Economic Order Quantity: The $545 Million Formula

I recently wrote about the importance of managing inventory due to its direct impact on working capital.  In the article I mentioned Quids
November 16, 2010

I recently wrote about the importance of managing inventory due to its direct impact on working capital.  In the article I mentioned Quidsi, the parent company of Diapers.com, Soap.com and BeautyBar.com, which used effective inventory management to generate respectable profit margins in the otherwise cutthroat business of online retailing.  Quidsi is on track to surpass $300 million in sales this year.  The company was doing so well that it caught the eye of Amazon.com.  The online retailer is expected to purchase Quidsi for $500 million in cash plus the assumption of $45 million in debt.

 

Quidsi was able to use the inventory management method of Economic Order Quantity to help achieve the performance, which ultimately led to this acquisition and a successful exit for its founders and investors.

 

What is Economic Order Quantity?

Economic Order Quantity (EOQ) is the level of inventory held by a business that minimizes the sum of the holding and ordering costs.  It was originally developed in 1913 by F. W. Harris, and was further refined and enhanced by R. H. Wilson.  Despite its existence for nearly 100 years, companies like Quidsi are using it as the basis for effective inventory management.   Even in very expensive supply chain software implemented by large companies, the core inventory management algorithm is based in many instances on EOQ.  In low margin businesses like electronic retailing, running short on inventory for a single month or overestimating demand (and therefore holding too much inventory) can mean the difference between success and failure.

 

EOQ Variables

In order to determine the EOQ for your company, the following data points are required:

 

  • Demand or usage – This represents the total number of units your company is forecasted to sell during the year.
  • Order costs – This is the sum of the fixed costs associated with the placing of each order.  This is primarily based on the cost of employee time required to place orders, obtain approvals and process the necessary paperwork.
  • Carrying costs – These include the costs associated with keeping the inventory on hand such as interest on borrowings to maintain the inventory, insurance and storage costs.

EOQ Constraints

In order to use the formula effectively, there are certain assumptions that have to be taken into consideration:

 

1.  The ordering cost is constant.

2.  Demand is constant.

3.  Lead time doesn’t change.

4.  Purchase price is constant.

The Economic Order Quantity Formula 

The goal of using EOQ is to determine the inventory level that will minimize total cost for the year:

 

Total cost = purchase costs + ordering cost + holding costs.

 

As we work through this formula, we will use the following variables:

 

  • Q = order quantity
  • Q* = economic order quantity
  • D = annual demand quantity of the product
  • P = purchase cost per unit
  • S = fixed cost to place an order
  • H = annual carrying cost per unit 

Let’s break down the total cost formula into its component parts:

 

Purchase Costs

Purchase costs equal the purchase price multiplied by the annual demand, or P*D.

 

Ordering Costs

Ordering costs equal the fixed cost to place an order multiplied by the number of orders placed throughout the year.  We can calculate the number of orders placed by dividing the demand by the order quantity.  Therefore our formula for ordering costs would be:  S*D/Q.

 

Holding Costs

Holding costs for the year equal the product of the annual carrying cost per unit and the average number of units held throughout the year.  The formula would be H*Q/2.  We divide by two to obtain the average inventory between zero (when no units are in stock) and the full order quantity.

 

Expressing the formula in these terms, we have:

 

Total cost = (P*D) + (S*D/Q) + (H*Q/2)

 

The low cost point will be achieved when the ordering costs equal the holding costs. 

 

Therefore we set them equal to each other:

 

(S*D/Q) = (H*Q/2)

 

Then we solve for Q.  After some basic algebra, we obtain the final formula:

 

 

Working Through an EOQ Example

 

Let’s assume that:

 

  • D = annual demand quantity of the product = 100,000 units
  • P = purchase cost per unit = $4.00
  • S = fixed cost to place an order = $150
  • H = annual carrying cost per unit = $1.15

Using our formula,

 

 

  Q* = 5,107 units

 

More In-Depth Resources Available

This is just an initial primer on EOQ.  If you are interested in learning more about Economic Order Quantity and its applications for your inventory management, I recommend reviewing the following resources: InventoryOps.com and Supply Chain Resource Cooperative.

 

Mike Periu is the founder of EcoFin Media, LLC an independent producer of financial, economic and entrepreneurial content for television, radio, print and the internet.  Over the past ten years he has started three companies and advised over 50 companies on financial strategies including fundraising.  Mike also hosts regular small business webinars on a range of topics relevant to business owners.