# How Annual Ordering Cost is Inversely Related to Order Size: A Guide for Inventory Management

If you are running a business that involves ordering and storing inventory, you might be wondering how to optimize your ordering process and reduce your costs. One of the key concepts that can help you achieve this goal is the economic order quantity (EOQ), which is the ideal size of order that minimizes the total cost of holding and ordering inventory.

In this article, we will explain what EOQ is, how it is calculated, and how it relates to the annual ordering cost and the order size. We will also provide some examples and tips on how to use EOQ in your inventory management.

## What is EOQ and how is it calculated?

EOQ is a formula that calculates the optimal number of units to order for each inventory item, based on the following factors:

• Annual demand: This is the total number of units that you expect to sell or use in a year.
• Ordering cost: This is the fixed cost that you incur every time you place an order, regardless of the number of units ordered. It may include shipping fees, inspection costs, administrative costs, etc.
• Holding cost: This is the variable cost that you incur for storing each unit of inventory for a year. It may include rent, utilities, insurance, depreciation, opportunity cost, etc.

The EOQ formula is:

���=2×������������×�����������������������EOQ=HoldingCost2×AnnualDemand×OrderingCost​​

The EOQ formula assumes that:

• The ordering cost and the holding cost are constant and known
• The annual demand is constant and known
• The order quantity is delivered in one batch
• There are no shortages or stockouts

## How does EOQ relate to annual ordering cost and order size?

The EOQ formula balances the trade-off between the ordering cost and the holding cost. If you order too few units, you will have to place more orders per year, which will increase your ordering cost. If you order too many units, you will have to store more inventory, which will increase your holding cost.

The EOQ formula finds the optimal point where the total cost of ordering and holding inventory is minimized. At this point, the annual ordering cost and the annual holding cost are equal.

The annual ordering cost can be calculated by multiplying the number of orders per year by the ordering cost per order. The number of orders per year can be found by dividing the annual demand by the order size. Therefore, the annual ordering cost formula is:

������������������=���������������������×������������AnnualOrderingCost=OrderSizeAnnualDemand​×OrderingCost

From this formula, we can see that the annual ordering cost is inversely related to the order size. This means that as the order size increases, the annual ordering cost decreases, and vice versa.

For example, suppose that your annual demand is 1000 units, your ordering cost is \$50 per order, and your holding cost is \$10 per unit per year. Using the EOQ formula, you can find that your optimal order size is:

���=2×1000×5010=100EOQ=102×1000×50​​=100

This means that you should order 100 units at a time to minimize your total inventory cost. At this point, your annual ordering cost and your annual holding cost are both:

1000100×50=100×10=5001001000​×50=100×10=500

Now, suppose that you decide to increase your order size to 200 units. This will reduce your number of orders per year to 5, and your annual ordering cost to:

1000200×50=2502001000​×50=250

However, this will also increase your average inventory level to 100 units (half of your order size), and your annual holding cost to:

100×10=1000100×10=1000

As you can see, by increasing your order size, you have reduced your annual ordering cost by \$250, but increased your annual holding cost by \$500. Your total inventory cost has increased by \$250.

Similarly, if you decide to decrease your order size to 50 units, this will increase your number of orders per year to 20, and your annual ordering cost to:

100050×50=1000501000​×50=1000

However, this will also decrease your average inventory level to 25 units (half of your order size), and your annual holding cost to:

25×10=25025×10=250

As you can see, by decreasing your order size, you have increased your annual ordering cost by \$500, but decreased your annual holding cost by \$250. Your total inventory cost has also increased by \$250.

Therefore, you can conclude that the optimal order size that minimizes your total inventory cost is 100 units, which is the EOQ.

## How to use EOQ in inventory management?

EOQ is a useful tool that can help you optimize your inventory management and reduce your costs. However, it is not a fixed value that you should always follow blindly. You should also consider other factors that may affect your inventory decisions, such as:

• Demand variability: If your demand is not constant and predictable, you may need to adjust your order size to account for fluctuations and uncertainties. You may also need to maintain a safety stock to avoid stockouts and lost sales.
• Lead time: This is the time between placing an order and receiving the delivery. If your lead time is long and variable, you may need to order more units in advance to avoid running out of stock.
• Discounts: If your supplier offers discounts for ordering larger quantities, you may want to take advantage of them and order more than the EOQ. However, you should also compare the savings from the discounts with the additional holding costs that you will incur.
• Inventory turnover: This is the ratio of annual sales to average inventory. It measures how efficiently you are using your inventory to generate sales. A higher inventory turnover means that you are selling your inventory faster and reducing your holding costs. A lower inventory turnover means that you are holding more inventory than necessary and increasing your holding costs. You should aim for a balance between having enough inventory to meet demand and having too much inventory that ties up your capital.

To use EOQ effectively, you should monitor your inventory levels and costs regularly and adjust your order size accordingly. You should also communicate with your suppliers and customers to improve your forecasting accuracy and reduce uncertainties. By doing so, you can optimize your inventory management and achieve your business goals.

## Disclaimer

This article is for informational purposes only and does not constitute professional advice. You should always consult with a qualified expert before making any inventory decisions. The information in this article is based on sources that we believe are reliable, but we do not guarantee its accuracy or completeness. We are not responsible for any errors or omissions, or for any consequences arising from the use of this information.