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Home /  Cost and Management Accounting
  • 2512 Views
  • Estimated reading time : 157 Minutes
  • Economic Order Quantities | EOQ by Trial and Error Method | EOQ

  • Arjun EP
  • Published on: September 8, 2021

  •  

     

    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 2nd 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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