The Economic Order Quantity Model The Economic Order Quantity (EOQ) model helps us determine what

The Economic Order Quantity Model The Economic Order Quantity (EOQ) model helps us determine what

quantity of inventory to order each time we order so that total inven- tory costs throughout the period are minimized. The economic order quantity model assumes that:

Management of Receivables and Inventory

■ Inventory is received instantaneously. ■ Inventory is used uniformly over the period. ■ Inventory shortages are not desirable.

With these assumptions, firms can minimize the costs of inventory— the sum of the carrying costs and the ordering costs—by ordering a spe- cific amount of inventory, referred to as the economic order quantity, each time they run out of inventory.

The economic order quantity is the value of Q in:

----- Q

----- Total cost S = c + K

that minimizes the total cost. Invoking a bit of calculus to minimize total costs with respect to Q, d(total cost)/d(Q), it turns out that the economic order quantity, Q*, is:

Economic order quantity = ------------------------------------------------------------------------------------------------------ ( 2 Cost per transaction ) Total demand ( )

Carrying cost per unit or,

Q* = 2 ----------- KS

(20-6)

If, c = $0.20 per unit, K = $100 per transaction, and S = 500,000 units, then:

2 $100 Q* = ------------------------------------------------ ( ) 500,000 ( ) = 22,361 units

Then for this order quantity: Total inventory cost = Holding cost + Ordering cost

= $0.20  ------------------ 22,361

 500,000 + $100  --------------------- 

MANAGING WORKING CAPITAL

Are costs minimized at this point? Let’s check it out by looking the costs at a couple of other order quantities. If the order quantity were 10,000 units, the total costs would be:

--------------------- 500,000 Total costs at  Q of 20,000 = $0.20   + $100  

If the order quantity were 30,000 units, the total costs would be:

  Total costs at Q of 30,000 = $0.20  ------------------ 30,000

 500,000 + $100  --------------------- 

The costs are lowest at Q = 22,361 units. We can modify the EOQ model to include factors such as: (1) safety stock, (2) lead time, and (3) allowance for stock-out. Safety stock is an additional level of inventory intended to enable the firm to continue to meet demand in case sales levels turn out to be higher than predicted and in case there are unexpected delays in either receiving raw materials or in producing goods. The level of safety stock depends on the degree of uncertainty in our sales and production and the cost of lost sales (where the cost of lost sales comprises sales lost and the loss of customer goodwill).

For example, a large portion of automobile manufacturers’ employ- ees are unionized. A strike in one plant that makes parts can cause a rip- ple effect throughout the company, shutting down production at not only the striking plant but all others. The employees at one of General Motors’ Canadian parts plants struck the firm in fall of 1996. General Motors had stocked sufficient parts at several U.S. locations and was able to maintain operations at its U.S. plants throughout the three-week strike.

Lead time is the time it takes between placing an order for more inventory and the time when it is received or produced. We can modify the EOQ model so that ordering takes place early enough so that the new inventory arrives just as the existing inventory runs out. If it takes, say, three days to receive inventory, having three days worth of inven- tory demand prior to reaching the reorder point is prudent.

The allowance for stock-out is the tolerance for a shortage of goods for sale. We can modify the EOQ model to permit shortages—though we risk the loss of sales and customer goodwill.

Management of Receivables and Inventory

The EOQ model is useful in pointing out the trade off between holding and ordering costs. But there are some problems applying it to actual inventory management. One problem is that it does not consider the possibility that inventory may be held in several locations. For example, if a firm has many retail outlets and regional warehousing, the model has to be altered to consider order quantities for the firm as a whole, each warehouse, and each store. Another problem is that there may be different types of inventory—raw materials, work-in-process, and finished goods—and many different goods, requiring EOQ models for each one. Still another problem is that EOQ is not useful in cases where the demand for inventory is seasonal. Furthermore, EOQ is not readily adapted to cases when quantity discounts available.