# Operations Research: Economic Order Quantity (EOQ) in Inventory Model

The concept of economic ordering quantity was first developed by F. Harris in 1916.

The concept is that management is con fronted with a set of opposing costs - as the lot size  (q) increases, the carrying charges (C1) will increase while the ordering costs (C3) will decrease. On the other hand, as the lot size (q) decreases, the carrying cost (C1) will decrease but the ordering costs will increase (assuming that only minor deviations from these trends may occur).

Thus, economic ordering quantity (EOQ) is that size of order which minimizes total annual (or other time period as determined by individual firms) cost of carrying inventory and cost of ordering under the assumed conditions of certainty and that annual demands are known.

There are two ways EOQ can be determined:

1. Trial and Error Method

2. Graphical Method

Determination of EOQ by Trial and Error Method

Step 1. Select a number of possible lot sizes to purchase.
Step 2. Determine total cost for each lot size chosen.
Step 3. Finally, select the ordering quantity which minimizes total cost.

Following illustrative example will make the procedure clear.

For example, suppose annual demand (D) equals 8000 units, ordering cost (C3) per order is ₹ 12.50, the carrying cost of average inventory is 20% per year, and the cost per unit is ₹ 1.00. The following table is computed.

No. of
Orders
Per
Year
Lot
Size
Average
Inventory
Carrying Charges
20%
Per Year
Ordering Costs
₹ 12.50
Per Order
Total
Cost
Per
Year
(₹)
(1)
(2)
(3)
(4)
(5)
(6)=(4)+(5)
1
2
4
->8
12
16
32
8,000
4,000
2,000
1,000
667
500
50
4,000
2,000
1,000
500
333
250
125

₹.800.00
400.00
200.00
100.00
66.00
50.00
25.00

₹.12.50
25.00
50.00
100.00
150.00
200.00
400.00

₹.812.50
425.00
250.00
200.00
216.00
250.00
425.00

This table indicates that an order size of 1000 units will give us the lowest total cost among all the seven alternatives calculated in the table. Also, it is important to note here that this minimum total cost occurs when

Carrying costs = Ordering costs.

Disadvantage of Trial and Error Method.

In above example we were fortunate enough in finding the lowest possible cost. But, suppose the computation for 8 orders per year had not been made. Then, we could choose only among the six remaining alternatives for the lowest cost solution. This imposes a serious limitation of this method. So, a relatively large number of alternatives must be computed before the best possible least cost solution is obtained. In this situation, the graphical method may be advantageous.

In the next post we'll discuss about the graphical method.