EOQ

Economic order quantity (EOQ) is the order size that minimizes total inventory costs for a single item when demand is known and constant. It is a foundational concept in inventory management and was first developed by Ford W. Harris in 1913, with later enhancements by others including R. H. Wilson.

Under the classic EOQ model, the optimal order quantity Q* is given by the square root of (2DS/H), where D is the annual demand, S is the fixed cost of placing an order, and H is the annual holding cost per unit. The model seeks to balance ordering costs, which decrease as order size increases, against holding costs, which rise with larger inventories. The total annual cost is approximately DS/Q + HQ/2, ignoring purchase cost variations.

Assumptions include: constant, known demand; fixed lead time; no stockouts or quantity discounts; a single product with stable prices; and no interactions with other items. In practice, reorder points (R = d × L) are used to trigger orders, where d is the demand rate and L is lead time; EOQ provides the optimal size, not the timing of orders.

Extensions of the model address production settings (production-order quantity, POQ), quantity discounts, shortages allowances, safety stock for uncertainty, and service-level planning. Limitations include sensitivity to cost estimates, applicability to uncertain or seasonal demand, and neglect of price dynamics or capacity constraints.