Economic Order Quantities | EOQ by Trial and Error Method | EOQ

 

 

Economic Order Quantities (EOQ)

EOQ is also known as re-order 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.

 

 

(A) Annual Requirement

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 half-yearly, monthly or weekly. 

 

(B) Ordering Cost

Ordering cost is a re-purchase 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, e-mail etc related to purchasing.

Cost of paperwork as tender, quotation, advertisement etc.

 

(C) Carrying Cost

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 go-down 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, e-mail 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 re-ordering 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:

 

 

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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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