Last updated: 2026-07-02

The order-size trade-off

Every time a business reorders stock it faces two opposing costs. Placing an order carries a fixed ordering cost — the paperwork, shipping, and setup that come with each purchase, no matter how many units it covers. Holding the stock that arrives carries a holding cost — the storage, insurance, spoilage, and tied-up capital that scale with how much sits on the shelf.

Order in large batches and ordering cost drops, because there are fewer orders across the year, but holding cost climbs as average inventory rises. Order in small batches and holding cost falls while ordering cost climbs. The economic order quantity is the batch size that sits at the bottom of the combined-cost curve, where these two forces balance.

The formula

The economic order quantity comes from setting annual ordering cost equal to annual holding cost and solving for the order size. With annual demand $D$, cost per order $S$, and annual holding cost per unit $H$:

Once the order size is known, two follow-on figures describe the reorder rhythm. The number of orders per year is annual demand divided by the order size:

At the economic order quantity, annual ordering cost and annual holding cost turn out to be equal, so the total inventory cost simplifies to a single square root:

Worked example: reordering a stock item

A warehouse sells 12,000 units of a part each year. Each purchase order costs $75 to raise and receive, and holding one unit in stock for a year costs $3.

The economic order quantity divides the ordering pressure by the holding pressure inside a square root:

At that batch size the warehouse reorders about 15 times a year:

And the combined annual cost lands at:

Ordering far more or far less than 775 units at a time raises this total. A batch of 1,500 would cut orders to 8 a year but roughly double average inventory; a batch of 300 would keep shelves nearly empty but push the annual order count past 40. The economic order quantity is the middle ground where neither cost dominates.

What the model assumes

The Wilson model is deliberately simple, and its assumptions are worth stating:

• Demand is steady and known. The formula spreads a single annual figure evenly across the year.
• Costs are constant. The cost per order and the holding cost per unit do not change with volume.
• Orders arrive complete. There is no partial delivery and no lead-time variation.
• No discounts or stockouts. Bulk-purchase discounts and the cost of running out are outside the model.

Real demand is lumpier than this, and suppliers often offer price breaks that reward larger orders. Treat the economic order quantity as a well-grounded starting point for a reorder policy rather than an exact rule, and revisit it when demand or costs shift.

Where holding cost comes from

The holding cost per unit is the input most often estimated rather than measured. A common approach expresses it as a percentage of the unit's value — a carrying rate that bundles warehouse space, insurance, obsolescence, and the return that capital could earn elsewhere. A part worth $20 with a 15% annual carrying rate has a holding cost of $3 per unit per year. Because the order size depends on the square root of the cost ratio, moderate errors in this estimate move the economic order quantity only gently, which is part of why the model stays useful despite rough inputs.

To turn a per-unit contribution into the sales volume that covers fixed costs, pair this with the Break-Even Calculator.