## The Economic Order Quantity Model

The economic order quantity (EOQ) model is the best-known approach for explicitly establishing an optimal inventory level. The basic idea is illustrated in Figure 21.4, which plots the various costs associated with holding inventory (on the vertical axis) against inventory levels (on the horizontal axis). As shown, inventory carrying costs rise and restocking costs decrease as inventory levels increase. From our general discussion in Chapter 19 and our discussion of the total credit cost curve in this chapter, the general shape of the total inventory cost curve is familiar. With the EOQ model, we will attempt to specifically locate the minimum total cost point, Q*.

In our discussion that follows, an important point to keep in mind is that the actual cost of the inventory itself is not included. The reason is that the total amount of inventory the firm needs in a given year is dictated by sales. What we are analyzing here is how much the firm should have on hand at any particular time. More precisely, we are trying to determine what order size the firm should use when it restocks its inventory.

Inventory Depletion To develop the EOQ, we will assume that the firm's inventory is sold off at a steady rate until it hits zero. At that point, the firm restocks its inventory back to some optimal level. For example, suppose the Eyssell Corporation starts out today with 3,600 units of a particular item in inventory. Annual sales of this item are 46,800 units, which is about 900 per week. If Eyssell sells off 900 units of inventory each week, then, after four weeks, all the available inventory will be sold, and Eyssell will restock by ordering (or manufacturing) another 3,600 and start over. This selling and restocking

Ross et al.: Fundamentals VII. Short-Term Financial 21. Credit and Inventory of Corporate Finance, Sixth Planning and Management Management

Cost of holding inventory (\$) of inventory order

Restocking costs are greatest when the firm holds a small quantity of inventory. Carrying costs are greatest when there is a large quantity of inventory on hand. Total costs are the sum of the carrying and restocking costs.

of inventory order

Restocking costs are greatest when the firm holds a small quantity of inventory. Carrying costs are greatest when there is a large quantity of inventory on hand. Total costs are the sum of the carrying and restocking costs.

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