Economic Order Quantity (EOQ) Model

The economic order quantity model, commonly abbreviated EOQ, is a formula that calculates the optimum quantity a business should purchase, or produce, each time it places an order, specifically to minimize the combined total cost of carrying inventory and the cost of placing additional orders. Ordering too little too often drives up total ordering costs; ordering too much too rarely drives up total carrying costs, and the EOQ model finds the quantity that balances these two opposing cost pressures at their lowest combined total.

The standard formula is the square root of (2 times annual demand in units times the cost to place one order) divided by the annual carrying cost per unit. Plugging in a business's own estimated annual demand, its cost to process a single order, and its cost to hold one unit of inventory for a year produces the specific order quantity that minimizes the combined annual cost of ordering and carrying inventory for that particular item.

A retailer selling 10,000 units per year, at a cost of $50 to place each order and $2 per unit in annual carrying cost, calculates EOQ as the square root of (2 times 10,000 times $50) divided by $2, which works out to roughly 707 units per order. Ordering in batches of 707 units minimizes the retailer's combined annual ordering and carrying costs for that specific item, compared with ordering either smaller, more frequent batches or larger, less frequent ones.

Ordering costs include the administrative work of preparing a purchase order, receiving and inspecting the shipment, and processing the supplier's invoice, costs that are incurred each time an order is placed regardless of how large or small that order is, meaning more frequent, smaller orders drive up total annual ordering cost. Carrying costs include the cost of capital tied up in inventory, storage space, insurance, and the risk of obsolescence, all of which rise with the average amount of inventory held, meaning larger, less frequent orders drive up average inventory levels and therefore total carrying cost.

The basic EOQ model assumes constant, predictable demand and fixed costs per order and per unit carried, assumptions that do not always hold in practice, particularly for businesses facing seasonal demand swings, volume discounts for larger orders, or supply chain uncertainty. More advanced inventory management techniques build on the basic EOQ framework to address these limitations, incorporating safety stock for demand variability and adjusting for quantity discounts, but the basic EOQ model remains a useful starting point for understanding the fundamental trade-off between ordering frequently and holding larger average inventory levels.

A business typically calculates a distinct EOQ for every individual item it stocks, since demand, ordering cost, and carrying cost can all differ significantly from one item to the next, meaning a retailer might order a slow-moving, expensive item in small, frequent batches while ordering a fast-moving, cheap item in large, infrequent batches, each following its own separately calculated optimum quantity.