Formula & Calculator
Economic Order Quantity
The order quantity that minimizes total inventory holding and ordering costs.
Interpretation
EOQ = √(2DS/H). Calculates the optimal order quantity that minimises total inventory costs (ordering + holding). Used in inventory management to balance ordering frequency and carrying costs, assuming constant demand and known costs.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| EOQ | Optimal order size | units |
| D | Annual demand | units/yr |
| S | Ordering cost | $/order |
| H | Holding cost | $/unit/yr |
What it means
The Economic Order Quantity (EOQ) is a classic inventory management model that determines the ideal order size to minimise the total annual inventory costs, which include ordering costs and holding (carrying) costs. The formula EOQ = √(2DS/H) uses D = annual demand, S = ordering cost per order, and H = holding cost per unit per year. The model assumes constant demand, instantaneous replenishment, no quantity discounts, and no stockouts. The EOQ balances the trade‑off: ordering larger quantities reduces ordering frequency (lower ordering costs) but increases holding costs; smaller orders do the opposite. The optimal point occurs where the annual ordering cost equals the annual holding cost. This formula is widely used in manufacturing, retail, and distribution to manage raw materials, work‑in‑progress, and finished goods. It helps reduce waste, improve cash flow, and streamline supply chain operations. Despite its assumptions, it provides a solid starting point for inventory policy. Managers often adjust EOQ for real‑world constraints like supplier minimums, storage capacity, or seasonality. Understanding EOQ is fundamental for supply chain professionals and operations managers to control inventory expenses and improve profitability.
Worked example
Economic Order Quantity – Two Examples
Real‑World| Parameter | Value |
|---|---|
| D (annual demand) | 1,000 units |
| S (ordering cost) | $50/order |
| H (holding cost) | $2/unit/year |
| Parameter | Value |
|---|---|
| D | 2,000 tonnes |
| S | $60/order |
| H | $3/tonne/year |
Common mistakes
- Units: D (annual demand) and S (ordering cost) must be in the same time period. H (holding cost per unit per year) must be consistent with D.
- Square root: EOQ = √(2DS/H) – do not omit the square root.
- Assumptions: EOQ assumes constant demand, no quantity discounts, and instantaneous replenishment. If these do not hold, use adjusted models.
- Holding cost: Include all carrying costs (storage, insurance, obsolescence) – not just the purchase price.
- Ordering cost: Include all fixed costs per order (processing, transport, receiving).
Applications
The Economic Order Quantity (EOQ) is the optimal order quantity that minimises the total inventory holding and ordering costs for a product, derived from the square root of (2DS/H) where D is annual demand, S is ordering cost per order, and H is holding cost per unit per year. This classic inventory model is used by supply chain managers, procurement specialists, and inventory planners to balance the trade‑off between frequent, small orders (high ordering cost) and large, infrequent orders (high holding cost). EOQ is applied in retail, manufacturing, and distribution to determine reorder quantities, to negotiate supplier discounts, and to set safety stock levels. By implementing EOQ, companies can reduce inventory carrying costs, improve cash flow, and ensure product availability. Although its assumptions (constant demand, no quantity discounts) may not always hold, it provides a robust starting point for inventory optimisation.
- Inventory management in retail, wholesale, and e‑commerce
- Manufacturing raw material ordering and batch sizing
- Distribution centre replenishment planning
- Cost reduction through optimal order frequency and quantity
- Integration with supplier management and Just‑in‑Time (JIT) systems
Frequently Asked Questions
The EOQ model determines the optimal order quantity that minimises the total inventory costs, which consist of ordering costs and holding costs. The formula is EOQ = √(2·D·S / H), where D is annual demand, S is the cost per order, and H is the annual holding cost per unit.
- D – annual demand (units/year).
- S – ordering cost per order ($/order).
- H – holding cost per unit per year ($/unit/year).
- Constant and known demand rate.
- Fixed ordering cost per order, independent of order quantity.
- Fixed holding cost per unit per year.
- Instantaneous replenishment (no lead time).
- No quantity discounts.
- Infinite planning horizon.
If holding cost H increases, the EOQ decreases (since EOQ is inversely proportional to √H). This means you should order smaller quantities more frequently to reduce the average inventory holding cost.
At the EOQ, the total annual inventory cost (excluding purchase cost) is TC = √(2·D·S·H). This is the sum of ordering and holding costs, which are equal at the optimum.
The EOQ itself does not include lead time; it determines the order quantity. The reorder point (ROP) is calculated separately: ROP = d × LT, where d is the daily (or weekly) demand and LT is the lead time in the same time units.
Calculate the EOQ for each price tier (using the discounted H if it changes with price). Then compute the total cost (purchase cost + ordering + holding) for each feasible quantity (including the EOQ and the price‑break quantities). Choose the quantity with the lowest total cost.
- Assumes demand is constant and known – in reality, demand fluctuates.
- Does not account for supply chain uncertainties (supplier lead time, quality issues).
- Ignores capacity constraints or storage space limitations.
- Not suitable for multiple items with shared ordering costs.
Most inventory systems include an EOQ calculator that uses historical demand data and cost parameters. It is often used as a starting point for setting reorder quantities, which are then adjusted based on real‑time demand and supplier constraints.
- Retail: ordering consumer goods from wholesalers.
- Manufacturing: ordering raw materials (steel, plastics).
- Healthcare: managing medical supplies.
- Food service: ordering perishable items.