What is economic order quantity?

What economic order quantity is

Economic order quantity, almost always abbreviated to EOQ, is the order size that minimises the total annual cost of holding and ordering a product. It is one of the foundational results in inventory theory, and despite being more than a century old it remains the starting point for almost every modern inventory replenishment policy.

The intuition is simple. Order in larger quantities and the per-order cost falls — fewer purchase orders, fewer shipping events, fewer setup costs — but average inventory rises, and with it the cost of holding stock. Order in smaller quantities and holding cost falls, but order frequency and the costs that come with it rise. Somewhere in between sits an order size that minimises the sum of the two cost curves. That order size is the EOQ.

The Wilson formula

The classical EOQ formula, often called the Wilson formula or Wilson lot-size model after one of its early popularisers, is:

EOQ = √((2 × D × S) ÷ H)

Where:

• D is annual demand in units
• S is the cost per order placed (the fixed cost incurred each time an order is raised, independent of order size)
• H is the holding cost per unit per year (the cost of holding one unit of inventory in stock for a year, including capital cost, storage, insurance, and obsolescence allowance)

The formula falls out of differentiating the total cost function with respect to order quantity and setting the derivative to zero — it is the order size at which the marginal increase in holding cost just offsets the marginal decrease in ordering cost.

A worked example

Consider a product with the following parameters:

• Annual demand of 12,000 units
• Order cost of $50 per order (purchase order processing, freight setup, receiving labour)
• Holding cost of $4 per unit per year (capital cost, warehouse space, insurance)

The EOQ is √((2 × 12,000 × 50) ÷ 4) = √300,000 ≈ 548 units.

At this order size:

• The number of orders per year is 12,000 ÷ 548 ≈ 22 orders
• Annual order cost is 22 × $50 = $1,100
• Average inventory is 548 ÷ 2 = 274 units
• Annual holding cost is 274 × $4 = $1,096

Annual total inventory cost is approximately $2,196. Any other order size — larger or smaller — produces a higher total. Order in lots of 200 and total cost rises to roughly $3,400; order in lots of 1,500 and total cost rises to roughly $3,400 as well. The EOQ sits at the bottom of a fairly flat curve.

What EOQ assumes

The simplicity of the Wilson formula comes from a long list of simplifying assumptions. Understanding which ones matter for a given product is half the skill of using EOQ in practice.

Demand is constant and known. The formula assumes D is a fixed annual rate, knowable in advance. Real demand is rarely constant and never perfectly known.

Lead time is zero or constant. The formula assumes that when an order is placed, replenishment is instantaneous or arrives at a known fixed delay. Variable lead times require additional safety stock and a separate reorder-point analysis.

Order cost is fixed per order. The formula treats S as a constant, regardless of order size or supplier. In reality, order costs may include volume-dependent components.

Holding cost is constant per unit. H is treated as constant in the formula. In practice, holding cost can step up at warehouse capacity thresholds — the next pallet of inventory may be cheap to hold up to capacity, then trigger an additional storage facility cost.

No quantity discounts. The formula does not account for price breaks at higher order quantities. Where suppliers offer volume discounts, the analysis must compare EOQ against each discount tier and choose the lowest total cost.

No stockout cost. The formula assumes perfect availability and ignores the cost of running out. In practice, stockout cost — lost sales, expedited freight, customer dissatisfaction — must be addressed through safety stock policy, separately from EOQ.

Single product, independent demand. The formula treats each SKU independently. In reality, products often share warehouse capacity, freight loads, and supplier relationships, and joint replenishment can produce lower total cost than isolated EOQs.

Where EOQ holds up and where it does not

For products with stable demand, modest variability in lead time, fixed order costs, and predictable holding costs, EOQ gives a near-optimal answer and is robust to small changes in the inputs. The cost curve is fairly flat near the optimum, so an EOQ calculation that is wrong by ±20% on order or holding cost still produces a near-optimal total cost.

EOQ is less useful for:

• Highly seasonal demand where annual demand is a poor representation of actual order timing
• Products with sharply tiered supplier discounts where the EOQ may be far below the next discount break
• Items with significant obsolescence risk where holding cost rises non-linearly with order size
• Joint replenishment scenarios where multi-product order costs dominate single-product economics

For these cases, EOQ is best treated as a starting reference and adjusted using either modified models (the EOQ with quantity discounts, the production EOQ, the joint replenishment problem) or simulation.

EOQ and reorder point are different

A common confusion is treating EOQ as the answer to “when should I order.” It is not. EOQ answers “how much should I order.” The companion question — at what inventory level should the order be placed — is answered by the reorder point, which depends on lead time demand and safety stock policy.

A complete inventory replenishment policy combines both:

• EOQ sets the order quantity
• Reorder point sets the trigger inventory level

Either without the other is incomplete. EOQ alone produces correctly sized orders at unpredictable times; reorder point alone produces predictable order timing at incorrect quantities.

The cost of getting EOQ wrong

The flatness of the total cost curve around the EOQ is a useful property — small errors do not destroy the answer — but the curve is not flat far from the optimum. Ordering in lots of 100 against an EOQ of 500 produces order frequency five times the optimum; ordering in lots of 2,000 produces holding costs four times the optimum. Order quantities chosen by habit, supplier preference, or freight container capacity can sit far from the EOQ and carry a real annual cost.

The most common organisational pattern is over-ordering. Buyers tend to favour fewer orders for administrative simplicity, and suppliers reinforce this with full-pallet or full-container minimums. The result is over-stocked warehouses with hidden holding cost.

How the calculator helps

The HoldingCost economic order quantity calculator computes EOQ from configurable demand, order cost, and holding cost inputs. It also shows the total annual cost at the EOQ and at alternative order sizes, so the user can see how sensitive the answer is to the underlying assumptions.

Use it as a starting point for replenishment policy on stable-demand products, as a sanity check against current order quantities, and as a baseline for negotiating with suppliers on minimum order sizes.

Practical takeaways

EOQ is a powerful tool when its assumptions hold and a misleading one when they do not. Use it as a default replenishment policy for stable, independent-demand products, but pair it with a thoughtful reorder point and an honest assessment of which assumptions are violated for the product in question. For most inventory categories, the cost saving from moving from intuition-based ordering to EOQ-based ordering is in the range of 10–30% of total inventory cost, which is rarely a small number.

Pair the EOQ calculator with the inventory holding cost calculator and the warehouse cost calculator for a complete view of inventory economics across your product range.

This guide is general information only and does not constitute professional logistics advice. Inventory policy depends on supplier terms, capacity constraints, and demand patterns specific to each operation. Validate any model output against operational realities before changing replenishment policy.