Economic Order Quantity (EOQ): Formula and Limits

The economic order quantity is the order size that minimizes the combined cost of placing orders and holding stock, and it is a classic piece of inventory theory that is still useful when applied with care. Order too often and ordering costs mount up. Order too rarely in large lots and holding costs rise. The EOQ finds the balance. In real consumer product businesses, minimum order quantities, case packs, quantity discounts, shelf life and cash constraints often override the pure formula, but the formula remains a valuable guide to the cost of deviating from the optimum and to the right order of magnitude. This guide gives the formula, works through an example with checked arithmetic, shows how flat the cost curve is near the optimum, explains how to handle practical constraints and says when not to use it. It is part of demand planning and inventory optimization, follows reorder point formula and safety stock formula, and leads to ABC analysis and inventory carrying cost. Order sizes drive the cash described in cash flow management.

The formula

EOQ = √(2 × D × S ÷ H), where D is annual demand in units, S is the cost of placing one order and H is the annual holding cost per unit.

Holding cost per unit is the unit cost times the annual carrying cost rate. Ordering cost includes the administrative effort, freight and receiving costs that occur per order, regardless of order size, not the cost of the goods themselves. The formula assumes steady demand, constant costs and a fixed lead time, and ignores quantity discounts and capacity limits.

A worked example

Annual demand is 12,000 units. Placing an order costs $60. The unit cost is $20 and the carrying cost rate is 25 percent, so holding one unit for a year costs 0.25 × 20 = $5 (illustrative).

• EOQ = √(2 × 12,000 × 60 / 5) = √(288,000) = 536.7, about 537 units
• Orders per year: 12,000 / 537 = 22.3
• Ordering cost: 22.3 × 60 = $1,341.6
• Average inventory: 537 / 2 = 268.5 units; holding cost: 268.5 × 5 = $1,342.5
• Total relevant cost: about $2,684

Check: 2 × 12,000 × 60 = 1,440,000; divided by 5 is 288,000; its square root is 536.66. At the optimum, ordering cost and holding cost are equal, which is a handy check: both are about $1,342. The total cost equals √(2 × D × S × H) = √(2 × 12,000 × 60 × 5) = √7,200,000 = $2,683.

How flat is the curve?

Compare alternatives. If the company orders 1,000 units at a time, there are 12 orders a year. Ordering cost is 12 × 60 = $720. Average inventory is 500 units and holding cost is 500 × 5 = $2,500. Total = $3,220, which is 20 percent above the optimum (3,220 / 2,683 = 1.20). If it orders 250 units at a time, there are 48 orders: ordering cost 48 × 60 = $2,880, holding cost 125 × 5 = $625, total $3,505, 31 percent above the optimum (3,505 / 2,683 = 1.306). Ordering 600 units instead of 537 results in a total of (12,000 / 600) × 60 + (600 / 2) × 5 = 1,200 + 1,500 = $2,700, only 0.6 percent above. The lesson is that the cost curve is flat near the optimum: rounding to a convenient case pack or a supplier minimum near the EOQ costs very little, while large departures cost more. This is useful to know when the practical quantity differs from the theoretical one.

Practical constraints

Minimum order quantities. If the supplier's minimum is above the EOQ, you pay a holding-cost penalty. Quantify it and use it in negotiation: if a minimum of 2,000 units on this item raises annual cost from $2,683 to (12,000 / 2,000) × 60 + 1,000 × 5 = 360 + 5,000 = $5,360, the extra $2,677 a year is the cost of the minimum.

Quantity discounts. A lower unit price at higher volumes changes the calculation. Compute total annual cost, including purchase cost, at each price break, and choose the lowest. A 3 percent discount on a $20 item purchased 12,000 times a year is worth 0.03 × 20 × 12,000 = $7,200, which can outweigh the extra holding cost of larger orders.

Case packs and pallet quantities. Round to full cases or pallets. Because the cost curve is flat, rounding costs little.

Shelf life. For perishable or fashion items, order sizes must not exceed what can be sold within the life of the product, even if the EOQ is larger.

Cash and storage limits. A cash constraint or limited warehouse space may cap order quantities below the EOQ.

Freight breaks. Container or truckload economies may argue for larger consolidated orders. Include freight in the ordering cost where it varies by order and not by unit.

Demand uncertainty and seasonality. The EOQ assumes constant demand. For seasonal items, apply it within a season or use planned orders.

When to use it

Use EOQ for steady, repeatedly purchased items where ordering costs and holding costs are meaningful and can be estimated: raw materials, packaging, core finished goods. It is less suitable for new or highly seasonal products, for make-to-order items and for items where lot sizes are fixed by production runs. Even then, it helps with negotiating minimums and justifying changes in order frequency.

Estimating the inputs

The weakest inputs are usually the ordering cost and the holding cost rate. For ordering cost, include the time to prepare and approve the order, receiving and inspection labor, per-order freight and payment processing, and exclude fixed overhead that does not vary with the number of orders. For holding cost, use the carrying cost rate that reflects the true cost of capital and storage. See inventory carrying cost. Do a sensitivity check: if the ordering cost is 30 percent higher, the EOQ rises by about 14 percent (the square root of 1.3 is 1.14). Because EOQ depends on the square root of the ratio, errors in the inputs are dampened.

Common mistakes

1. Including the unit cost of goods in ordering cost.
2. Using a carrying cost that excludes capital cost.
3. Ignoring minimums, discounts and shelf life.
4. Treating the result as exact when the curve is flat.
5. Using it for highly seasonal or one-time buys.
6. Forgetting to update when demand changes.

FAQs

What is economic order quantity?

The order size that minimizes the sum of ordering and holding costs, calculated as the square root of twice annual demand times order cost, divided by holding cost per unit.

What does EOQ assume?

Steady demand, constant costs, a fixed lead time, no quantity discounts and no capacity limits.

What if my supplier's minimum is higher than the EOQ?

Quantify the extra annual cost of the minimum and use it in negotiations or as a basis for consolidating orders.

Is EOQ still relevant?

Yes, as a guide to the cost of order size decisions. Apply it with judgment, given minimums, discounts and shelf life.

How do quantity discounts affect EOQ?

Compute total annual cost, including purchase price, at each price break and choose the lowest, which may differ from the plain EOQ.