EOQ is also known as reorder quantity (ROQ) or optional order quantity.
It is the order size which minimizes the total inventory cost.
In EOQ, total carrying cost and ordering cost are equal.
The annual requirement can be procured (acquire or purchase) at once and stored in the warehouse (godown) and consumed for the year.
Materials can be ordered frequently in a fewer lots.
When a company orders requirements in one order, the ordering cost is less but the carrying cost is more.
When a company orders requirements frequently, ordering cost is more but carrying cost is less.
Therefore, EOQ is the order size which reduces the total inventory cost and equally total ordering cost.
While determining EOQ, annual requirement, ordering cost and carrying cost should be considered.
Keep In Mind (KIM)
If purchasing quantity increases, carrying/holding cost also increases but ordering cost decreases. 
If purchasing quantity decreases, carrying cost also decreases but ordering cost increases. 
Carrying cost is calculated always on purchase price, not on sales price. 
When manufacturing needs raw materials for production purpose, an annual requirement is needed.
Raw materials are converted into work in progress and finished goods.
The quantity of material is measured in annual requirements.
Annual requirement may be in halfyearly, monthly or weekly.
Ordering cost is a repurchase cost and is repeated in nature.
The purchase of a large quantity of materials helps to reduce ordering costs; it includes:
Salary of staff related to purchasing, inspection and tour etc.
Transportation expenses, transit insurance etc.
Cost of stationery, postage, telephone, fax, email etc related to purchasing.
Cost of paperwork as tender, quotation, advertisement etc.
It is also known as keeping cost and holding cost.
The carrying cost suggests purchasing a small quantity of materials.
If a small quantity is purchased, the storage cost will be low.
It is the expenses related to after material purchased. It includes:
Salary of storekeeper and related to holding of materials.
Rent of godown or warehouse.
Insurance cost of materials.
Interest on capital which is blocked on materials purchased.
Losses due to breakage, spoilage (date expired), obsolescence (old fashioned), vermin damage.
Desire rate of return from investment in inventory.
Cost of stationery, postage, telephone, fax, email etc related to holding of materials etc.
Keep in Mind (KIM)
Some important synonyms or abbreviations of EOQ 

A 
= annual requirement or need. 
O 
= ordering cost per order, administrative cost per order, procurement cost per order. 
C 
= carrying cost per order, holding cost per order, production cost per order. 
P 
= purchase price per unit, cost per unit, material cost per unit. 
Q 
= quantity or order size. 
The assumption to determine the economic order quantity
The fixed quantity is ordered at each reordering point.
Time lag in the placement of an order and its delivery, annual demand, carrying cost and ordering are certain.
The purchase price of an item is unaffected by the quantity ordered.
No stock outs occur (viz no theft, no lost, no date expiry) etc.
EOQ can be determined in three ways:
Mathematical or formula method
Trial and error method
Graphic method
Keep in Mind (KIM)
The value of carrying cost (C) is less than the value of ordering cost (O). 
Annual demand may be weekly, monthly and yearly. 
Value of O and C also should be weekly, monthly and yearly. 
If order size (Q) is not given, EOQ units are taken for EOQ cost. 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2A
ABC Trading Concern has following information:
Annual require 
6,000 units 
Materials cost per unit 
Rs 60 
Ordering cost per order 
Rs 500 
Carrying cost per unit per year 
Rs 15 
Required: (a) Economic order quantity; (b) No. of order; (c) Total cost without materials
[Answer: (a) 632 units; (b) 9 times; (c) Rs 9,487]
Solution:
Economic order quantity (EOQ)
= SQRT (2AO ÷ C) [∵ SQRT = square root]
= SQRT (2 x 6,000 x 500 ÷ 15)
= SQRT (400,000)
= 632 units
Explain: EOQ in units is the order of the units where an organization does not suffer about minimum stock or maximum stock level.
Economic order quantity in order
= A ÷ EOQ
= 6,000 ÷ 632
= 9.49 or 9 times
Explain: EOQ in order is the order time during the period. It shows the number order for annual consumption.
Economic order quantity (total cost)
= SQRT (2AOC) [∵ SQRT = square root]
= SQRT (2 x 6,000 x 500 x 15)
= SQRT (9,00,00,000)
= Rs 9,487
Explain: EOQ in total cost is the sum of ordering and holding cost of materials without unit cost. It does not contain the value of materials.
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2B
ABC Group of Company has following information:
Annual require 
8,000 units 
Materials cost per unit 
Rs 96 
Ordering cost per order 
Rs 40 
Holding cost per unit per year 
4% per annum per unit 
Interest on capital on materials purchase 
10% per annum per unit 
Required: (a) Economic order quantity; (b) No. of order;
(c) Total cost with materials if the order size is 4,000 units;
(d) Total cost with materials if suppliers allowed 2% discount at 8,000 units in one order;
(e) Should the company accept the option?
[Answer: (a) 218 units; (b) 37 times; (c) Rs 794,960; (d) Rs 806,440; (e) No]
Solution:
Given and working note:
A = 8,000 
C = (4% +10%) of P 
O = 40 
= 96@14% 
P = 96 
= Rs 13.44 
Economic order quantity (EOQ)
= SQRT (2AO ÷ C) [∵ SQRT = square root]
= SQRT (2 x 8,000 x 40 ÷ 13.44
= SQRT (47,619)
= 218 units
Economic order quantity in order
= A ÷ EOQ
= 8,000 ÷ 218
= 36.69 or 37 times
Total cost with materials cost if order size is 4,000 units
Value of materials = 8,000 units x Rs 96 = Rs 768,000
= (AP) + (AO ÷ Q) + (QC ÷ 2)
= (8,000 x Rs 96) + (8,000 x 40 ÷ 4,000) + (4,000 x Rs 13.44 ÷ 2)
= 768,000 + 80 + 26,880
= Rs 794,960
Total cost with materials if suppliers allowed 2% discount at 8,000 units in one order
Value of materials = 8,000 units x Rs 96 = Rs 768,000
Discount = 768,000 @ 2% = Rs 15,360
Including cost of materials
= (AxP – Discount) + (AO ÷ Q) + (QC ÷ 2)
= (8,000 x Rs 96 – 15,360 ) + (8,000 x 40 ÷ 8,000) + (8,000 x Rs 13.44 ÷ Rs 2)
= 752,640 + 40 + 53,760
= Rs 806,440
Decision: the company should not accept the option offered by suppliers; because, it has a higher value.
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2C
The extracted data are taken from Anuj Metal Industries:
Monthly materials required 
6,000 kg 
Materials cost per kg 
Rs 60 
Ordering cost per order 
Rs 160 
Economic order quantity 
800 units 
Required: (1) Holding cost per month; (2) Total cost with materials if order size is 2,000 units
[Answer: (1) Rs 3; (2) = Rs 363,480
Solution:
Given and working note:
Monthly require (A) 
= 6,000 kg 

Materials cost per kg (P) 
= Rs 60 

Ordering cost per order (O) 
= Rs 160 

EOQ 
= 800 units 

Total cost with materials if order size is 2,000 units
= (AP) + (AO ÷ Q) + (QC ÷ 2)
= (6,000 x Rs 60) + (6,000 x 160 ÷ 2,000) + (2,000 x Rs 3 ÷ Rs 2)
= 360,000 + 480 + 3,000
= Rs 363,480
#####
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#####
EOQ by Trial and Error Method
This method is also known tabular method and analytical method.
Under this method, first of all, order size is fixed.
Then an average order size is found out.
Then carrying cost and ordering cost is calculated.
The lowest cost (net cost) is EOQ by trial and error method.
Step 1, 
Estimate number of orders 


Step 2, 
to find out the number of sizes, 
Order size 
= Annual requirement ÷ No. of order 
Step 3, 
to find out the average quantity, 
Average quantity 
= Order size ÷ 2 
Step 4, 
to find out carrying cost, 
Carrying cost 
= Average quantity x Carrying cost per unit 
Step 5, 
to find out ordering cost, 
Ordering cost 
= No. of order x Ordering cost per order 
Step 6, 
to find out the total cost, 
Total cost 
= Carrying cost + Ordering cost 
EOQ by Trial and Error Method
No. of order 
a g 
Hint 
1 
2 
3 
4 
5 
Order size 
b 
A ÷ a 





Average quantity 
c 
b ÷ 2 





Carrying cost 
d 
c x Rs 





Ordering cost 
e 
a x Rs 





Total cost 
f 
d + e 





Less: Discount 
g 
working note 





Net cost 
h 
f – g 





Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2D
The following extracted information is given to you ABC Company:
Annual require 
5,000 units 
Set up cost (O) 
Rs 1,500 
Carrying cost 
Rs 2.40 
Required: EOQ by formula and trial and error method
[Answer: EOQ = 2,500 units, EOQ by T&E = 2 order; 2,500 units]
Solution:
Economic order quantity (EOQ)
= SQRT (2AO ÷ C) [∵ SQRT = square root]
= SQRT (2 x 5,000 x 1,500 ÷ 2.40)
= SQRT (62,50,000)
= 2,500 units
EOQ by Trial and Error Method
No. of order 
a g 
Hints 
1 
2 
4 
5 
8 
Order size 
b 
A ÷ a 
5,000 
2,500 
1,250 
1,000 
625.0 
Average quantity 
c 
b ÷ 2 
2,500 
1,250 
625 
500 
312.5 
Carrying cost 
d 
c x Rs 2.40 
6,000 
3,000 
1,500 
1,200 
750.0 
Ordering cost 
e 
a x Rs 1,500 
1,500 
3,000 
6,000 
,500 
12,000.0 
Total cost 
f 
d + e 
7,500 
6,000 
7,500 
8,700 
12,750.0 
Less: Discount 
g 
working note 
Nil 
Nil 
Nil 
Nil 
Nil 
Net cost 
h 
f – g 
7,500 
6,000 
7,500 
8,700 
12,750.0 
The minimum cost of Rs 6,000 is in the 2^{nd} number of orders.
Therefore, EOQ is 2,500 units.
Keep in Mind (KIM)
Generally, EOQ by trial and error method is equal where carrying cost and ordering costs are equal 
But it not always correct. We should take always the lowest net cost as EOQ. 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2E
ABC Company needs a monthly requirement of an inventory is 1,200 units. The ordering cost per order is Rs 30 and the carrying cost is Re 0.80 per unit. The company’s supplier agrees to offer quantity discount as under:
Lot size 
Discount rate 
1 to 399 
Nil 
400 to 599 
2% 
600 to 799 
3% 
Above 800 
5 % 
Required: (a) Economic order quantity without considering the offer of discount.
(b) Economic order quantity by considering the discount rate.
[Answer: (a) 300 units; (b) 400 units at 3 times]
Solution:
Annual required (A) = 1,200 units
Ordering cost (O) = Rs 30
Carrying cost (C) = Re 0.80
EOQ (in units)
= SQRT (2AO ÷ C) [∵ SQRT = square root]
= SQRT (2 x 1,200 x 30 ÷ 0.80
= SQRT (90,000)
= 300 units
EOQ by Trial and Error Method
No. of order 
a 
Hints 
1 
2 
3 
4 
Order size 
b 
A ÷ a 
1,200 
600 
400 
300 
Average quantity 
c 
b ÷ 2 
600 
300 
200 
150 
Carrying cost 
d 
c x Re 0.80 
480 
240 
160 
120 
Ordering cost 
e 
a x Rs 30 
30 
60 
90 
120 
Total cost 
f 
d + e 
510 
300 
250 
240 
Less: Discount 
g 
working note 
60 
36 
24 
– 
Net cost 
h 
f – g 
450 
264 
226 
240 
The minimum net cash is Rs 226 at 400 units.
Therefore, the discount offer can be accepted.
Working note for discount: There does not cost per unit. So we can calculate without a price per unit
Discount 
= 1,200 units xgiven% 


For order No. 1 
= 1,200 units x 5% 
= Rs 60 

For order No. 2 
= 1,200 units x 3% 
= Rs 36 

For order No. 3 
= 1,200 units x 2% 
= Rs 24 

Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2F
The following extracted information is given by BK Company:
Annual requirement 26,000 units
Cost per order Rs 30
Carrying cost 20%
Price per unit Rs 7.80
Complete the table below and determine the economic order quantity:
No of order 






Order Size 
250 
500 
1,000 
2,000 
13,000 
26,000 
Average inventory 






Carrying cost 






Ordering cost 






Total cost 






[Answer: EOQ is 1,000]
SOLUTION
Carrying cost = Rs 7.80@ 20% = Rs 1.44
EOQ by Trial and Error or Tabular Method
No of order 

104 
52 
26 
13 
2 
1 
Order Size 
A ÷ Order size 
250 
500 
1,000 
2,000 
13,000 
26,000 
Average inventory 
Order size ÷ 2 
125 
250 
500 
1,000 
6,500 
13,000 
Carrying cost 
Average Qty x Rs 1.44 
195 
390 
780 
1,560 
10,140 
20,280 
Ordering cost 
No. of order x Rs 30 
3,120 
1,560 
780 
390 
60 
30 
Total cost 

3,315 
1,950 
1,560 
1,950 
10,200 
20,310 
The minimum cost is Rs 1,560 at the order size of 1000 units.
Therefore, EOQ is 1,000 units
EOQ by Graphic Method
In this method, total ordering cost, total carrying cost and total cost are presented in a graph.
When numbers of orders are increased, it will increase ordering cost and similarly when quantities of orders are increased it will increase carrying cost and vice versa.
Where ordering cost and carrying cost intercept each other, it will be economic order quantity.
Because this point represents to the minimum total cost.
The economic order quantity can be shown in a diagram as follows:
#####
PROBLEMS AND ANSWERS OF EOQ 
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2A
Form the following information, calculate economic order quantity:
Annual requirement 
12,000 units 
Cost of material per unit 
Rs 50 
Cost of placing and receiving per order 
Rs 300 
Annual inventory carrying cost per unit 
20% of inventory value 
Required: (a) Economic order quantity in units; (b) Economic order quantity in order
(c) Economic order quantity in cost
[Answer: (a) 849 units; (b) 14 times; (c) Rs 8,485;
Hint: answers are approximately]
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2B
The following extracted information is given to you XY Company:
Consumption during the year 
2,000 Kg 
Economic order quantity 
200 Kg 
Carrying cost 
5 % of inventory value 
Price per unit 
Rs 20 
Required: (1) Ordering cost per order; (2) Total cost of materials if order size 500 units
[Answer: (1) Rs 10; (2) Rs 40,290]
Here, Amount = Rs = $ = £ = € = ₹ = Af = ৳ = Nu = Rf = රු = Br = P = Birr = Currency of your country
PROBLEM: 2C
Durga Metal Industries has following data:
Annual require of raw materials 
5000 kg 
Materials cost per kg 
Rs 70 
Transport cost for materials receive 
Rs 700 per order 
Annual holding cost of materials 
10% of value 
Required: EOQ by trial and error method upto 5 order
[Answer: 1,000 units; Rs. 7,000]
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