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MANAGING INVENTORIES

Let us take a look at what economists have had to say about managing inventories and then see whether some of these ideas can help us manage cash balances. Here is a simple inventory problem.

A builders` merchant faces a steady demand for engineering bricks. When the merchant every so often runs out of inventory, it replenishes the supply by placing an order for more bricks from the manufacturer.

There are two costs associated with the merchant`s inventory of bricks. First, there is the order cost. Each order placed with a supplier involves a fixed handling expense and delivery charge. The second type of cost is the carrying cost. This includes the cost of space, insurance, and losses due to spoilage or theft. The opportunity cost of the capital tied up in the inventory is also part of the carrying cost. Here is the kernel of the inventory problem:

As the firm increases its order size, the number of orders falls and therefore the order costs decline. However, an increase in order size also increases the average amount in inventory, so that the carrying cost of inventory rises. The trick is to strike a balance between these two costs.

Let`s insert some numbers to illustrate. Suppose that the merchant plans to buy 1 million bricks over the coming year. Each order that it places costs $90, and the annual carrying cost of the inventory is $.05 per brick. To minimize order costs, the merchant would need to place a single order for the entire 1 million bricks on January 1 and would then work off the inventory over the remainder of the year. Average inventory over the year would be 500,000 bricks and therefore carrying costs would be 500,000 $.05 = $25,000. The first row of Table 2.10 shows that if the firm places just this one order, total costs are $25,090: Total costs = order costs + carrying costs $25,090 = $90 + $25,000

To minimize carrying costs, the merchant would need to minimize inventory by placing a large number of very small orders. For example, the bottom row of Table 2.10

shows the costs of placing 100 orders a year for 10,000 bricks each. The average inventory is now only 5,000 bricks and therefore the carrying costs are only 5,000 $.05 = $250. But the order costs have risen to 100 $90 = $9,000.

Each row in Table 2.10 illustrates how changes in the order size affect the inventory costs. You can see that as the order size decreases and the number of orders rises, total inventory costs at first decline because carrying costs fall faster than order costs rise. Eventually, however, the curve turns up as order costs rise faster than carrying costs fall.

Figure 2.6 illustrates this graphically. The downward-sloping curve charts annual order costs and the upward-sloping straight line charts carrying costs. The U-shaped curve is the sum of these two costs. Total costs are minimized in this example when the order size is 60,000 bricks. About 17 times a year the merchant should place an order for 60,000 bricks and it should work off this inventory over a period of about 3 weeks. Its

inventory will therefore follow the sawtoothed pattern in Figure 2.7.

Note that it is worth increasing order size as long as the decrease in total order costs outweighs the increase in carrying costs. The optimal order size is the point at which these two effects offset each other. This order size is called the economic order quantity. There is a neat formula for calculating the econ omic order quantity. The formula is

Economic order quantity =_2_annual sales_cost per order carrying cost In the present example, Economic order quantity =_2 1,000,000 90 = 60,000 bricks .05

You have probably already noticed several unrealistic features in our simple example. First, rather than allowing inventories of bricks to decline to zero, the firm would want to allow for the time it takes to fill an order. If it takes 5 days before the bricks can be delivered and the builders` merchant waits until it runs out of stock before placing an order, it will be out of stock for 5 days. In this case the firm should reorder when its

stock of bricks falls to a 5-day supply.

The firm also might want to recognize that the rate at which it sells its goods is subject to uncertainty. Sometimes business may be slack; on other occasions the firm may land a large order. In this case it should maintain a minimum safety stock below which it would not want inventories to drop.

The number of bricks the merchant plans to buy in the course of the year, in this case 1 million, is also a forecast that is subject to uncertainty. The optimal order size is proportional to the square root of the forecast of annual sales.

These are refinements: the important message of our simple example is that the firm needs to balance carrying costs and order costs. Carrying costs include both the cost of storing the goods and the cost of the capital tied up in inventory. So when storage costs or interest rates are high, inventory levels should be kept low. When the costs of restocking are high, inventories should also be high.

In recent years a number of firms have used a technique known as just-in-time inventory management to make dramatic reductions in inventory levels. Firms that use the just-in-time system receive a nearly continuous flow of deliveries, with no more than 2 or 3 hours` worth of parts inventory on hand at any time. For these firms the extra cost of restocking is completely outweighed by the saving in carrying cost. Just-in-time inventory management requires much greater coordination with suppliers to avoid the costs of stock-outs, however.

Just-in-time inventory management also can reduce costs by allowing suppliers to produce and transport goods on a steadier schedule. However, just-in-time systems rely heavily on predictability of the production process. A firm with shaky labor relations, for example, would adopt a just- in-time system at its peril, for with essentially no inventory on hand, it would be particularly vulnerable to a strike.

ECONOMIC ORDER QUANTITY Order size that minimizes total inventory costs.