Economic Order Quantity (EOQ): Formula, Assumptions & Sample Calculation

What Is Economic Order Quantity?

Every time you place an order you pay an ordering cost (time, admin, delivery fee). Every unit you hold ties up capital and incurs storage costs. These two forces pull in opposite directions:

• Ordering in large quantities reduces ordering frequency → lower ordering cost, but higher average inventory → higher holding cost.
• Ordering in small quantities reduces average inventory → lower holding cost, but requires more frequent orders → higher ordering cost.

The EOQ is the order quantity at the crossover point — where total cost (ordering + holding) is at its minimum. At EOQ, the annual ordering cost and annual holding cost are exactly equal.

The EOQ Formula

Where:

• D — Annual demand (units/year)
• S — Ordering cost per order ($/order)
• H — Annual holding cost per unit ($/unit/year)

The result is the number of units to order in each replenishment batch.

Model Assumptions

The classic EOQ model is built on six assumptions. Understanding them helps you know when to apply EOQ directly and when to adjust:

In practice, almost none of these hold perfectly. EOQ should be treated as a starting benchmark, refined using safety stock and sensitivity analysis.

Understanding Each Variable

Annual Demand (D)

Total units sold or consumed in a year. Use historical data to estimate. For seasonal items, EOQ can be recalculated per season using seasonal demand rates.

Ordering Cost (S)

The cost incurred each time an order is placed, regardless of order size. Typically includes:

• Purchasing department labor (time to issue PO, communicate with supplier)
• Delivery and freight charges (if flat per order)
• Receiving and inspection labor
• Invoice processing cost

Ordering costs are often underestimated. A thorough analysis typically reveals €50–€200+ per order for most B2B procurement processes.

Holding Cost (H)

The annual cost of holding one unit in stock. This is usually expressed as a holding cost rate (%) multiplied by unit cost:

Holding cost rate typically includes:

• Capital cost (cost of money tied up): 5–15%
• Storage space: 2–5%
• Obsolescence and shrinkage: 2–8%
• Insurance: 1–3%

Industry rules of thumb place total holding cost rates at 20–35% of inventory value per year.

Total Inventory Cost

Total inventory cost in the EOQ model is the sum of annual ordering cost and annual holding cost:

Where Q is the order quantity.

• D/Q = number of orders per year
• D/Q × S = annual ordering cost
• Q/2 = average inventory (assuming linear drawdown)
• Q/2 × H = annual holding cost

At the EOQ, these two components are equal, and their sum is minimized. Deviating from EOQ in either direction increases total cost — though the total cost curve is relatively flat near the optimum, meaning small deviations have modest cost impact.

Worked Example

Given Data

Step 1: Calculate EOQ

Step 2: Calculate Number of Orders per Year

Step 3: Calculate Total Annual Cost

Notice that ordering cost and holding cost are approximately equal at the EOQ — this is always the case by definition of the formula.

Step 4: Compare with Alternative Order Sizes

EOQ Sensitivity

The EOQ formula is fairly robust. Because of the square root, a doubling of demand only increases EOQ by about 41% (√2 ≈ 1.41). This means:

• Errors of 20–30% in demand estimates change EOQ by only 10–15%.
• The total cost curve is flat near the optimum — ordering 10–20% above or below EOQ typically increases total cost by only 1–3%.

Limitations of EOQ

Despite its usefulness, EOQ has well-known limitations that must be considered in real-world applications:

• Constant demand assumption — Real demand varies seasonally and stochastically. EOQ can be applied per period using period-specific demand rates, or overridden during peaks.
• No quantity discounts — Suppliers often offer price breaks for larger orders. When discounts are available, a modified total cost analysis (including purchase price) is needed to find the true optimum.
• Single item focus — EOQ does not account for multi-item order coordination (ordering from the same supplier) or joint replenishment.
• No stockout allowance — EOQ assumes perfect delivery timing. In practice, a safety stock buffer and reorder point must be layered on top.
• Ignores capacity constraints — Storage capacity limits may prevent ordering the full EOQ.
• Cash flow — Smaller, more frequent orders (below EOQ) may be preferred when cash is constrained.

EOQ Extensions

Production Order Quantity (POQ)

When items are produced in-house rather than purchased, stock builds up gradually during the production run rather than arriving all at once. The Production Order Quantity model adjusts for this:

Where d is daily demand rate and p is daily production rate. The term (1 − d/p) reduces effective holding cost to reflect that some production is consumed as it is made.

Quantity Discount Model

When suppliers offer lower unit prices for larger orders, the total cost analysis must include purchase cost. The optimal order quantity may be larger than the basic EOQ if the price saving outweighs the extra holding cost.

Compare total annual cost (ordering + holding + purchase) at each discount break point and at the EOQ for each price tier. Select the quantity with the lowest total cost.

EOQ with Backorders

If planned stockouts (backorders) are acceptable and have a known cost, the EOQ can be modified to allow a controlled shortfall. The resulting EOQ is larger, with orders placed slightly later (lower reorder point).

Frequently Asked Questions

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