Economic Order Quantity (EOQ)

The economic order quantity (EOQ) is the quantity of an item that should be ordered to minimize the relevant costs of placing orders and carrying inventory.

The EOQ is most appropriate for items used on a regular basis for which demand is relatively stable and independent. In a health care environment, the EOQ could help to minimize costs associated with providing basic items such as sanitary gloves, surgical masks, and bandages.

The basic idea of the simple EOQ model is that a cost is associated with placing an order for the item, and a cost is associated with carrying the item in inventory if more is ordered than is immediately needed. These two costs conflict and must be traded off to find the best ordering plan.

The EOQ assumes the order cost is fixed and is incurred each time an order is placed regardless of the order size. This cost is associated with administrative costs, transportation, and handling.

The annual inventory carrying cost per unit is usually estimated to be a percentage of the item cost. The percentage includes the cost of capital, representing the opportunity cost of having money invested in inventory.

EOQ makes the cost tradeoff as shown in the following example. Suppose a hospital uses 12,000 packs of sanitary gloves each year. The cost of each pack is $10, and the cost to process each order with the supplier is estimated to be $75. The annual carrying cost rate is 8%. The hospital currently orders 3,000 glove packs each quarter. The general form of the EOQ model, using the data just given, is

• D = annual demand for the item in units (12,000)
• O = fixed cost to place an order in dollars ($75)
• C = unit cost of the item in dollars ($10)
• I = annual carrying cost rate (8%)
• Q = order quantity (to be determined)
• Total cost = average annual ordering cost + average annual holding cost

We can use expression (1) to find the cost of the current policy, in which Q = 3,000:

The EOQ is the value of Q that minimizes expression (1). The general formula is found through differential calculus, resulting in the basic EOQ model shown in expression (2).

[Page 148]Plugging in estimates from the sanitary glove packs into the EOQ model in expression (2) shows that the best order quantity is 1,500 packs.

From expression (1), the total annual cost of ordering 1,500 packs with each order is $1,200, representing a savings of 20% over the current quarterly ordering plan.

In situations where the item unit cost varies with the quantity ordered, the total costs must include the purchase costs in addition to the order costs and carrying costs.