Which of the following is are the assumptions of economic order quantity EOQ )?

EOQ: Economic Ordering Quantity Model (Assumptions and Determination of EOQ)!

One of the important decisions to be taken by a firm in inventory management is how much to buy at a time, or say, for how much inventory to place order at a time. This is called ‘Economic Ordering Quantity.’

In fact, EOQ gives solutions to other problems like:

(i) How frequently to buy?

(ii) When to buy? and

(iii) What should be the reserve stock?

Assumptions:

Like other economic models, EOQ mode is also based on certain assumptions that:

1. The firm knows with certainty how much items of particular inventories will be used or demanded for within a specific period of time.

2. The use of inventories or sales made by the firm remains constant or unchanged throughout the period.

3. The moment inventories reach to the zero level, the order of the replenishment of inventory is placed without delay.

4. The above assumptions are also called as limitations of EOQ model.

Determination of EOQ:

EOQ model is based in Baumol’s cash management model.

How much to buy at a time, or say, how much will be EOQ is to be decided on the basis of the following two costs:

1. Ordering Costs:

It is the cost concerned with the placing of an order to acquire inventories. Yes, it may vary from time to time depending upon the number of orders placed and the number of items ordered in each order. It is also referred to as the ‘cost of acquiring inventories.’

2. Carrying Costs:

It is cost related to carrying or keeping inventories in a firm, examples of carrying costs are interest on investment, obsolescence losses, insurance premium, rent, store-keeping costs, etc. The volume of inventory and carrying costs are positively associated. Larger the former, more will be latter and vice versa. Carrying cost is also called as ‘cost of holding inventories.’

The above two costs are inversely associated. If holding inventory cost increases, ordering cost decreases and vice versa. A balance is, therefore, struck between the two opposing costs and economic ordering quantity is determined at a level for which the aggregate of the two costs is the minimum.

Let us illustrate the two costs with their components.

Table 26.1 bears components of ordering costs and carrying costs:

Table 26.1: Components of Ordering and Carrying Costs:

Based on above information, EOQ can be determined by following three approaches. These are discussed one by one.

1. The Order Formula Approach:

One way to determine EOQ is to use the Order Formula Approach. There are a number of mathematical formulae to calculate EOQ. Yet, the most frequently used formula in this connection is as given by Van Home (1976: 497-500):

Q = √2u x p/s

Where:

Q = Economic Ordering Quantity (EOQ)

U = Quantity purchased in a year or month.

P = Cost of placing an order.

S = Annual or monthly cost of storage of one unit known as ‘carrying cost’.

Let us illustrate this with an imaginary example.

Let us assume the following data for a firm:

Annual requirements 800 units

Ordering cost (per order) Rs. 50

Carrying cost (per unit) Rs. 2

Purchasing cost (per unit) Rs. 100

Now, using the EOQ formula, EOQ quantity will be as follows:

EOQ = √2 x 800 x 50/2

= √80,000/2

= √40,000

= 200 Units

2. Trial and Error Approach:

As the name of the approach itself indicates, the firm cans trial a number of alternatives to determine its volume of inventory. In case of above example, the firm may purchase its all 800 units in the beginning of the year in one single lot or in 12 monthly lots of 67 units each. But, while following any alternative, implications of both carrying and ordering costs should be studied.

For example, if the firm places only one order of 800 units, the firm may have 800 units as starting inventories in the beginning of the year. In this way, the average inventory held in the firm during the year will be 400 units (800 x 1/2)’ holding Rs. 40,000 (400 x Rs. 100) in inventories.

In case, the firm places 12 monthly orders, the average inventory held during the month will be 34 (67 units/2), holding and average value of Rs. 3,400 (34 Units x Rs. 100). Many other possibilities can be worked out in the same manner to determine the EOQ as shown in Table 26.2.

Table 26.2: Ordering Costs, Carrying Costs and Total Costs of Various Orders:

Thus, we see that the total cost is minimum at Rs. 400 when 200 units are ordered in an order. This well corresponds with the answer found out by the Order Formula Approach also.

3. The Graphic Approach:

The Economic Ordering Quantity can also be found out by drawing a graph. This is illustrated in Figure 26.1. Taking the same example, all three costs, i.e., total costs, carrying costs, and ordering costs are plotted on vertical axis and number of orders on horizontal axis.

We notice, in the Figure 26.1, that carrying cost decreases with number of orders whereas ordering cost increases as the number of orders increases. Here, the behaviour of the total cost is noticeable. Firstly, total cost decreases to a certain point, then it starts increasing when the decrease in average carrying cost is more than off­set by the increase in ordering cost, thus, EOQ takes place at the point where the total cost is minimum.

One last word before we leave Economic Ordering Quantity (EOQ) Model, how much EOQ Model is relevant. The various assumptions, on which the EOQ Model is built, do not hold true. For example, while there is very likelihood of a difference between actual and estimated demands for a particular item of inventory, doubts also remain for instantaneous replenishment of inventories.

Then, when the basic assumptions themselves prove invalid, the EOQ Model is inevitable to give wrong estimates. Nonetheless, this is the commonly used model for inventory management by most of the enterprises/ firms.