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The Concept Behind EOQ ( Economic Order Quantity) ?

Vikas Kumar Gupta (Student IPCC) (408 Points)

02 December 2008

I want to know that, How the formula EOQ = Under root 2AS Divided by C is created and whats the concept is used ?

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(Guest)

Underlying assumptions

The ordering cost is constant.
The rate of demand is constant

Variables

$Q$ = order quantity
$Q *$ = optimal order quantity
$D$ = annual demand quantity of the product
$P$ = purchase cost per unit
$C$ = fixed cost per order (not per unit, in addition to unit cost)
$H$ = annual holding cost per unit (also known as carrying cost) (warehouse space, refrigeration, insurance, etc. usually not related to the unit cost)

The Total Cost function

The single-item EOQ formula finds the minimum point of the following cost function:

Total Cost = purchase cost + ordering cost + holding cost

- Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P×D

- Ordering cost: This is the cost of placing orders: each order has a fixed cost C, and we need to order D/Q times per year. This is C × D/Q

- Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is H × Q/2

$TC = PD + {\frac{CD}{Q}} + {\frac{HQ}{2}}$ .

In order to determine the minimum point of the total cost curve, set its derivative equal to zero:

${\frac{dTC(Q)}{dQ}} = {\frac{d}{dQ}}\left(PD + {\frac{CD}{Q}} + {\frac{HQ}{2}}\right)=0$ .

The result of this derivation is:

$-{\frac{CD}{Q^2}} + {\frac{H}{2}}=0$ .

Solving for Q gives Q* (the optimal order quantity):

${\frac{H}{2}}={\frac{CD}{Q^2}}$

$Q^2={\frac{2CD}{H}}$

Therefore: $Q^* = \sqrt{\frac{2CD}{H}}$ .

Note that interestingly, Q* is independent of P, it is a function of only C, D, H

(Guest)

Let x be eoq. Thus if the level is x, then at x, then Carrying cost = ordering cost.

No of order = (A/x)

Ordering cost = (A/x)*S------(1)

Carrying cost - (X/2)*c --------(2)

Since 1 = 2 you get

(A/x)*s = (x/2)*c

Solvng for x you get

X = (2AS/c)^1/2

and hence the above equation..

(Guest)

The objective of EOQ is to reduce the associated cost of material. They are ordering cost and carrying cost. As the quantity ordered were higher, then frequency of order will come down so too ordering cost. But this will increase the carrying cost as the period of carrying will be more on account of higher qty. If the quantity ordered were to be lesser, frequency of buying will be more so too ordering cost but carrying cost will eventually be lesser. If u plot these two costs(ordering and carrying) then there will be least of the total cost will occur at a point. THis point will be referred to as Economic order quantity. It will also be a point of intersection of ordering and carrying cost. In mathematical terms OC=CC.

OC = [Annual demand/QTY] xO, CC=[QTY/2] x CC per unit. If u equate these two OC and CC then u automatically get what is QTY

[A/Q] x O=[Q/2] x C==> Q^2 = 2AO/C==> Q = Sqrt[2AO/c]

Please confirm my dear....

I hope i ve made it simpler

Vikas Kumar Gupta (Student IPCC) (408 Points)
Replied 03 December 2008

Thank You For Sharing Your knowledge. But from where you have gotted I mean it is not mention in ICAI PCC study material.

Thank You Once again!!!

Sumit Shaw (2 Points)
Replied 02 January 2017

You can view my video on YouTube by clicking below given link:- https://www.youtube.com/watch?v=KrHxTvdUzC4

This is own analysis to be used by mine and your common sense usage and intention of knowing logic behind everything and it is nowhere mentioned in anybook.