# Economic Order Quantity Model

Fixed point reordering system: A pre-established point at which inventory is replenished:

Economic order quantity (EOQ): A technique for balancing purchase ordering carrying and stock out costs to derive the optimum quantity for purchase order.

When you order checks from a bank, have you noticed that the reorder from is placed about two thirds of the way through your supply of checks? This practice is a simple example of a fixed point reordering system. At some pre-established point in the process, the system is deigned to flag the fact that the inventory needs to be replenished. The objective is to minimize inventory carrying cost while at the same time limiting the probability of stocking out of the inventory item. In recent years, retail stores have increasingly been using their computers to perform this reordering activity. Their cash registers are connected tot heir computers, and each sale automatically adjusts the store’s inventory record. When the inventory of an item hits the critical point, the computer tells management to reorder.

One of the best known techniques for mathematically deriving the optimum quantity for a purchase order is the economic order quantity (EOQ) model. The EOQ model seeks to balance four costs involved in ordering and carrying inventory the purchase costs (purchase price plus delivery charges less discounts) the ordering costs (paperwork, follow up inspection when the item arrives and other processing costs) carrying costs (money tied up in inventory, storage, insurance, taxes, and so forth), and stock out costs (profits forgone from orders lost, the cost of reestablishing goodwill and additional expenses incurred to expedite late shipments). When these four costs are known, the model identifies the optimal order size for each purchase.

The objective of the economic order quantity (EOQ) model is to minimize the total costs associated with the carrying and ordering costs as the mount ordered gets larger, average inventory increases and so do carrying costs. For example, if annual demand for an inventory item is 26,000 units, and a firm orders 500 each time, the firm will place 52 [26,000/500] orders per year. This order frequency gives the organizations an average inventory of 250 [ 500/ 2] units. If the order quantity is increased to 2,200 units, fewer orders (13) [26,000 / 2,000] will be placed. However, average inventory on hand will increased to 1,000 [2,000 / 2] units. Thus, as holding cost go up, ordering costs go down, and vice versa. The optimum economic order quantity is reached at the lowest point on the total cost curve. That’s the point at which ordering costs equal carrying cost – or the economic order quantity.
To compute this optimal order quantity you need the following data: forecasted demand for the item during the period (D); the cost of placing (OC) the value or purchase price of the item (V); and the carrying cost (expressed as a percentage) of maintaining the total inventory (CC). Given these data, the formula for EOQ is as follows:

EOQ = √2 x D x OC / V x CC

Let’s work an example of determining the EOQ. Take for example. Shah Electronics a retailer of high quality sound and video a equipment. The owner wishes to determine the company’s economic order quantities of high quality sound and video equipment. The item in question is a Sony compact voice recorder. The forecast of sales is 4,000 units a year. The cost of the sound system should be Rs 2,000. Estimated costs of placing an order for those systems are Rs 1,400 per order and annual insurance taxes, and other carrying at 20 percent of the recorder’s value. Using the EOQ formula and the preceding, he can calculate the EOQ as flows:

EQO = √2 x 4,000 x 1,400 / 2,000 x .20

EOQ = √28,000

EOQ = 167.33 or 168 units.