Economic Ordering Quantity (EOQ): Inventory control fundamentally deals with the two basic issues: (1) when to order and (2) how much to order. The problem of when to order is decided by prescribing that reorder level of each of the inventory item. The other incidental issue is how to order i.e. what should be the size of each order. The issue of how much to order is decided on the basis of Economic Ordering Quantity (EOQ).

EOQ is an important technique of inventory control. EOQ prescribes the size of the order at which the ordering cost and the inventory carrying cost will be the minimum. The ordering cost consists of the cost of paper work for placing an order like use of paper, typing, posting, filing etc, the cost of the staff involved in this work, the costs incidental to order like follow up, receiving, inspection etc. Ordering cost is more or less fixed and it is ascertained on per order basis. If the annual requirements are met by placing orders of small quantity instead of single large order, the number of orders placed during the year will increase resulting into higher total ordering cost.

The other side of the scene is the inventory carrying costs. When the inventories are stored, it involves following types of costs:

(1) Interest cost due to locking up of funds (2) Cost of storage space (3) Cost of insurance and taxes.

As all these costs are directly related with the certain percentage of value of materials stored; e.g. say carrying cost is 15%, i.e. 15% of the value of materials stored. The ordering cost and the carrying cost is mutually exclusive. If the annual requirements are met by placing a single large order, the ordering cost will be less due to single order. But as the single order will be for a huge quantity (i.e. for the entire annual requirement), the average stockholding would be very high resulting into greater carrying cost. The relationship of ordering cost and carrying cost is as under:

Number and use of order Ordering cost Carrying cost

Few orders, each order of large size Low High

More orders, each order of small size High Low

The technique of economic ordering quantity (EOQ) strikes a balance between the ordering cost and the carrying cost. It devices such a quantity of each order at which the total ordering cost and carrying cost would be minimum. As both these costs are mutually exclusive the total of both costs will be minimum at a point where ordering cost equates carrying cost.

It can be seen from above that ‘B’ indicates the size of order where:

1) The total ordering cost and carrying cost (i.e. AB) is at minimum. Any deviation from point B on left hand side will increase ordering cost and reduce carrying cost resulting into grater cost. If the deviation is made on right hand side from point B, it will result in carrying cost and reduction in ordering cost with high total cost.

2) At point B, the ordering cost and carrying equates each other. Thus, B is the economic order quantity (EOQ) where the total ordering cost and carrying cost tend to be minimum.

EOQ formula: The economic order quantity phenomenon can also be explained mathematically with the help of the formula. The formula is derived as under:

Ordering cost: Ordering Cost (OC) is ascertained as under:

OC = Annual Requirement (R)/Size of order x cost per order (D)

Assume that the size of order is economic ordering quantity (EOQ)

OC = R / EOQ x D —- (1)

It should be noted that {R / EOQ} will give the number of orders placed during the year.

Thus, OC is nothing but numbers of orders i.e. {R / EOQ} multiplied by the cost per order (i.e. D)

Storing cost: The storing cost (or the inventory carrying cost) is ascertained as under:

SC = Value of the units stored x Storing cost represented as certain percentage of the value of materials stored.

The value of the units stored is nothing but the average units stored x cost per unit.

Now it is assumed that the periodic consumption of materials is uniform and so the average units stored will be equal to –

Size of the order / 2

The materials will be consumed on uniform basis and a new order will be placed the moment the earlier lot is consumed and such process will continue for the further ordering. Thus, the above formula of storing cost can be reproduced as under;

SC = Size of the order / 2 x cost per unit x storing cost

Now in this case we have assumed that size of order is nothing but EOQ.

SC = EOQ / 2 x C x S

Where SC = Total storing cost

EOQ = Economic ordering quantity

C= Cost per unit

S= Storing cost as a percentage of value of materials stored.

Now principally we derive following two important characteristics of EOQ

1) EOQ is the ordering level at which the total ordering cost plus total storing cost is at the minimum

2) EOQ is the ordering level at which total ordering cost will equate the total storing cost.

On the basis of the above (1) characteristics, the aforesaid derivation (1) and (2) can be presented as under:

OC = SC

or R / EOQ x D = EOQ /2 x C x S

2RD / CS = EOQ2

EOQ = √ 2RD / CS

Where

R = Annual requirements in units

D= Ordering cost per order

C= Cost per unit

S= Storing cost as percentage of value of materials stored.

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