EconomicOrderQuantityFormel

Economic Order Quantity (EOQ) is a foundational inventory management model that helps determine the optimal order size to minimize total inventory costs. By balancing the fixed costs of placing orders with the variable costs of holding inventory, EOQ provides a quantitative rule for when and how much to order.

In the standard formulation, let D be the annual demand for a single item, S the fixed cost per order, and H the annual holding cost per unit. The optimal order quantity is Q* = sqrt(2 D S / H). The corresponding minimum total annual cost is C* = 2 sqrt(D S H), and the number of orders per year is D / Q*. The model assumes constant demand and lead times, instantaneous replenishment, and no stockouts.

Several important assumptions underpin EOQ. Demand must be steady and known, ordering costs are fixed per order, holding costs are proportional to average inventory, lead times are negligible or fixed, and only a single item is considered with no quantity discounts. Prices are constant, and there is no uncertainty about demand or supply.

Extensions address real-world complexity. EOQ with quantity discounts modifies the objective to account for price reductions on larger orders. Production-order EOQ models adapt the formula when items are produced internally and arrive gradually rather than in a single batch. Other variants handle stochastic demand, multiple items, safety stock, and service level constraints.

EOQ remains a widely taught and used model for determining reorder quantities in manufacturing and retail, forming the basis for many inventory planning and enterprise resource planning systems.