How this calculator works
Ordering in large batches lowers the number of orders and the ordering cost, but it raises the average stock on hand and the cost of holding it. Ordering in small batches does the reverse. The economic order quantity is the batch size where the two costs are equal and their sum is at its minimum. The model assumes demand is steady, that orders arrive instantly at the moment stock runs out, and that holding cost is proportional to the number of units in stock. Real demand varies, so most businesses add a safety stock on top of the EOQ and review the assumption when lead times change.
Formula
EOQ = square root of (2 × annual demand × ordering cost per order ÷ holding cost per unit per year). Orders per year = annual demand / EOQ. Total annual cost = orders per year × ordering cost + EOQ / 2 × holding cost.
Worked example
Annual demand of 10,000 units, an ordering cost of $50 and a holding cost of $5 per unit per year give EOQ = square root(2 × 10,000 × 50 / 5) = square root(200,000) = 447.21 units. The business orders about 22.36 times a year and spends roughly $2,236 in total ordering and holding cost.
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Frequently asked questions
What costs belong in the holding cost?
Storage, insurance, obsolescence, the opportunity cost of the cash tied up and any handling. A common shortcut is 20 to 30 per cent of unit cost per year, but the right figure depends on the product and the space it occupies.
Why does the EOQ ignore purchase price?
If the unit price is constant regardless of order size, it adds the same total to every policy and does not change the optimum. Once quantity discounts or minimum order sizes enter, the optimum can jump to a discount break and the plain EOQ is only a starting point.
What is the relationship between EOQ and safety stock?
EOQ sets the batch size, safety stock covers unexpected demand during the lead time. They answer different questions. A business can use a small EOQ and a large safety stock at the same time.