Economic Order Quantity (EOQ)
Estimate theoretical and whole-unit EOQ, annual ordering and holding costs, and order intervals using the classical model.
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Estimate the order size that balances annual ordering and cycle-stock holding costs. Compare the theoretical optimum with a whole-unit order quantity.
Worked example
Example output from the starting values. Enter your figures and press Calculate for your result.
- Theoretical EOQ
- 28.2843 units/order
- Whole-unit order quantity
- 28 units/order
- Average cycle stock
- 14 units
- Implied orders per year
- 35.7143 orders/year
- Implied interval between orders
- 10.22 days
- Annual ordering cost
- 71.4286 currency units/year
- Annual cycle-stock holding cost
- 70 currency units/year
- Annual ordering + holding cost
- 141.4286 currency units/year
Formula
EOQ = √(2 × annual demand × fixed ordering cost ÷ annual holding cost per unit). Annual ordering cost = (demand ÷ quantity) × ordering cost. Annual cycle-stock holding cost = (quantity ÷ 2) × holding cost.
How to use this calculation
For 1,000 units/year, 2 currency units per order and 5 per unit/year in holding cost, the theoretical EOQ is 28.2843 units. Comparing adjacent whole-unit costs gives 28 units/order, with 141.4286 in annual ordering plus cycle-stock holding costs.
- The classical model assumes steady demand, fixed ordering and holding costs, and replenishment without stockouts. Seasonal demand, quantity discounts, minimum orders and supplier pack sizes can require a different policy.
- The whole-unit quantity minimizes the model cost among the adjacent positive integers, rather than always rounding up. Average cycle stock excludes safety stock; annual ordering plus holding cost excludes purchasing cost and other fixed costs. Orders/year and intervals are long-run averages, not a dated purchase schedule.
- Demand and both costs must be positive. Use one currency and annual units; a carrying-cost percentage must first be converted to a cost per unit per year. This estimates order size, not a reorder trigger, and places no purchase order.
Formula reference: Investopedia: Economic Order Quantity formula and example. General planning information, not a guarantee of business results.
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