.3 = \$ 20,236.6

As you may have noticed, both the C x Q / 2 and the S x D / Q values equal 118.3. This is because we have previously calculated the EOQ that impacted these numbers.

However, sometimes suppliers can offer quantity discounts to encourage their customers to place larger orders, which affects the EOQ. Therefore, it is important for small business owners to find out if it is worth accepting the quantity discount proposal by doing the following:

1. Calculate EOQ according to the formula.
2. Calculate the total cost of inventory for the EOQ.
3. Select the order quantity that provides the minimum total cost. Let’s suppose that the business owner from our previous example has got a volume discount offer. Under this offer, if they order 50 shirts, they will get their shirts for \$8 per unit instead of \$10. The owner should also be aware that the increased order quantity will also increase the inventory carrying costs.

So let’s find out if this order is profitable for the owner by calculating the total costs with the following values:

Total Cost (TC) = P x D + C x Q / 2 + S x D / Q, where

• P (purchase price) = \$ 8
• D (demand) = 2,000 units
• C (carrying costs) = \$ 10
• Q (EOQ) = 50 units
• S (setup costs) = \$ 2

\$ 8 x 2,000 units + \$ 10 x 50 units / 2 + \$ 2 x 2,000 units / 50 units = 16,000 + 250 + 80 = \$ 16,255

As you see, the business owner will save almost \$ 4,000 per year if they accept the offer.

## How Else Can Companies Use This EOQ Formula?

Companies can also adapt the EOQ formula and model it according to the specifics of their business and industry.

For example, instead of demand rate, they can use the predicted intensity of demand when figuring out order lead time. They can also use the carrying costs per unsold unit during order lead time instead of carrying costs per unit. Finally, they can extend the model by new variables, such as discounts, backordering costs, multiple items, and imperfect quality items.

## Now you know what EOQ is and how to calculate economic order quantity

This process seems complex as it involves lots of calculations. However, specialized inventory management software can help you automate these calculations. Dynamic Inventory will help you find the best order quantity to meet the needs of both your business and your customers. As a result, you will hardly ever experience any inventory shortages or high carrying costs. Adam is the Assistant Director of Operations at Dynamic Inventory. He has experience working with retailers in various industries including sporting goods, automotive parts, outdoor equipment, and more. His background is in e-commerce internet marketing and he has helped design the requirements for many features in Dynamic Inventory based on his expertise managing and marketing products online.

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