Economic Order Quantity (EOQ), also known as Economic Buying Quantity (EPQ), is the order quantity that minimizes the total holding costs and ordering costs in inventory management. It is one of the oldest classical production scheduling models. The model was developed by Ford W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, and K. Andler are given credit for their in-depth analysis. Overview EOQ applies only when demand for a product is constant over the year and each new order is delivered in full when inventory reaches zero. There is a fixed cost for each order placed, regardless of the number of units ordered; an order is assumed to contain only 1 unit. There is also a cost for each unit held in storage, commonly known as holding cost, sometimes expressed as a percentage of the purchase cost of the item. While the EOQ formulation is straightforward there are factors such as transportation rates and quantity discounts to consider in actual application. We want to determine the optimal number of units to order so that we minimize the total cost associated with the purchase, delivery, and storage of the product. The required parameters to the solution are the total demand for the year, the purchase cost for each item, the fixed cost to place the order for a single item and the storage cost for each item per year. Note that the number of times an order is placed will also affect the total cost, though this number can be determined from the other parameters. Variables = total annual inventory cost = purchase unit price, unit production cost = order quantity = optimal order quantity = annual demand quantity = fixed cost per order, setup cost (not per unit, typically cost of ordering and shipping and handling. This is not the cost of goods) = annual holding cost per unit, also known as carrying cost or storage cost (capital cost, warehouse space, refrigeration, insurance, opportunity cost (price x interest), etc. usually not related to the unit production cost) The total cost function and derivation of EOQ formula The single-item EOQ formula finds the minimum point of the following cost function: Total Cost = purchase cost or production cost + ordering cost + holding cost Where: Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P ×