Page 200 - DCOM505_WORKING_CAPITAL_MANAGEMENT

Unit 12: Inventory Management

Non-zero Lead Time Notes

The basic EOQ model assumes that orders to replenish the inventory of an item are filled
instantaneously; that is, the lead time is zero. In practice, however, some time usually elapses
between when a purchase order is placed and when the item actually is received in inventory.
This lead time consists of the time it takes to manufacture the item, the time it takes to package
and ship the item, or both.
If the lead time is constant and known with certainty, the optimal order quantity, Q*, is not
affected, although the time when an order should be placed is. Specially, a company should not
wait to reorder unit the end of the inventory cycle, when the inventory level reaches zero such
as at points T , T , and T , in Figure 12.3. Instead, it should place an order n days prior to the end
1 2 3
of each cycle, n being equal to the replenishment lead time measured in days. The reorder point
is defined as the inventory level at which an order should be placed for replenishment of an
item. Assuming that demand is constant over time, the reorder point, Q , is equal to the lead
1
time, n (measured in days), multiplied by daily demand:
Q = n × D/365
r
Where D/365 is daily demand (based on 365 days per year)

Figure 12.3: Non-zero Replenishment Lead Case of an Inventory Cycle
Order Q uantity Q

Reorder Point
Q 1

T1 n T1 T2 n T2 T3 n T3 Time

Quantity Discounts

Large orders often permit a company to realize substantial per-unit savings (that is, economies
of scale) in manufacturing, order processing, and transport. Many companies encourage their
customers to place large orders by passing on to them a portion of these savings in the form of
quantity discounts. With a quantity discount, the cost per unit to the customer is variable and
depends on the quantity discount on the optimal order quantity.
First, the EOQ is determined, using equation next, the annual net returns when the order quantity
is increased from the EOQ level up to the size necessary to receive the discount are calculated.
The annual net returns are equal to the discount savings on the annual demand less any increase
in annual inventory costs, as defined in equation, if the annual net returns are positive, the
optimal order quantity is the order size necessary to receive the discount: if they are not, the
optimal order quantity is the smaller EOQ value.

Probabilistic Inventory Control Models

So far the analysis has assumed that demand or usage is uniform throughout time and known
with certainty, as well as the lead time necessary to procure additional inventory is also fixed,
known value. However, in most practical inventory management problems either (or both) of

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