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Friday, May 29, 2009


While the total ordering costs can be decreased by increasing the size of order, the carrying costs increase with the increase in order size indicating the need for a proper balancing of these two types of costs behaving in opposite directions with changes in order size.

Again, if a company wants to avert stock-out costs it may have to maintain larger inventories of materials and finished goods, which will result in higher carrying costs. Here also proper balancing of the costs becomes important.

Thus, the importance of effective inventory management is directly related to the size of the investment in inventory. To manage its inventories effectively, a firm should use a systems approach to inventory management. A systems approach considers in a single model all the factors that affect the inventory.


The economic order quantity (EOQ) refers to the optimal order size that will result in the lowest total of order and carrying costs for an item of inventory given its expected usage, carrying costs and ordering cost. By calculating an economic order quantity, the firm attempts to determine the order size that will minimize the total inventory costs.

Total inventory cost = Ordering cost + Carrying cost
Total ordering costs = Number of orders x Cost per order
= $ U / Q X F

U = Annual usage
Q = Quantity ordered
F = Fixed cost per order
The total carrying costs = Average level of inventory x Price per unit x Carrying cost (percentage)

Total carrying costs
= $ Q / 2 x P x C
= $ QPC over 2

Q = Quantity ordered
P = Purchase price per unit
C = Carrying cost as %

As the lead-time (i.e., time required for procurement of material) is assumed to be zero an order for replenishment is made when the inventory level reduces to zero.
The level of inventory will be equal to the order quantity (Q units) to start with. It progressively declines (though in a discrete manner) to level O by the end of period 1. At that point an order for replenishment will be made for Q units. In view of zero lead-time, the inventory level jumps to Q and a similar procedure occurs in the subsequent periods. As a result of this the average level of inventory will remain at (Q/2) units, the simple average of the two end points Q and Zero.

From the above discussion the average level of inventory is known to be (Q/2) units.
From the previous discussion, we know that as order quantity (Q) increases the total ordering costs will decrease while the total carrying costs will increase. The economic order quantity, denoted by Q*, is that value at which the total cost of both ordering and carrying will be minimized. It should be noted that total costs associated with inventory
T= $ UF / Q + $QPC / 2

Where the first expression of the equation represents the total ordering costs and the second expression the total carrying costs.

The total cost curve reaches its minimum at the point of intersection between the ordering costs curve and the carrying costs line. The value of Q corresponding to it will be the economic order quantity Q*. We can calculate the EOQ formula.

Behavior of costs associated with inventory for changes in order quantity. For order quantity Q to become EOQ the total ordering costs at Q should be equal to the total carrying costs.

Using the notation, it amounts to stating:
UF/Q + QPC / 2 (i.e.) 2UF = Q²PC or Q² = 2UF / PC units
To disguish EOQ from other order quantities, we can say:
2 UF*

In the above formula, when `U' is considered as the annual usage of material, the value of Q* indicates the size of the order to be placed for the material, which minimizes the total inventory-related costs. When `U' is considered as the annual demand Q* denotes the size of production run.

Suppose a firm expects a total demand for its product over the planning period to be 10,000 units, while the ordering cost per order is $100 and the carrying cost per unit is $2. Substituting these values, EOQ = 2 x10, 000 x100 = 1000 units. 2

Thus, if the firm orders in 1000-unit lot size, it will minimize its total inventory costs.

Inflation affects the EOQ: model in two major ways. First, while the EOQ model can be modified to assume constant price increases, many times major price increases occur only once or twice a year and are announced ahead of time.
Read more about Inflation point information


In the EOQ model discussed we have made the assumption that the lead-time for procuring material is zero. Consequently, the reorder point for replenishment of stock occurs when the level of inventory drops down to zero. In view of instantaneous replenishment of stock the level of inventory jumps to the original level from zero level. In real life situations one never encounters a zero lead-time. There is always a time lag from the date of placing an order for material and the date on which materials are received. As a result the reorder level is always at a level higher than zero, and if the firm places the order when the inventory reaches the reorder point, the new goods will arrive before the firm runs out of goods to sell. The decision on how much stock to hold is generally referred to as the order point problem, that is, how low should the inventory be depleted before it is reordered.

The two factors that determine the appropriate order point are the procurement or delivery time stock which is the Inventory needed during the lead time (i.e., the difference between the order date and the receipt of the inventory ordered) and the safety stock which is the minimum level of inventory that is held as a protection against shortages.

Therefore Reorder Point = Normal consumption during lead-time + Safety Stock.

Several factors determine how much delivery time stock and safety stock should be held. In summary, the efficiency of a replenishment system affects how much delivery time is needed. Since the delivery time stock is the expected inventory usage between ordering and receiving inventory, efficient replenishment of inventory would reduce the need for delivery time stock. And the determination of level of safety stock involves a basic trade-off between the risk of stock-out, resulting in possible customer dissatisfaction and lost sales, and the increased costs associated with carrying additional inventory.

Another method of calculating reorder level involves the calculation of usage rate per day, lead time which is the amount of time between placing an order and receiving the goods and the safety stock level expressed in terms of several days' sales.

Reorder level = Average daily usage rate x lead-time in days.

From the above formula it can be easily deduced that an order for replenishment of materials be made when the level of inventory is just adequate to meet the needs of production during lead-time.

If the average daily usage rate of a material is 50 units and the lead-time is seven days, then Reorder level =Average daily usage rate x Lead time in days = 50 units x 7 days = 350 units

When the inventory level reaches 350 units an order should be placed for material. By the time the inventory level reaches zero towards the end of the seventh day from placing the order materials will reach and there is no cause for concern.

Learn about safety stock - Once again in real life situations one rarely comes across lead times and usage rates that are known with certainty. When usage rate and/or lead time vary, then the reorder level should naturally be at a level high enough to cater to the production needs during the procurement period and also to provide some measure of safety for at least partially neutralizing the degree of uncertainty.

The Reorder Point Formula - Even in a relatively simple situation considered in the example above, the amount of calculations involved for arriving at the reorder level is large. In real life situations the assumption of independence in the probability distributions made in the example above may not be valid and the number of time periods may also be large. In such cases the approach adopted earlier can become much more complex.


This stock level subsystem keeps track of the goods held by the firm, the issuance of goods, and the arrival of orders. It maintains records of the current level of inventory. For any period of time, the current level is calculated by taking the beginning inventory, adding the inventory received, and subtracting the cost of goods sold. Whenever this subsystem reports that an item is at or below the reorder-point level, the firm will begin to place an order for the item.

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