The question it answers
Every time a business replenishes an item, it must decide how much to order. Small, frequent orders keep average stock low but multiply the work and cost of ordering. Large, infrequent orders cut the number of orders but fill the warehouse. Economic order quantity, usually shortened to EOQ, is a classic model that finds the order size at which the combined cost of ordering and holding is lowest, under a set of simplifying assumptions.
The two costs in tension
Ordering cost is the cost of placing and receiving one order, regardless of its size. It can include purchasing staff time, administrative work, inbound transport charges per delivery and receiving effort. In manufacturing, the equivalent is a setup cost for starting a production run.
Holding cost is the cost of keeping a unit in stock for a year. It typically includes storage, handling, insurance, loss and damage, and the cost of the money tied up in the stock. It is often expressed per unit per year, or as a percentage of the item’s value.
Raising the order size reduces ordering cost per year but raises holding cost, because the average stock goes up. Lowering it does the opposite. The total cost curve is U-shaped, and EOQ is the bottom of the U.
The formula
With the usual assumptions, the formula is:
EOQ = square root of (2 × D × S ÷ H)
where D is annual demand in units, S is the cost per order, and H is the holding cost per unit per year.
A worked example (hypothetical numbers)
Suppose a business uses 1,200 units a year (D), each order costs $50 to place and receive (S), and holding one unit for a year costs $3 (H).
- 2 × 1,200 × 50 = 120,000
- 120,000 ÷ 3 = 40,000
- The square root of 40,000 is 200
The EOQ is 200 units. That means 1,200 ÷ 200 = 6 orders per year.
Now check the costs. Average stock under this model is half the order size, so 100 units.
- Ordering cost: 6 orders × $50 = $300
- Holding cost: 100 units × $3 = $300
- Total: $600
Notice that at the optimum, the two costs are equal. Compare two alternatives:
- Order 400 at a time: 3 orders × $50 = $150, plus average stock of 200 × $3 = $600, for $750.
- Order 100 at a time: 12 orders × $50 = $600, plus average stock of 50 × $3 = $150, for $750.
Both cost more than $600. Also, note that being somewhat away from the optimum costs little: the curve is fairly flat near the bottom, which is why a rough order size can be nearly as good as the exact one.
The assumptions behind it
The basic model assumes:
- Demand is steady and known.
- Ordering and holding costs are constant per unit and per order.
- The entire order arrives at once, and the lead time is constant.
- No quantity discounts, and no shortages allowed.
- Items are considered independently of one another.
Real conditions seldom match this tidy picture. The model is best seen as a starting point or a sanity check and not a precise answer.
Where it falls short
- Demand varies. Seasonality, trends and promotions break the steady-demand assumption. Buffer stock, discussed under safety stock, is added on top for uncertainty.
- Costs are hard to pin down. Holding cost in particular is an estimate, since part of it, like the cost of capital, is not a line item on an invoice. Because the formula uses a square root, modest estimation errors have a smaller effect on the result, but large ones still matter.
- Suppliers set rules. Minimum order quantities, pallet or case sizes and truckload economics often decide order size more than a formula does. Rounding to full pallet loads is common.
- Discounts change the picture. Price breaks for larger orders mean total cost must include the purchase price, so the calculation has to be extended.
- Shared transport. When several items ship together, the cost of a delivery is shared and ordering decisions are made for groups of items.
- Perishable goods. Items with a short shelf life cannot be ordered in large lots without risking spoilage.
How it is used in practice
Many inventory systems use EOQ or a variation to suggest default order quantities, and buyers adjust them for real constraints. It is most useful for steady, repeat items, such as many parts and supplies. It is least helpful for new products, highly seasonal goods and items made to order.
A related shift in thinking has come from lean practice, which aims to reduce ordering or setup cost so that smaller batches become economical. If the cost per order falls, the formula itself recommends smaller orders. Technology that automates purchasing, for instance, can cut ordering costs and so shift the optimum.
Key takeaways
EOQ is a way of thinking as much as a formula: ordering more at once is not automatically cheaper, and ordering less is not automatically leaner. The best quantity depends on what each order really costs and what holding stock really costs, and both deserve honest estimates.