What is the Economic Order Quantity?

EOQ is the order size that minimises the combined cost of placing orders and holding inventory. Order too much and holding cost rises; order too little and you pay ordering cost too often. The EOQ is the balance point where both costs are equal.

What is the Wilson EOQ formula?

EOQ equals the square root of (2 times annual demand times ordering cost, divided by annual holding cost per unit). It comes from setting the derivative of the total cost curve to zero, which occurs where annual ordering cost equals annual holding cost.

What counts as a holding cost?

Holding cost (H) covers everything tied to storing one unit for a year: warehouse space, capital tied up, insurance, shrinkage, and obsolescence. It is often estimated as a percentage of unit value, for example 20 to 30 percent of the item cost.

Does EOQ account for quantity discounts or lead time?

The basic Wilson model assumes constant demand, fixed costs, and no discounts. It does not set a reorder point, which depends on lead time and safety stock. For volume price breaks you compare EOQ total cost against each discount tier separately.

Why does total cost barely change near the EOQ?

The total cost curve is flat near its minimum, so ordering 10 to 20 percent above or below the EOQ raises total cost only slightly. This makes EOQ robust to imperfect cost estimates and lets you round to a convenient pack or pallet size.

Economic Order Quantity (EOQ) Calculator

The Economic Order Quantity answers a core procurement question: how much should you order at a time? Order in large batches and you tie up cash and warehouse space in holding cost; order frequently in small batches and you rack up ordering cost. The EOQ is the sweet spot that minimises the two combined.

How it works

The classic Wilson EOQ formula is derived by minimising the total annual cost:

total cost = ordering cost + holding cost
           = (D / Q) × S  +  (Q / 2) × H

EOQ (Q*) = sqrt( 2 × D × S / H )

where D is annual demand in units, S is the fixed cost per order, and H is the cost to hold one unit for a year. At the EOQ the annual ordering cost and the annual holding cost are exactly equal, which is the condition that minimises the sum. Average inventory is Q / 2 because stock draws down linearly from Q to 0 between deliveries.

Example and tips

Suppose annual demand is 12,000 units, each order costs 75 to place, and holding one unit for a year costs 3. Then EOQ = sqrt(2 × 12,000 × 75 / 3) = sqrt(600,000) ≈ 775 units. You would place about 12,000 / 775 ≈ 15.5 orders per year, roughly every 24 days, and the minimised total cost is about 2,324 per year. Because the cost curve is flat near the minimum, rounding 775 up to an 800-unit pallet adds only a few units of cost — round to whatever pack size your supplier ships.