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

In the previous post, you understand the Trial and Error Method to determine EOQ (Economic Order Quantity) in an inventory model.

Let us try to understand the graphical approach to computing EOQ.

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

The data calculated in the above table can be graphed below to demonstrate the nature of the opposing costs involved in an EOQ model.

This graph shows that annual total costs of inventory, carrying costs and ordering costs first decrease, then hit the lowest point where inventory carrying costs equal ordering costs, and finally increases as the ordering quantity increases. Our main objective is to find a numerical value for EOQ that will minimize the total variable costs on the graph.

The disadvantage of the graphical Method.

Without specific costs and values an accurate plotting of the carrying costs, ordering costs, and total costs are not feasible.

To solve the EOQ models the following two are more accurate methods:

1. Algebraic Method

2. Differentiation Method

1. Algebraic method. This method is based on the fact that the most economical point in terms of total inventory cost is where the inventory carrying cost equals the ordering cost.

2. Differentiation method. This method is based on the technique of finding the minimum total cost by utilizing differentiation. This is the best method since it does not suffer from the limitations of previous methods.

We shall discuss these in detail in the next post.