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Assumptions of the Economic Order Quantity Model
Users must carefully consider several assumptions when determin-
ing the economic order quantity:
1. The demand must be known and constant. For example, if there are 
360 days per year and the annual demand is known to be 720 units, 
then daily usage must be exactly two units throughout the entire 
year.
2. Delivery time is known and constant. For example, if the delivery 
time is known to ten days, each and every delivery will arrive exactly 
ten days after the order is placed.
3. Replenishment is instantaneous. The entire order is delivered at 
one time, and partial shipments are not allowed.

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Notes
191
4. Price in constant. Quantity or price discounts are not allowed
5. The holding cost is known and constant. The cost or rate to hold 
inventory must be known and constant.
6. Ordering cost is known and constant. The cost of placing an order 
must be known and remains constant for all orders.
7. Stock-outs are not allowed. Inventory must be available at all times.
Deriving the Economic Order Quantity
The economic order quantity can be derived easily from the total 
annual inventory cost formula using simple calculus. The total annual 
inventory cost is the sum of the annual purchase cost, the annual holding 
cost, and the annual order cost. 
The formula can be shown as:
TAIC = APC+AHC+AOC= (R*C)+(Q/2*K*C)+(R/Q*S)
Where
TAIC = total annual inventory cost 
APC = purchase cost
AHC = annual holding cost
AOC = annual ordering cost
R = annual requirement or demand
C = purchase cost per unit
S = cost of placing one order
K = holding cost rate, where annual holding cost per unit k*c
Q = order quantity
Since R, C, K and S are assumed to be constant, Q is the only 
unknown variable in th TAIC equation. The optimum Q (the EOQ) can 
be obtained by taking the first derivative of TAIC with respect to Q and 
then setting it equal to zero. A second derivative of TAIC can also be taken 
with respect to Q to prove that the TA IC is at the minimum.
==> dTAIC/dQ = 0 + (1/2*k*c) + (-1*R*S*1/Q
2 )
= kC/2 - RS/Q
2

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Notes
192
then setting equal to zero,
(kC/2 - RS/Q
2
) = 0
or 
kC/2 = RS/Q
2
or Q
2
= 2RS/kC
then
EOQ = √
2RS/kC
The second derivative of TAIC is; 
(d
2
ATC/dQ
2
) = 0 - (-2 * (RS/Q
3
)) = (2RS/Q
3
) >= 0
Implying the TAIC is at its minimum.
The annual purchase cost drops off after the first derivative is taken. 
The managerial implication here is that purchase cost does not affect the 
order decision if there is no quantity discount (the annual purchase cost 
remains constant as long as the same annual quantity is purchase). Thus, 
the annual purchase cost is ignored in the classic EOQ model.