What Is Economic Order Quantity (EOQ)?
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- Economic order quantity (EOQ) is the order quantity that gives the lowest total variable cost to order and hold inventory. It balances two costs that move in opposite directions: larger orders mean fewer orders and lower ordering costs each year, but more average inventory and higher holding costs. EOQ decides how much to order.
Also called: EOQ
How it works
The Association of Chartered Certified Accountants (ACCA) explains the trade-off this way: as order quantity rises, average inventory and the total annual cost of holding it rise, while the number of orders and the total annual reordering cost fall. Their total first decreases, then increases, and the point where cost is lowest is the EOQ.
In ACCA's notation:
- D: annual demand
- Co: cost of placing an order
- Ch: cost of holding one unit of inventory for a year
The formula is EOQ = √(2 x Co x D / Ch). Shopify's guide to minimum order quantity writes the same formula as EOQ = √(2DS / H), with S for the cost per order and H for the holding cost per unit. ACCA warns to include only costs that change with order quantity and to keep units consistent: annual demand with the cost of holding a unit for a year.
Assumptions and limits
ACCA lists the assumptions behind the calculation:
- Constant purchase price
- Constant demand and constant lead time
- Holding cost that depends on average inventory
- Order costs that don't depend on order quantity
When a supplier offers a bulk discount, ACCA's approach is trial and error: compare total annual cost, including the purchase cost, at the EOQ and at each quantity where a discount starts, and take the lowest.
The US Department of Defense requires its components to use EOQ methods to set target order quantities. They can use the standard Wilson EOQ, a variation that recognizes back orders, quantity discounts or real world constraints, or an EOQ-equivalent method within an enterprise resource planning system. The manual also calls for validating and updating the cost to order and cost to hold every year.
Example
A distributor sells 7,200 cases of an item a year. Placing an order costs $50, and holding one case for a year costs $2.
- EOQ: √(2 x 50 x 7,200 / 2) = √360,000 = 600 cases
- Orders a year: 7,200 / 600 = 12, costing 12 x $50 = $600
- Holding: average inventory is 600 / 2 = 300 cases, costing 300 x $2 = $600
Total: $1,200 a year. Compared with that, ordering 1,200 cases at a time costs 6 x $50 + 600 x $2 = $1,500, and ordering 300 at a time costs 24 x $50 + 150 x $2 = $1,500. If the supplier's minimum order quantity were 1,000 cases, the smallest order it would accept would still be 1,000.
On Shopify
The inputs for EOQ come from your own sales and costs. Shopify's Inventory sold daily by product report displays the average number of items sold per day for each variant, and multiplying that figure by 365 gives an annual demand estimate for D.
When it is time to order, Shopify's purchase orders record the products, quantities, costs, payment terms and supplier details for an order, and you might use one to order new inventory from a supplier. The order cost and holding cost behind Co and Ch come from your accounting or ERP.
How Uncap helps
Uncap's guide to multi-warehouse inventory visibility describes what happens when purchasing teams can't see what is actually available at each location: they tend to over-order at every warehouse to create a buffer, and that buffer ties up working capital in stock sitting on shelves. Uncap Connect syncs inventory, pricing, and order data between the ERP and the storefront in real time.
Sources
Frequently asked questions
What is EOQ and its formula?
EOQ is the order quantity with the lowest total variable cost to order and hold inventory. In ACCA's notation, EOQ = √(2 x Co x D / Ch), where D is annual demand, Co is the cost of placing an order and Ch is the cost of holding one unit for a year.
What is the difference between EOQ and MOQ?
MOQ is the minimum amount a supplier will let you buy, set on the supplier's costs and profitability. EOQ is what your business should buy to be most cost-effective, balancing ordering costs against holding costs. If the MOQ is higher than your EOQ, the MOQ still sets the smallest order.
What are the limitations of EOQ?
The standard calculation assumes a constant purchase price, constant demand and lead time, holding costs that depend on average inventory, and order costs that don't change with order size. Bulk discounts need a separate total cost comparison.
