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.

Why inventory is maintained?

Variables in Inventory Problems

What is the Average Inventory?

Economic Order Quantity - Trial and Error Method