Inventory Management
Manufacturing companies take raw materials and turn them into finished products. Merchandising companies buy product and resell it. Both types of companies must manage their inventory. If you order too much, you risk obsolescence, spoilage, or inability to sell. If you order too little, you may lose sales you could have made and risk upsetting your customers. This section will help you understand how companies manage their inventory to minimize overall costs.
Economic Order Quantity Technique
Economic order quantity is the order quantity that minimizes total inventory holding costs and ordering costs:
Learning Objective

Calculate a company's optimal order quantity
Key Points
 Economic order quantity is the order quantity that minimizes total inventory holding costs and ordering costs.
 EOQ determines the optimal number of units to minimize the total cost associated with the purchase, delivery, and storage of the product.
 where order quantity, optimal order quantity, annual demand quantity, fixed cost per order, annual holding cost per unit.
Key Terms
 holding cost: In business management, holding cost is money spent to keep and maintain a stock of goods in storage.
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, 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.
Underlying assumptions are:
 The ordering cost is constant.
 The rate of demand is known, and spread evenly throughout the year.
 The lead time is fixed.
 The purchase price of the item is constant (i.e., no discount is available).
 The replenishment is made instantaneously; the whole batch is delivered at once.
 Only one product is involved.
The singleitem EOQ formula finds the minimum point of the following cost function:
Economic order quantity Economic order quantity function solving for Q.
 Purchase cost: This is the variable cost of goods: purchase unit price annual demand quantity. This is .
 Ordering cost: This is the cost of placing orders: each order has a fixed cost , and we need to order times per year. This is .
 Holding cost: the average quantity in stock (between fully replenished and empty) is , so this cost is .
To determine the minimum point of the total cost curve, partially differentiate the total cost with respect to (assume all other variables are constant) and set to :
Equation Equation to determine the minimum point of the total cost curve.