What formula calculates the optimal order quantity to minimize total inventory costs?

The economic order quantity formula calculates the optimal order quantity that minimizes total inventory costs.

EOQ balances two opposing expenses: ordering cost and holding cost. Larger orders mean fewer purchase orders and lower annual ordering expense, but they leave more stock in storage. Smaller orders reduce average inventory but require more frequent replenishment. Under the classic model, the best quantity is Q* = √(2DK/h), where D is annual demand, K is fixed cost per order, and h is annual holding cost per unit.

The model is associated with Ford W. Harris, who published the underlying work in 1913. Consultant R. H. Wilson later applied and popularized the analysis, which is why the method is sometimes linked with both names.

EOQ is not the same as a reorder point or safety stock. EOQ answers “how much should be ordered?” A reorder point answers “when should the order be placed?”, while safety stock protects against uncertainty. The basic formula assumes relatively constant demand, fixed ordering costs, known holding costs, and replenishment arriving all at once.