Control de inventarios

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9
9.1

Inventory Control

ECONOMIC ORDER QUANTITY (EOQ)

The economic order quantity (EOQ) is the optimal quantity to order to replenish inventory, based on a trade-off between inventory and ordering costs. The tradeoff analysis assumes the following: • • • • Let D A c r H Q = = = = = = demand (number of items per unit time) ordering cost ($ per order) cost of an item ($ per item)inventory carrying charge (fraction per unit time) cr = holding cost of an item ($ per item per unit time) order quantity (number of items per order) Demand for items from inventory is continuous and at a constant rate. Orders are placed to replenish inventory at regular intervals. Ordering cost is fixed (independent of quantity ordered). Replenishment is instantaneous.

Figure 9.1 plots cumulativecurves of orders and demand over time. The curve for orders increases in steps of size Q each time an order is placed, and the demand curve increases linearly with slope D. The height between these two curves at any point in time is the inventory level. Figure 9.2 plots this inventory level, which displays the classic sawtooth pattern over time. Inventory increases by Q each time an order is placed,and decreases at rate D between orders. The average inventory level in Figure 9.2 is Q/2, which determines the inventory cost in the EOQ model.

©2001 CRC Press LLC

FIGURE 9.1 Cumulative orders and demand over time in EOQ model.

FIGURE 9.2 Inventory level over time in EOQ model.

Total cost per unit time C(Q) is given by
C(Q) = Inventory Cost + Ordering Cost = HQ AD + 2 Q

(9.1)

Theoptimal quantity Q* to order (i.e., the order quantity that minimizes total cost) is given by
d C (Q ) = 0 dQ

Hence

©2001 CRC Press LLC

Q*

2 AD H

(9.2)

Equation 9.2 for Q* is known as the EOQ formula. Figure 9.3 illustrates the tradeoff between the inventory and ordering costs. (Arrow, Karlin and Scarf, 1958; Cohen, 1985; Harris, 1913; Hax and Candea, 1984; Hopp and Spearman,1996; Nahmias, 1989; Stevenson, 1986; Tersine, 1985; Wilson, 1934; Woolsey and Swanson, 1975).

FIGURE 9.3 Trade-off between inventory and ordering costs in EOQ model.

9.2

ECONOMIC PRODUCTION QUANTITY (EPQ)

The economic production quantity (EPQ) is the optimal quantity to produce to replenish inventory, based on a trade-off between inventory and production set-up costs. The trade-offanalysis assumes the following: • Demand for items from inventory is continuous and at a constant rate. • Production runs to replenish inventory are made at regular intervals. • During a production run, the production of items is continuous and at a constant rate. • Production set-up cost is fixed (independent of quantity produced). The EPQ model is similar to that for the EOQ model. The differenceis in the time to replenish inventory. The EOQ model assumes replenishment is instantaneous, while the EPQ model assumes replenishment is gradual, due to a finite production rate.

©2001 CRC Press LLC

Let D P A c r H Q = demand (number of items per unit time) = production rate during a production run (number of items per unit time) = production set-up cost ($ per set-up) = cost of an item ($per item) = inventory carrying charge (fraction per unit time) = cr = holding cost of an item ($ per item per unit time) = production quantity (number of items per production run)

The EPQ model assumes P > D. Figure 9.4 plots cumulative curves of production and demand over time. The slope of the production curve during a production run is P. The slope of the demand curve is D. The height betweenthese two curves at any point in time is the inventory level. Figure 9.5 plots this inventory level over time. Inventory increases at rate P – D during a production run, and decreases at rate D between production runs. The average inventory level in Figure 9.5 is

(1 − D / P)Q
2

which determines the inventory cost in the EPQ model.

FIGURE 9.4 Cumulative production and demand over time...
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