Economic order quantity (EOQ)

Economic order quantity, abbreviated to EOQ, is the order size that minimises the total annual cost of inventory replenishment for a single product. It balances two opposing cost forces: ordering cost, which falls as orders become larger and less frequent, and holding cost, which rises as average inventory grows.

The Wilson formula

The classical EOQ formula — sometimes called the Wilson formula after one of its early popularisers — is:

EOQ = √((2 × D × S) ÷ H)

Where:

• D is annual demand in units
• S is the cost of placing one order (purchase order processing, freight setup, receiving labour)
• H is the holding cost per unit per year (capital, storage, insurance, obsolescence)

The formula is the result of differentiating the total annual cost function with respect to order quantity and setting the derivative to zero.

A worked example

For a product with annual demand of 12,000 units, an order cost of $50, and a holding cost of $4 per unit per year:

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

At this order size, the firm places about 22 orders per year and holds an average inventory of about 274 units. Annual ordering cost and annual holding cost are roughly equal — the defining property of the EOQ.

What it assumes

EOQ is built on a long list of simplifying assumptions: constant demand, fixed order cost, constant holding cost per unit, no quantity discounts, no stockout cost, and instantaneous or fixed-lead-time replenishment. These assumptions hold reasonably well for many stable-demand products and break down for seasonal items, products with sharp supplier discount tiers, or items subject to obsolescence risk.

EOQ and reorder point

EOQ answers the question of how much to order, not when to order. The companion question — at what inventory level to trigger a replenishment — is answered by the reorder point, which depends on lead time demand and safety stock. A complete inventory policy combines both.

Why it matters

Order quantities chosen by intuition, supplier preference, or container capacity can sit far from the EOQ and carry meaningful annual cost. Moving from rule-of-thumb ordering to EOQ-based ordering typically reduces total inventory cost by 10–30% for stable-demand products, which on a large product range can run into substantial annual savings.