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The Economic order Quantity Model attempts to determine the orders size that will minimize the total inventory cost.

It is assumed that

        Total inventory cost = Total carrying cost + Total ordering cost

The EOQ model as a technique of inventory management defines three parameters of any inventory item.

1)    Minimum level of inventory of that item depending upon the usage rate of that item , time lag in procuring that item & unforeseen circumstances, if any.
2)    The re-order level of that item , at which next order for that item must be placed to avoid any chance of a stock-out, and
3)    The re-order quantity for each order must be placed.

The EOQ model attempts to determine quantity to be ordered at a time so as to optimize the cost of carrying & holding inventory and also ensuring availability of that item whenever needed. The most economic size of the order is determined by considering the cost of carrying the inventory, its purchasing ,its ordering costs and usage rate.
The EOQ model based on the following assumptions.

a)    The total usage of a particular item for a given period (usually a year) is known with certainty and that the usage rate is even through out the period.
b)    That there is no time gap between placing a order & getting its supply.
c)    The cost per order of an item is constant and the cost of carrying the inventory is also fixed & is given as a percentage of average value of inventory.
d)    That there is only two costs associated with the inventory , and these are the cost of ordering & the cost of carrying the inventory.

Given the above assumption, the EOQ model may be presented as follows:

                   EOQ = √ (2AO/C)

  Where         EOQ = Economic quantity per order
                           A = Total annual requirement for the item
                           O = Ordering cost per order of that item
                           C = Carrying cost per unit per annum

The EOQ model can also be presented graphically as in figure.

                                Fig.: Graphical presentation of the EOQ model.
The figure shows that the total ordering cost of any particular item is decreased as the size per order is increasing. This will happen because with the increase in size of the order , the total no. of order for a particular item will decrease resulting in decrease in the total order cost. The total annual carrying cost is increasing with increase in order size. This will happen because the firm would be keeping more & more items in the stores. However , the total cost of inventory initially reduces with the increase in size of the order  but then increase with the increase in size of order. The trade off of these two costs is attained at the level at which the total annual cost is the least. At this particular level, the order size is designated as the economic order quantity. If the firm places the orders for that item of this economic order quantity, then the total annual cost of inventory of that item will be minimized.           

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