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Chapter 2: Materials Topic 1: E.O.Q (Economic Order Quantity) Practice Questions Question 1. From the following information, calculate (a) Economic order quantity, (b) for EOQ, the number of orders per year, (c) for EOQ how frequently should orders be placed, (d) for EOQ, Total Ordering Cost, (e) for EOQ, Total Carrying Cost and (f) Total Annual Carrying and Ordering Cost at that quantity. Annual Consumption of input Annual Carrying Cost
48,000 units Purchase Price of input unit 12% Ordering Cost per order
โน 25 โน 180
Solution: (a) EOQ = โ
2๐ด๐ ๐ถ
=
โ
2ร48000รโน180 โน3
= 2400 Units
Where, A = Annual Demand O = Ordering cost per order C = Inventory carrying cost per unit per annum
(b) No. of orders per year = (c) Frequency of Orders = (d) Total Ordering Cost = = (e) Total Carrying Cost =
Total Annual Consumption Order Size 365 Days
No.of Order
=
365 Days 20 Orders
Annual Consumption Order Size 48,000 2,400
48,000 Units 2,400 Units
= 20 Orders
= 18.25 days
ร Ordering Cost per order
ร โน180 = โน3,600
Order Size 2
=
ร Carrying Cost per unit p.a. = 2400/2 ร โน3 = โน3,600
(f) Total Annual Carrying & Ordering Cost =[(
๐ด๐๐๐ข๐๐ ๐ถ๐๐๐ ๐ข๐๐๐ก๐๐๐ ๐๐๐๐๐ ๐๐๐ง๐
ร ๐๐๐๐๐๐๐๐ ๐ถ๐๐ ๐ก ๐๐๐ ๐๐๐๐๐) + (
Contact - 09228446565
๐๐๐๐๐๐ ๐๐๐ง๐ 2
www.konceptca.com
ร ๐ถ๐๐๐๐ฆ๐๐๐ ๐๐๐ ๐ก ๐. ๐ข. ๐. ๐ )]
[email protected]
=(
48,000 2,400
ร โน180 ) + (
2400 2
ร โน3)
= โน3,600 + โน3,600 = โน7,200
Question 2.
Compute E.O.Q. and the total variable cost for the following: Annual Demand
5,000 units
Unit price
20.00
Order cost
16.00
Storage rate
2% per annum
Interest rate
12% per annum
Obsolescence rate
6% per annum
Determine the total variable cost that would result for the items if an incorrect price of โน 12.80 is used Solution: (i) Carrying Cost =
Storage cost Interest Rate Obsolescence Rate Total
= 2% = 12% = 6% = 20%
C= 20% of 20 = 4 per unit per annum. 2๐ด๐
EOQ = โ
๐ถ
2โ5000โ16
=โ
4
= โ40000 = 200 units.
Total variable cost: Purchase price of 5000 units @ 20 per unit 5000 Ordering Cost = 200 = 25 orders @ 16
Contact - 09228446565
www.konceptca.com
=1,00,000 = 400
[email protected]
Carrying cost of average inventory =
200 2
= 100 units @ 4
Total variable cost (ii)
= 400 = 1,00,800
If an incorrect price of 12.80 is used : C = 20% of 12.80 = 2.56 per unit per annum 2โ5000โ16
E.O.Q = โ
2.56
= 250 units
Total variable cost: Purchase price of 5000 units @12.80 per unit 5000 Ordering Cost = 250 = 25 orders @ 16
= 64,000 = 320
Carrying cost of average inventory =
= 320
250 2
= 125 units @ 2.56
Total variable cost
= 64,640
Question 3. SHRI XYZ & CO. which manufactures a product โEver Youngโ, provides you the following information: Monthly demand of โEver Youngโ Cost of Placing an order Carrying Cost per unit p.m. Cost of Input to be purchase Output per kg. of Input
= 900 units = 75 = 2% = 50 per kg. = 1.5 units
Required: What percentage of discount in the price of input should be negotiated if the company proposes to rationalize placements of orders on monthly basis? Suppose the company followed the policy of economic order quantity and at the end of the year, it was found that the cost of placing an order was 108 instead of 75 and all other estimates were correct. What is the difference in cost on account of this error? Solution: (i) Carrying Cost per unit p.a. (C) = 2% ร 12 ร โน 50 = โน 12
Contact - 09228446565
www.konceptca.com
[email protected]
Annual Usage (A) = (900 ร 12)/1.5 = 7200 kg. EOQ = โ
2AO C
=โ
2ร7200ร75 12
= 300 Kg.
Total Cost when order quantity is 300 kg. = Ordering Cost + Carrying Cost + Purchase Cost 1
7200
= ( 300 ร โน75) + (2 ร 300 ร โน12) + (7200 ร โน50) = 1,800 + 1,800 + โน3,60,000 = โน3,63,600 Suppose new negotiated purchase price is X, carrying cost will be 24X Now, Total Cost when order quantity is 600 kg. will be โ 7200
1
=( 300 ร โน75) + (2 ร 600 ร 0.24๐) + (7200X) =900 + 72X + 7200X = โน900 + 7272X In order to rationalize the placements of orders on monthly basis, the above cost should be equal to total cost when order size is of economic order quantity. Thus, โน900+7272X = โน3,63,600 7272X = โน3,63,600 - โน900 X = โน3,62,700/7272 = โน49.88 (approx...) Discount Desired = โน50 - โน49.88 = โน0.12 % of Discount to be negotiated = โน 0.12/50 ร 100 = 0.24% (ii) Revised EOQ = โ
2ร7200ร108 12
= 360 Units
(a) Revised Total Ordering and Carrying Cost 7200
1
= ( 360 ร โน108) + (2 ร 360 ร โน12) = โน2,160 + โน2,160 = โน4,320 Contact - 09228446565
www.konceptca.com
[email protected]
(b) Total Ordering and Carrying Cost at actual economic order size of 300 and correct ordering cost of โน108 7200
1
= ( 300 ร โน108) + (2 ร 300 ร โน12) = โน2,592 + โน1,800 = โน4,392 (c) Difference in the relevant cost on account of wrong estimation of ordering cost [B-A] = โน4,392 - โน4,320 = โน72.
Question 4. The complete Gardener is deciding on the economic order quantity for two brands of lawn fertilizer. Super Grow and Natureโs Own. The following information is collected:
Annual demand Relevant ordering cost per purchase order Annual relevant carrying cost per bag
Fertilize r Super Grow 2,000 โน bags 1,200 โน 480
Natureโs Own 1,280 โน bags 1,400 โน 560
Required: (i)
Compute EOQ for Super Grow and Natureโsown.
(ii)
For the EOQ, what is the sum of the total annual relevant ordering costs and total annual relevant carrying costs for Super Grow and Natureโsown?
(iii) For the EOQ, compute the number of deliveries per year for Super Grow and
Natureโsown. Solution: EOQ =
2AO C
Where, A = Annual Demand O = Ordering cost per order C = Inventory carrying cost per unit per annum (i) Calculation of EOQ:
Contact - 09228446565
www.konceptca.com
[email protected]
Super Grow EOQ=
Natureโs own
2ร2,000ร1,200
EOQ=
2ร1,280ร1,400
480 =
560
10,000 or 100bags
=
6,400
or 80bags
(ii)Total annual relevant cost = Total annual relevant ordering costs + Total annual relevant carryingcost Super Grow
Natureโs own
= (2,000/100 ร โน1,200) + (ยฝ ร 100 bags ร โน480) = โน 24,000 + โน 24,000 = โน 48,000
= (1,280/80 ร โน1,400) + (ยฝ ร 80 bags ร โน 560) = โน 22,400 + โน 22,400 = โน 44,800
(iii)Number of deliveries for Super Grow and Natureโs own fertilizer per year =
Annaul Demand for fertilizers bags EOQ
Super Grow 2,000 bags = = 20 orders 100 bags
Natureโs own 1,280bags = = 16 orders. 80 bags
Question 5. ZED Company supplies plastic crockery to fast food restaurants in metropolitan city. One of its products is a special bowl, disposable after initial use, for serving soups to its customers. Bowls are sold in pack 10 pieces at a price of โน 50 per pack. The demand for plastic bowl has been forecasted at a fairly steady rate of 40,000 packs every year. The company purchases the bowl direct from manufacturer at โน 40 per pack within a three days lead time. The ordering and related cost is โน 8 per order. The storage cost is 10%per annum of average inventory investment. Required: (i)
Calculate Economic OrderQuantity.
(ii)
Calculate number of orders needed every year.
(iii)
Calculate the total cost of ordering and storage bowls for the year.
Contact - 09228446565
www.konceptca.com
[email protected]
(iv)
Determine when should the next order to be placed. (Assuming that the company does maintain a safety stock and that the present inventory level is 333 packs with a year of 360 workingdays.)
Solution: (i) Economic OrderQuantity 2 ๏ดA ๏ดO
EOQ =
=
2*40,000packs *โน8
= 400packs.
โน40*10%
Ci (ii) Number of orders per year
Annual requirements E.O.Q
=
40,000 Packs 400 Packs
= 100 orders a year
(iii) Ordering and storagecosts
(โน) Ordering costs :โ 100 orders รโน8.00
800
Storage cost :โ ยฝ (400 packs ร 10% of โน40)
800
Total cost of ordering & storage
1,600
(iv) Timing of nextorder (a) Dayโs requirement served by eachcorder.
Number of days requirements =
No.of working days No.of order in a year
=
360 100
= 3.6 days supply
This implies that each order of 400 packs supplies for requirements of 3.6 days only. (b) Days requirements covered by inventory =
Units in Inventory EOQ
ร (Dayโs requirement served by an order)
333 Packs
=400 Packs ร 3.6 Days = 3 days requirement (c) Time interval for placing next order Contact - 09228446565
www.konceptca.com
[email protected]
Inventory left for dayโs requirement โ Lead time of delivery 3 days = 3 daysโ 3 days = 0days This means that next order for the replenishment of supplies has to be placed immediately.
Question 6. The following information relating to a type of Raw material is available: Annualdemand
2,000units
Unitprice
โน20.00
Ordering costperorder
โน20.00
Storagecost
2%p.a.
Interestrate
8%p.a.
Leadtime
half-month
Calculate economic order quantity and total annual inventory cost of the raw material. Solution:
EOQ=
2ร Annual demand ร Cost per order
=
Storage cost๏ดโน20 per unit per 2๏ด2,000units 80,000 annum =โ = 200Units โน 20 ๏ด๏ (2 ๏ซ8) % 2
Total Annual Inventory Cost = Purchasing cost of 2,000 units @ โน20perunit 2,000 Units
Ordering Cost ( 200 Units ร โน20) Carrying Cost of Inventory ยฝ (200 Units รโน20ร10%)
= = =
โน40,000 โน โน
200 200
โน 40,400
Contact - 09228446565
www.konceptca.com
[email protected]
Question 7. An engineering company consumes 50,000 units of a component per year. The ordering, receiving and handling costs are 3 per order while trucking costs are 12 per order. Further details are as under: Interest 0.06 per unit per year. Deterioration cost 0.004 per unit per annum. Storage cost 1,000 per annum for 50,000 units, calculate the EOQ. Solution: Buying cost per order ADD: Trucking Total Buying cost per order
3.00 12.00 15.00
Storage ( 1,000/50,000) Deterioration Interest Total Carrying cost per unit p.a
0.020 0.004 0.060 0.084
We know that: ๐๐จ๐ถ
EOQ = โ
๐ช
๐โ๐๐๐๐๐โ๐๐
=โ
๐.084
= 4226 units Question 8.
8 Marks
The Stock Control Policy of a company is that each stock is ordered twice a year. The quantum of each order being one-half of the years forecast demand. The Materials Manager, however wishes to introduce a policy in which for each item of stock, Re-Order Levels and EOQ is calculated. For one of the items X, the following information is available Forecast annual demand Cost per Unit Contact - 09228446565
3,600 Units โน100 www.konceptca.com
[email protected]
Cost of placing an order โน40 Stock holding cost 20% of Average Stock Value Lead Time 1 month It is estimated by the materials manager that for item X, a Buffer Stock of additional 100 Units should be provided to cover fluctuations in demand. If the new policy is adopted, calculate for Stock Item X โ 1. Re-Order Level that should be set by the Material Manager. 2. Anticipated Reduction in the value of the average stock investment. 3. Anticipated Reduction in the Total Inventory Costs in the first and subsequent years. Solution: ๐๐จ๐ถ
1. EOQ = โ
๐ช
Where, A=Annual Requirement of Raw Materials= 3,600 units (given) O=Ordering Cost= โน40 per Order (given) C=Carrying Cost per unit per annum = โน100ร20% = โน20 p.u. p.a. On Substitution, EOQ = 120 Units. 2. Re-Order Level = Safety Stock + Lead Time Consumption (1 Month) = 100Units + (3,600ร1/12) = 400 Units 3. EOQ vs Half-Yearly Purchase Policy Particulars
EOQ Existing Policy (half-yearly)
(a) Quantity Ordered every time (Q) (b) Number of Orders p.a. (c)Buying Costs p.a. at โน40 (d) Average Inventory = ยฝ of (a) (e) Value of Avg. Inventory=(dรโน100) (f) Carrying Cost p.a. at 20% of (e)
Contact - 09228446565
120 Units 3600/120 = 30 Orders
3600/2 = 1,800 Units (Half-Yearly) = 2 Orders
30รโน40 = โน1,200
2รโน40 = โน80
Safety Stock+1/2EOQ = 100+60=160 Units โน16,000
ยฝ ร โน1,800 = โน900 Units
โน3,200
โน18,000
www.konceptca.com
โน90,000
[email protected]
(g) Associated Cost p.a. = (c+ f)
โน4,400
โน18,080
Anticipated reduction in value of average stock Investment = โน90,000 โ โน16,000 = โน74,000. Anticipatory reduction in total inventory-related costs = โน18,080 โ โน4,400 = โน13,680 However, in the first year, Safety Stock of 100 Units is to be purchased at cost of โน10,000 (100 Unitsรโน100). So, while the saving would be of โน13,680, the cost reduction in the system would be only โน3,680. In subsequent years, however, the cost reduction will be โน13,680.
Question 9. X Ltd. Is committed to supply 24,000 bearings per annum to Y Ltd. On steady basis. It is estimated that it costs 10 paise as inventory holding cost per bearing per month and that the set-up cost per run of bearing manufacture is 324. (a) What would be the optimum run size for bearing manufacture? (b) Assuming that the company has a policy of manufacturing 6,000 bearing per run, how much extra costs the company would be incurring as compared to the optimum run suggested in (a) above? (c) What is the minimum inventory holding cost? Solution: (a) Optimum Production run (batch) size = EOQ = โ
๐๐จ๐ถ ๐ช ๐โ๐๐๐๐๐โ๐๐๐
=โ
๐.๐๐โ๐๐
= 3600 bearing (b) For finding out the extra inventory cost, it is necessary to work out the total cost when production run sizes are 3600 & 6000. Total Cost = Total set-up + Total Carrying Cost
Contact - 09228446565
www.konceptca.com
[email protected]
Total set-up cost = production run orders * cost per production run 24000 = 3600 * 324 = 2,160 Total set-up cost when Q is 6000 =
24000 6000
* 324 = 1296
Total carrying cost when Q is 3600 = ยฝ * Q * carrying cost p.a = ยฝ * 3600* 0.10*12 = 2160 Total carrying cost when Q is 6000 = ยฝ * 6000* 0.10*12 = 3600 Total cost when Q is 6000 = 1296+3600 = 4896 Total cost when Q is 3600 = 2160+2160 = 4320 Extra cost = 4896- 4320 = 576 (c) Minimum Inventory holding cost = ยฝ * Q * carrying cost p.a = ยฝ * 3600 * 0.10 * 12 = 2160.
Question 10. The annual cost of Material X is 3.60 per unit and its Total Carrying Cost is 9,000 per annum. What would be the Economic Order Quantity for Material X, If there is no Safety Stock of Material X? Solution: Average Inventory * Carrying cost per unit p.a = 9000 ยฝ of EOQ * 3.6 = 9000 EOQ =
9000โ2 3.6
= 5000 units
Contact - 09228446565
www.konceptca.com
[email protected]
48,000 units Purchase Price of input unit 12% Ordering Cost per order
โน 25 โน 180
Solution: (a) EOQ = โ
2๐ด๐ ๐ถ
=
โ
2ร48000รโน180 โน3
= 2400 Units
Where, A = Annual Demand O = Ordering cost per order C = Inventory carrying cost per unit per annum
(b) No. of orders per year = (c) Frequency of Orders = (d) Total Ordering Cost = = (e) Total Carrying Cost =
Total Annual Consumption Order Size 365 Days
No.of Order
=
365 Days 20 Orders
Annual Consumption Order Size 48,000 2,400
48,000 Units 2,400 Units
= 20 Orders
= 18.25 days
ร Ordering Cost per order
ร โน180 = โน3,600
Order Size 2
=
ร Carrying Cost per unit p.a. = 2400/2 ร โน3 = โน3,600
(f) Total Annual Carrying & Ordering Cost =[(
๐ด๐๐๐ข๐๐ ๐ถ๐๐๐ ๐ข๐๐๐ก๐๐๐ ๐๐๐๐๐ ๐๐๐ง๐
ร ๐๐๐๐๐๐๐๐ ๐ถ๐๐ ๐ก ๐๐๐ ๐๐๐๐๐) + (
Contact - 09228446565
๐๐๐๐๐๐ ๐๐๐ง๐ 2
www.konceptca.com
ร ๐ถ๐๐๐๐ฆ๐๐๐ ๐๐๐ ๐ก ๐. ๐ข. ๐. ๐ )]
[email protected]
=(
48,000 2,400
ร โน180 ) + (
2400 2
ร โน3)
= โน3,600 + โน3,600 = โน7,200
Question 2.
Compute E.O.Q. and the total variable cost for the following: Annual Demand
5,000 units
Unit price
20.00
Order cost
16.00
Storage rate
2% per annum
Interest rate
12% per annum
Obsolescence rate
6% per annum
Determine the total variable cost that would result for the items if an incorrect price of โน 12.80 is used Solution: (i) Carrying Cost =
Storage cost Interest Rate Obsolescence Rate Total
= 2% = 12% = 6% = 20%
C= 20% of 20 = 4 per unit per annum. 2๐ด๐
EOQ = โ
๐ถ
2โ5000โ16
=โ
4
= โ40000 = 200 units.
Total variable cost: Purchase price of 5000 units @ 20 per unit 5000 Ordering Cost = 200 = 25 orders @ 16
Contact - 09228446565
www.konceptca.com
=1,00,000 = 400
[email protected]
Carrying cost of average inventory =
200 2
= 100 units @ 4
Total variable cost (ii)
= 400 = 1,00,800
If an incorrect price of 12.80 is used : C = 20% of 12.80 = 2.56 per unit per annum 2โ5000โ16
E.O.Q = โ
2.56
= 250 units
Total variable cost: Purchase price of 5000 units @12.80 per unit 5000 Ordering Cost = 250 = 25 orders @ 16
= 64,000 = 320
Carrying cost of average inventory =
= 320
250 2
= 125 units @ 2.56
Total variable cost
= 64,640
Question 3. SHRI XYZ & CO. which manufactures a product โEver Youngโ, provides you the following information: Monthly demand of โEver Youngโ Cost of Placing an order Carrying Cost per unit p.m. Cost of Input to be purchase Output per kg. of Input
= 900 units = 75 = 2% = 50 per kg. = 1.5 units
Required: What percentage of discount in the price of input should be negotiated if the company proposes to rationalize placements of orders on monthly basis? Suppose the company followed the policy of economic order quantity and at the end of the year, it was found that the cost of placing an order was 108 instead of 75 and all other estimates were correct. What is the difference in cost on account of this error? Solution: (i) Carrying Cost per unit p.a. (C) = 2% ร 12 ร โน 50 = โน 12
Contact - 09228446565
www.konceptca.com
[email protected]
Annual Usage (A) = (900 ร 12)/1.5 = 7200 kg. EOQ = โ
2AO C
=โ
2ร7200ร75 12
= 300 Kg.
Total Cost when order quantity is 300 kg. = Ordering Cost + Carrying Cost + Purchase Cost 1
7200
= ( 300 ร โน75) + (2 ร 300 ร โน12) + (7200 ร โน50) = 1,800 + 1,800 + โน3,60,000 = โน3,63,600 Suppose new negotiated purchase price is X, carrying cost will be 24X Now, Total Cost when order quantity is 600 kg. will be โ 7200
1
=( 300 ร โน75) + (2 ร 600 ร 0.24๐) + (7200X) =900 + 72X + 7200X = โน900 + 7272X In order to rationalize the placements of orders on monthly basis, the above cost should be equal to total cost when order size is of economic order quantity. Thus, โน900+7272X = โน3,63,600 7272X = โน3,63,600 - โน900 X = โน3,62,700/7272 = โน49.88 (approx...) Discount Desired = โน50 - โน49.88 = โน0.12 % of Discount to be negotiated = โน 0.12/50 ร 100 = 0.24% (ii) Revised EOQ = โ
2ร7200ร108 12
= 360 Units
(a) Revised Total Ordering and Carrying Cost 7200
1
= ( 360 ร โน108) + (2 ร 360 ร โน12) = โน2,160 + โน2,160 = โน4,320 Contact - 09228446565
www.konceptca.com
[email protected]
(b) Total Ordering and Carrying Cost at actual economic order size of 300 and correct ordering cost of โน108 7200
1
= ( 300 ร โน108) + (2 ร 300 ร โน12) = โน2,592 + โน1,800 = โน4,392 (c) Difference in the relevant cost on account of wrong estimation of ordering cost [B-A] = โน4,392 - โน4,320 = โน72.
Question 4. The complete Gardener is deciding on the economic order quantity for two brands of lawn fertilizer. Super Grow and Natureโs Own. The following information is collected:
Annual demand Relevant ordering cost per purchase order Annual relevant carrying cost per bag
Fertilize r Super Grow 2,000 โน bags 1,200 โน 480
Natureโs Own 1,280 โน bags 1,400 โน 560
Required: (i)
Compute EOQ for Super Grow and Natureโsown.
(ii)
For the EOQ, what is the sum of the total annual relevant ordering costs and total annual relevant carrying costs for Super Grow and Natureโsown?
(iii) For the EOQ, compute the number of deliveries per year for Super Grow and
Natureโsown. Solution: EOQ =
2AO C
Where, A = Annual Demand O = Ordering cost per order C = Inventory carrying cost per unit per annum (i) Calculation of EOQ:
Contact - 09228446565
www.konceptca.com
[email protected]
Super Grow EOQ=
Natureโs own
2ร2,000ร1,200
EOQ=
2ร1,280ร1,400
480 =
560
10,000 or 100bags
=
6,400
or 80bags
(ii)Total annual relevant cost = Total annual relevant ordering costs + Total annual relevant carryingcost Super Grow
Natureโs own
= (2,000/100 ร โน1,200) + (ยฝ ร 100 bags ร โน480) = โน 24,000 + โน 24,000 = โน 48,000
= (1,280/80 ร โน1,400) + (ยฝ ร 80 bags ร โน 560) = โน 22,400 + โน 22,400 = โน 44,800
(iii)Number of deliveries for Super Grow and Natureโs own fertilizer per year =
Annaul Demand for fertilizers bags EOQ
Super Grow 2,000 bags = = 20 orders 100 bags
Natureโs own 1,280bags = = 16 orders. 80 bags
Question 5. ZED Company supplies plastic crockery to fast food restaurants in metropolitan city. One of its products is a special bowl, disposable after initial use, for serving soups to its customers. Bowls are sold in pack 10 pieces at a price of โน 50 per pack. The demand for plastic bowl has been forecasted at a fairly steady rate of 40,000 packs every year. The company purchases the bowl direct from manufacturer at โน 40 per pack within a three days lead time. The ordering and related cost is โน 8 per order. The storage cost is 10%per annum of average inventory investment. Required: (i)
Calculate Economic OrderQuantity.
(ii)
Calculate number of orders needed every year.
(iii)
Calculate the total cost of ordering and storage bowls for the year.
Contact - 09228446565
www.konceptca.com
[email protected]
(iv)
Determine when should the next order to be placed. (Assuming that the company does maintain a safety stock and that the present inventory level is 333 packs with a year of 360 workingdays.)
Solution: (i) Economic OrderQuantity 2 ๏ดA ๏ดO
EOQ =
=
2*40,000packs *โน8
= 400packs.
โน40*10%
Ci (ii) Number of orders per year
Annual requirements E.O.Q
=
40,000 Packs 400 Packs
= 100 orders a year
(iii) Ordering and storagecosts
(โน) Ordering costs :โ 100 orders รโน8.00
800
Storage cost :โ ยฝ (400 packs ร 10% of โน40)
800
Total cost of ordering & storage
1,600
(iv) Timing of nextorder (a) Dayโs requirement served by eachcorder.
Number of days requirements =
No.of working days No.of order in a year
=
360 100
= 3.6 days supply
This implies that each order of 400 packs supplies for requirements of 3.6 days only. (b) Days requirements covered by inventory =
Units in Inventory EOQ
ร (Dayโs requirement served by an order)
333 Packs
=400 Packs ร 3.6 Days = 3 days requirement (c) Time interval for placing next order Contact - 09228446565
www.konceptca.com
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Inventory left for dayโs requirement โ Lead time of delivery 3 days = 3 daysโ 3 days = 0days This means that next order for the replenishment of supplies has to be placed immediately.
Question 6. The following information relating to a type of Raw material is available: Annualdemand
2,000units
Unitprice
โน20.00
Ordering costperorder
โน20.00
Storagecost
2%p.a.
Interestrate
8%p.a.
Leadtime
half-month
Calculate economic order quantity and total annual inventory cost of the raw material. Solution:
EOQ=
2ร Annual demand ร Cost per order
=
Storage cost๏ดโน20 per unit per 2๏ด2,000units 80,000 annum =โ = 200Units โน 20 ๏ด๏ (2 ๏ซ8) % 2
Total Annual Inventory Cost = Purchasing cost of 2,000 units @ โน20perunit 2,000 Units
Ordering Cost ( 200 Units ร โน20) Carrying Cost of Inventory ยฝ (200 Units รโน20ร10%)
= = =
โน40,000 โน โน
200 200
โน 40,400
Contact - 09228446565
www.konceptca.com
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Question 7. An engineering company consumes 50,000 units of a component per year. The ordering, receiving and handling costs are 3 per order while trucking costs are 12 per order. Further details are as under: Interest 0.06 per unit per year. Deterioration cost 0.004 per unit per annum. Storage cost 1,000 per annum for 50,000 units, calculate the EOQ. Solution: Buying cost per order ADD: Trucking Total Buying cost per order
3.00 12.00 15.00
Storage ( 1,000/50,000) Deterioration Interest Total Carrying cost per unit p.a
0.020 0.004 0.060 0.084
We know that: ๐๐จ๐ถ
EOQ = โ
๐ช
๐โ๐๐๐๐๐โ๐๐
=โ
๐.084
= 4226 units Question 8.
8 Marks
The Stock Control Policy of a company is that each stock is ordered twice a year. The quantum of each order being one-half of the years forecast demand. The Materials Manager, however wishes to introduce a policy in which for each item of stock, Re-Order Levels and EOQ is calculated. For one of the items X, the following information is available Forecast annual demand Cost per Unit Contact - 09228446565
3,600 Units โน100 www.konceptca.com
[email protected]
Cost of placing an order โน40 Stock holding cost 20% of Average Stock Value Lead Time 1 month It is estimated by the materials manager that for item X, a Buffer Stock of additional 100 Units should be provided to cover fluctuations in demand. If the new policy is adopted, calculate for Stock Item X โ 1. Re-Order Level that should be set by the Material Manager. 2. Anticipated Reduction in the value of the average stock investment. 3. Anticipated Reduction in the Total Inventory Costs in the first and subsequent years. Solution: ๐๐จ๐ถ
1. EOQ = โ
๐ช
Where, A=Annual Requirement of Raw Materials= 3,600 units (given) O=Ordering Cost= โน40 per Order (given) C=Carrying Cost per unit per annum = โน100ร20% = โน20 p.u. p.a. On Substitution, EOQ = 120 Units. 2. Re-Order Level = Safety Stock + Lead Time Consumption (1 Month) = 100Units + (3,600ร1/12) = 400 Units 3. EOQ vs Half-Yearly Purchase Policy Particulars
EOQ Existing Policy (half-yearly)
(a) Quantity Ordered every time (Q) (b) Number of Orders p.a. (c)Buying Costs p.a. at โน40 (d) Average Inventory = ยฝ of (a) (e) Value of Avg. Inventory=(dรโน100) (f) Carrying Cost p.a. at 20% of (e)
Contact - 09228446565
120 Units 3600/120 = 30 Orders
3600/2 = 1,800 Units (Half-Yearly) = 2 Orders
30รโน40 = โน1,200
2รโน40 = โน80
Safety Stock+1/2EOQ = 100+60=160 Units โน16,000
ยฝ ร โน1,800 = โน900 Units
โน3,200
โน18,000
www.konceptca.com
โน90,000
[email protected]
(g) Associated Cost p.a. = (c+ f)
โน4,400
โน18,080
Anticipated reduction in value of average stock Investment = โน90,000 โ โน16,000 = โน74,000. Anticipatory reduction in total inventory-related costs = โน18,080 โ โน4,400 = โน13,680 However, in the first year, Safety Stock of 100 Units is to be purchased at cost of โน10,000 (100 Unitsรโน100). So, while the saving would be of โน13,680, the cost reduction in the system would be only โน3,680. In subsequent years, however, the cost reduction will be โน13,680.
Question 9. X Ltd. Is committed to supply 24,000 bearings per annum to Y Ltd. On steady basis. It is estimated that it costs 10 paise as inventory holding cost per bearing per month and that the set-up cost per run of bearing manufacture is 324. (a) What would be the optimum run size for bearing manufacture? (b) Assuming that the company has a policy of manufacturing 6,000 bearing per run, how much extra costs the company would be incurring as compared to the optimum run suggested in (a) above? (c) What is the minimum inventory holding cost? Solution: (a) Optimum Production run (batch) size = EOQ = โ
๐๐จ๐ถ ๐ช ๐โ๐๐๐๐๐โ๐๐๐
=โ
๐.๐๐โ๐๐
= 3600 bearing (b) For finding out the extra inventory cost, it is necessary to work out the total cost when production run sizes are 3600 & 6000. Total Cost = Total set-up + Total Carrying Cost
Contact - 09228446565
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Total set-up cost = production run orders * cost per production run 24000 = 3600 * 324 = 2,160 Total set-up cost when Q is 6000 =
24000 6000
* 324 = 1296
Total carrying cost when Q is 3600 = ยฝ * Q * carrying cost p.a = ยฝ * 3600* 0.10*12 = 2160 Total carrying cost when Q is 6000 = ยฝ * 6000* 0.10*12 = 3600 Total cost when Q is 6000 = 1296+3600 = 4896 Total cost when Q is 3600 = 2160+2160 = 4320 Extra cost = 4896- 4320 = 576 (c) Minimum Inventory holding cost = ยฝ * Q * carrying cost p.a = ยฝ * 3600 * 0.10 * 12 = 2160.
Question 10. The annual cost of Material X is 3.60 per unit and its Total Carrying Cost is 9,000 per annum. What would be the Economic Order Quantity for Material X, If there is no Safety Stock of Material X? Solution: Average Inventory * Carrying cost per unit p.a = 9000 ยฝ of EOQ * 3.6 = 9000 EOQ =
9000โ2 3.6
= 5000 units
Contact - 09228446565
www.konceptca.com
[email protected]
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