GATE 2020 · BOranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401 1.1 In an ideal inventory...

GATE 2020Mechanical Engineering

(Volume - II)

TOPIC WISE GATE SOLUTIONS

1987 - 2019

TM

GATE A PCADEMY UBLICATIONS®

S. No. Topics Page No.

1. Engineering Mechanics 1.1 - 1.000

1. FBD & Equilibrium of Forces 1.1 - 1.00

2. Plane Trusses 1.00 - 1.00

3. Friction 1.00 - 1.00

4. Kinematics of Particles & Rigid Body 1.00 - 1.00

5. Kinetics of Particles & Rigid Body 1.00 - 1.00

6. Impulse, Momentum, Collision & Work Energy 1.00 - 1.00

2. Theory of Machines 2.1 - 2.000

1. Displacement, Velocity & Acceleration 2.1 - 2.00

2. Planer Mechanisms 2.00 - 2.00

3. Cams 2.00 - 2.00

4. Dynamic Analysis of Slider-Crank 2.00 - 2.00

5. Gear & Gear Trains 2.00 - 2.00

6. Flywheel 2.00 - 2.00

7. Vibration 2.00 - 2.00

8. Balancing 2.00 - 2.00

9. Gyroscope 2.00 - 2.00

3. Industrial Engineering 3.1 - 3.000

1. Inventory Control 3.1 - 3.0

2. Linear Programming Problem 3.0 - 3.00

3. Transportation & Assignment Model 3.00 - 3.00

4. CPM & PERT 3.00 - 3.00

5. Queuing Theory 3.00 - 3.00

6. Forecasting 3.00 - 3.00

7. Break Even Analysis 3.00 - 3.00

8. Sequencing 3.00 - 3.00

CONTENTS

9. Line Balancing Or Assembly Line 3.00 - 3.00

10. MRP 3.00 - 3.00

11. Work Study 3.00 - 3.00

12. Miscellaneous 3.00 - 3.00

4. Production Engineering 4.1 - 4.000

1. Casting 4.1 - 4.0

2. Welding 4.0 - 4.00

3. Machining 4.00- 4.00

4. Forming 4.00- 4.00

5. Sheet Metal Working 4.00- 4.00

6. Metrology & Inspection 4.00- 4.00

7. Computer Integrated Manufacturing 4.00- 4.00

8. Unconventional Machining 4.00- 4.00

9. Material Science 4.00- 4.00

5. Engineering Mathematics 5.1 - 5.000

1. Linear Algebra 5.1 - 5.0

2. Differential Equation 5.0 - 5.00

3. Integral & Differential Calculus 5.00 - 5.00

4. Vector Calculus 5.00 - 5.00

5. Maxima & Minima 5.00 - 5.00

6. Mean Value Theorem 5.00 - 5.00

7. Complex Variables 5.00 - 5.00

8. Limit and Series Expansion 5.00 - 5.00

9. Probability & Statistics 5.00 - 5.00

10. Numerical Methods 5.00 - 5.00

11. Transform Theory 5.00 - 5.00

© Copyrightwww.gateacademy.co.inH Oead ffice : A/114-115, Smriti Nagar, Bhilai (C.G.), Contact : 9713113156, 9589894176

B Oranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401

1.1 In an ideal inventory control system,

the economic lot size for a part is 1000. If the annual demand for the part is doubled, the new economic lot size required will be [2 Marks]

(A) 500 (B) 2000

(C) 10002

(D) 1000 2

1.2 When the annual demand of a product

is 24000 units, the EOQ (economic order quantity) is 2000 units. If the annual demand is 48000 units the most appropriate EOQ will be [2 Marks]

(A) 1000 units (B) 2000 units (C) 2800 units (D) 4000 units

1.3 If the demand for an item is doubled

and the ordering cost halved, the economic order quantity [1 Mark]

(A) Remains unchanged (B) Increases by factor of 2 (C) Is doubled (D) Is halved

1.4 Setup costs do not include [1 Mark] (A) Labour cost of setting up machines (B) Ordering cost of raw material (C) Maintenance cost of the machines (D) Cost of processing the work piece

1.5 One of the following statements about

PRS (Periodic Reordering System) is

not true identify. [1 Mark]

(A) PRS requires continuous monitoring

of inventory levels

(B) PRS is useful in control of

perishable items

(C) PRS provides basis for adjustments

to account for variations in demand

(D) In PRS, inventory holding costs are

higher than in Fixed Reorder

Quantity System

1.6 In inventory planning, extra inventory

is unnecessarily carried to the end of

the planning period when using one of

the following lot size decision polices :

[1 Mark]

(A) Lot for lot production

(B) Economic Order Quantity (EOQ)

lot size

(C) Period Order Quantity (POQ) lot

size

(D) Part period total cost balancing

1Inventory Control/

Management

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3.2 Topic Wise GATE Solutions [ME] GATE ACADEMY®



1.7 In computing Wilson's economic lot

size for an item, by mistake the demand rate estimate used was 40% higher than the true demand rate. Due to this error in the lot size computation, the total cost of setup plus inventory holding per unit time would rise above the true optimum by approximately [2 Marks]

(A) 1.4% (B) 3.3% (C) 18.3% (D) 8.7%

1.8 An item can be purchased for Rs.100.

The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is [1 Mark]

(A) 50 (B) 100 (C) 200 (D) 400

1.9 Market demand for springs is 8,00,000

per annum. A company purchases these spring in lots and sells them. The cost of making a purchase order is Rs. 1,200. The cost of storage of springs is Rs. 120 per stored piece per annum. The economic order quantity is

[2 Marks] (A) 400 (B) 2,828 (C) 4,000 (D) 8,000

1.10 There are two product P and Q with the

following characteristics Product P Q

Demand (Units) 100 400Order cost (Rs./order) 50 50 Holding cost (Rs. Unit/yr.) 4 1

The economics order quantity (EOQ) of products P and Q will be of the ratio

[1 Mark] (A) 1 : 1 (B) 1 : 2 (C) 1 : 4 (D) 1 : 8 1.11 A company has an annual demand of

1000 units, ordering cost of Rs.100 per order and carrying cost of Rs.100 per unit year. If the stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, the safety stock justified by the carrying cost will be [2 Marks]

(A) 4 (B) 20 (C) 40 (D) 100

1.12 The distribution of lead time demand

for an item is as follows : Lead time demand Probability

80 0.20 100 0.25 120 0.30 140 0.25

The recorder level is 1.25 times the expected value of the lead time demand. The service level is [2 Marks]

(A) 25% (B) 50% (C) 75% (D) 100%

1.13 Consider the following data for an item. Annual demand : 2500 units per year,

Ordering cost : Rs. 100 per order, Inventory holding rate : 25% of unit

price. Price quoted by a supplier : Order quantity

(units) Unit price

(Rs.) < 500 10 500 9

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3.3GATE ACADEMY® Industrial Engineering : Inventory Control/Management



The optimum order quantity (in units) is [2 Marks]

(A) 447 (B) 471 (C) 500 (D) 600 1.14 A stockist wishes to optimize the

number of perishable items he needs to stock in any month in his store. The demand distribution for this perishable item is

Demand (in units)

2 3 4 5

Probability 0.10 0.35 0.35 0.20 The stockist pays Rs. 70 for each item

and he sells each at Rs. 90. If the stock is left unsold in any month, he can sell the item at Rs. 50 each. There is no penalty for unfulfilled demand. To maximize the expected profit, the optimal stock level is [2 Marks]

(A) 5 units (B) 4 units (C) 3 units (D) 2 units 1.15 The maximum level of inventory of an

item 100 and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continues throughout the year. Ordering cost is Rs. 100 per order and inventory carrying cost is Rs. 10 per item per month. Annual cost (in Rs.) of the plan, neglecting material cost, is [2 Marks]

(A) 800 (B) 2800 (C) 4800 (D) 6800 1.16 In machine shop, pins of 15 mm

diameter are produced at a rate of 1000 per month and the same is consumed at a rate of 500 per month. The production and consumption continue simultaneously till the maximum inventory is reached.

Then inventory is allowed to reduce to zero due to consumption. The lot size of production is 1000. If backlog is not allowed, the maximum inventory level is [2 Marks]

(A) 400 (B) 500 (C) 600 (D) 700

1.17 A company uses 2555 units for an item

annually. Delivery lead time is 8 days. The reorder point (in number of units) to achieve optimum inventory is

[2 Marks] (A) 7 (B) 8 (C) 56 (D) 60

1.18 Annual demand for window frames is

10000. Each frame costs Rs. 200 and ordering cost is Rs. 300 per order. Inventory holding cost is Rs. 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should [2 Marks]

(A) Order 200 frames every time (B) Accept 2% discount (C) Accept 4% discount (D) Order Economic Order Quantity

1.19 Demand during lead time with associated

probabilities is shown below, Demand 50 70 75 80 85

Probability 0.15 0.14 0.21 0.20 0.30 Expected demand during lead time is

_______. [1 Mark]

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2014 IIT Kharagpur




1.20 Consider the following data with reference to elementary deterministic economic order quantity model Annual demand of an item 100000Unit price of the item (in Rs.) 10 Inventory carrying cost per unit per year (in Rs.)

1.5

Unit order cost (in Rs.) 30 The total numbers of economic orders

per year to meet the annual demand is_______. [2 Marks]

1.21 A manufacturer can produce 12000 bearings per day. The manufacturer received an order of 8000 bearings per day from a customer. The cost of holding a bearing in stock is Rs. 0.20 per month. Setup cost per production run is Rs. 500. Assuming 300 working days in a year, the frequency of production run should be [2 Marks]

(A) 4.5 days (B) 4.5 months (C) 6.8 days (D) 6.8 months

1.22 Annual demand of a product is 50000

units and the ordering cost is Rs.7000 per order. Considering the basic economic order quantity model, the economic order quantity is 10000 unit. When the annual inventory cost is minimized, the annual inventory holding cost (in Rs.) is _____. [1 Mark]

1.23 The annual requirement of rivets at a ship manufacturing company is 2000 unit/year. The rivets are supplied in units of 1 kg costing Rs. 25 each. If the costs Rs. 100 to place an order and the annual cost of carrying one unit is 9% of its purchase cost, the cycle length of the order (in days) will be ______.

[2 Marks]

1.24 The annual demand for as item is 10000

units. The unit cost is Rs. 100 and inventory carrying charges are 14.4% of the unit cost per annum. The cost of one procurement is Rs. 2000. The time between two consecutive orders to meet the above demand is _____ month (s).

[2 Marks] 1.25 A food processing company uses 25000

kg of corn flour every year. The quantity-discount price of corn flour is provided in the table below :

Quantity (kg) Unit price (Rs/kg) 1-749 70

750-1499 65 1500 and above 60

The order processing charges are Rs. 500/order. The handling plus carry-over charge on an annual basis is 20% of the purchase price of the corn flour per kg. The optimal order quantity (in kg) is ________. [2 Marks]

1.26 A local tyre distributor expects to sell

approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is [1 Mark]

(A) 64 (B) 212 (C) 300 (D) 1200

1.27 The annual demand of valves per year

in a company is 10000. The current order quantity is 400 per order. The holding cost of valve is Rs.24 per valve per year and the ordering cost is Rs.400 per order. If the current order quantity is changed to Economic order quantity, then the saving in the total cost of inventory per year will be Rs.______.

[2 Marks]

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2019 IIT Madras




1.1 D 1.2 C 1.3 A 1.4 D 1.5 C

1.6 B 1.7 C 1.8 D 1.9 C 1.10 C

1.11 C 1.12 D 1.13 C 1.14 B 1.15 D

1.16 B 1.17 A 1.18 C 1.19 74.55 1.20 50

1.21 C 1.22 35000 1.23 77.01 1.24 2 1.25 1500

1.26 C 1.27 943.6

Given : Economic lot size = 1000 Economic order quantity,

(EOQ) 2 o

h

C D

C

Where, D Annual demand, oC Ordering cost per order hC Unit holding cost per year

121000 o

h

C D

C …(i)

2 12D D (given)

Again, 12

2 2( ) o

h

C DEOQ

C

…(ii)

Dividing equation (ii) by (i), we get

1

2

1

2 2( ) 4 2

1000 2 2

o

h

o

h

C D

CEOQ

C D

C

2( ) 1000 2EOQ Hence, the correct option is (D).

Given : Annual demand of product 1( )D = 24000 units Economic order quantity 1 2000 ni( ) u tsEOQ Annual demand 2( )D = 48000 units.

Case 1 : 11

2( ) 2000o

h

C DEOQ

C

2 240002000 o

h

C

C

…(i)

Case 2 : 22

2( ) o

h

C DEOQ

C

22 48000( ) o

h

CEOQ

C

…(ii)

2

2 48000( ) 2

2000 2 24000

o

h

o

h

C

CEOQ

C

C

2( ) 2000 2 2828.42EOQ

2( ) 2800EOQ units

Hence, the correct option is (C).

Given : Case-1 : 1D D ,

1o oC C and 1h hC C

Case-2 : 2 2D D , 2 2

oo

CC and

2h hC C

12( ) o

h

D CEOQ

C

Answers Inventory Control/Management

Explanations Inventory Control/Management

1.1 (D)

1.2 (C)

1.3 (A)




and, 22 2 2( )

2o o

h h

D C DCEOQ

C C

So, 1 2( ) ( )EOQ EOQ

Hence, the correct option is (A).

Setup cost : It is the costs incurred to configure a machine for a production run. This cost is considered a fixed cost of the associated batch, so its cost is spread over the number of units produced. Setup costs include the following : 1. Labor to position tools and materials next

to the machine 2. Labor to configure the machine 3. Scrap cost of test units run on the machine The real cost of a setup is the time wasted while a machine is not operational, since this can represent lost income (if there is a backlog of work). Consequently, there is usually an emphasis on shortening equipment setup times in order to reduce setup costs. Hence, the correct option is (D).

Key Point Cost of processing the work piece comes under the production cost.

Periodic reordering system (PRS) does not provide basis for adjustment to account to variation in demand. Hence, the correct option is (C).

Inventory planning is the process of determining the optimal quantity and timing of inventory for the purpose of aligning it with sales and production capacity.

It has direct impact a company's cash flow and profit margins especially for smaller businesses that rely upon a quick turnover of goods or materials. Hence, the correct option is (B).

Given : Case-1 : 1D D ,

1o oC C and 1h hC C

Case-2 : 2 1.4D D , 2o oC C and

2h hC C

Total cost per year, 2 o hTC DC C

where, oC and hC are constants.

TC D % increase in total cost per year,

2 1

1

( ) ( ) 100( )

TC TC

TC

2

1

( ) 1 100( )TC

TC

2

1

1 100D

D

1.4 1 100D

D

1.4 1 100 18.3% Hence, the correct option is (C).

Given : Ordering cost ( ) Rs.200 / orderoC Unit cost ( ) Rs.100C Inventory carrying cost ( ) 10%hC of unit cost

So, 10 100 Rs.10/unit / year100hC

Annual demand ( ) 4000 units/yearD

2 2 4000 20010

o

h

DCEOQ

C

400unitsEOQ Hence, the correct option is (D).

1.4 (D)

1.5 (C)

1.6 (B)

1.7 (C)

1.8 (D)




Given : Demand ( ) 800000 units/yearD Ordering cost ( ) Rs.1200/orderoC Holding cost ( ) Rs.120/unit/yearhC

2 o

h

DCEOQ

C

2 800000 1200120

4000unitsEOQ Hence, the correct option is (C).

Given : Demand of product P ( ) 100unitsD Ordering cost of product P ( ) Rs.50 /orderoC Holding cost of product P ( ) Rs.4hC unit/year

Demand of product Q ( ) 400unitsD Ordering cost of product Q ( ) Rs.50 /orderoC Holding cost of product Q ( ) Rs.1hC unit/year Economic order quantity,

02

h

DCEOQ

C

Ratio of EOQ for two product P and Q,

2( )( ) 2

o

hP P

Q o

h Q

DC

CEOQ

EOQ DC

C

2 100 504( )

( ) 2 400 501

P P

Q

Q

EOQ

EOQ

( ) 1( ) 4

P

Q

EOQ

EOQ


Given : Demand of company ( ) 1000 units/yearD Ordering cost ( )= Rs.100 / orderoC

Holding cost ( ) Rs.100 / unit-yearhC Stock out cost ( ) Rs.400sC

2 50 unitso o s

h s

DC C CEOQ

C C

Number of shortage,

50 100 10units100 400

o

o s

EOQ CS

C C

Safety stock justified by carrying cost = Maximum positive inventory in one cycle

50 10 40unitsEOQ S


ROL = 1.25Expected lead time demand

ROL > Expected lead time demand

Since, service = Probability of no shortage level

. . 1S L Probability of shortage

. . 1 0 1 100%S L

Hence, the correct option is (D). Key Point Lead time demand : Numbers of units required to sell to customers during lead time (Time gape between placing & receiving an order). Reorder level : Number of units present in stock at the time of placing an order and, if ROL Expected lead time demand, that means there will be no shortage for any customers. So, probability of shortage = 0

Time

Inventorylevel

S

mI

+EOQ

+ +

1.9 (C)

1.10 (C)

1.11 (C)

1.12 (D)




Given : Demand of an item ( ) 2500 units/yearD

Ordering cost ( ) Rs.100/orderoC

Holding cost ( ) 0.25 Unit pricehC

Quantity and unit price matrix : Order quantity

(units) Unit price

(Rs.) Holding cost

( hC )

<500 10 2.5 500 9 2.25

Economic order quantity : Case-1 : When order quantity is less than 500 units. Unit price ( ) Rs.10C /unit

Holding cost 25%hC of 10 = Rs.2.50

2 2 100 25002.5

o

h

C DEOQ

C

447.21 447 unitsEOQ

477units( ) unit cost

2

Q

h o

TC D

Q DC C

Q

447 25002500 10 2.5 1002 447

Rs.26118

Case-2 : when order quantity 500 units, Unit price ( ) Rs.9C /unit.

Holding cost, 25% of 9 Rs.2.25hC

/unit/year

2 2 100 25002.25

o

h

C DEOQ

C

471.40 471unitsEOQ

But, to get product at Rs.9 per unit minimum lot size should be of 500 units. So, let 500 unitsQ

500units500( ) 2500 9 2.25

22500 100500

QTC

22500 562.5 500 23562.5 = Rs.23563 Since total cost of inventory per year is minimum for lot size of 500 units. So optimum lot size is 500 units. Hence, the correct option is (C).

Given : Purchasing price of an item ( ) Rs.70/itemC Selling price ( ) Rs.90/itemS Selling price of an item left in stock

1( ) Rs.50/itemS

: Method 1 : Profit ( ) 90 70p S C 20 Rs.20 / itemp Loss 1( ) 70 50l C S 20 Rs.20 / iteml Cumulative probability of demand of ( 1)S units = ( 1)P S Cumulative probability of demand of ( )S units = ( )P S

( 1) ( )pP S P S

p l

Demand (units) 2 3 4 5 Probability 0.10 0.35 0.35 0.20 Cumulative probability

0.10 0.45 0.80 1.0

20 0.520 20

p

p l

Since, 0.5 lines between the cumulative probability (0.45 0.8) i.e., 0.45 0.5 0.80 . Demand corresponding to cumulative probability (0.80) is equal to 4.

1.13 (C)

1.14 (B)




Therefore optimum stock level is 4 units .

Hence, the correct option is (B). : Method 2 : Given : Cost price per unit Rs.70 Selling price per unit Rs.90

Profit per unit Rs.20

Salvage value (if unsold) Rs.50

Loss per unit (if unsold) Rs.20

In first column the number of stock is 2 and demand is also 2, again profit per units is Rs. 20, so profit for 2 units is 40. Again second element of 1st column is 20, because stock level is 3 and demand is 2, which given 40 – 20 = Rs. 20.

Demand

Stock level

2 3

2 3 4 5 40 40 40 40 20 60 60 60

4 5

0 40 80 80 - 20 20 60 100 0.1 0.35 0.35 0.2

Demand probability Profit table :

Stock level Expected profit

2 0.1 40 0.35 40 0.35 40 0.2 40 Rs. 40

3 0.1 20 0.35 60 0.35 60 0.2 60 Rs. 56

4 0.1 0 0.35 40 0.35 80 0.2 80 Rs. 58

5 0.1 20 0.35 20 0.35 60 0.2 100 Rs. 46

Since expected profit is maximum of Rs. 58 for stock level form four units. So, optimum stock level is 4 units.

Hence, the correct option is (B).

Given : Maximum inventory level ( ) 100 unitQ Cycle time ( ) 1.5 monthT Ordering cost ( ) Rs.100/orderoC

Holding cost ( ) Rs.10/unit/monthhC Demand of an inventory items per year,

QD

T

100 121.5

800 unit/year

Total annual cost, Holding cost +Ordering costTC

02 h

Q DTC C C

Q

Holding cost per year ( ) Rs.120 /unit-yearhC

100 800120 1002 100

TC Rs.6800

Hence, the correct option is (D).

Given : Production rate of pins ( ) 1000/monthP Consumption rate of pin ( ) 500/monthr Economic lot size ( ) 1000pinsEOQ Maximum inventory level,

Lot size P r

P

1000 50010001000

500 pins

Hence, the correct option is (B).

Given : Demand ( ) 2555 units/yearD Delivery lead time ( ) 8 daysLT One year 365 days

Consumption rate, 2555 7 units/day365

r

1.15 (D)

1.16 (B)

1.17 (A)




Reorder point, R.O.P Consumption rateLead time R.O.P 7 8 56units Hence, the correct option is (A).

Given : Demand of window frame ( ) 10000unit/yearD Purchasing cost ( ) Rs.200/ unitC


Holding cost ( ) Rs.40/unit-yearhC

Quantity (q) Discount Unit price (C) 0-999 0% 200

1000-1999 2% 196 2000 4% 192

Economic order quantity,

2EOQ o

h

DC

C

2 10000 30040

EOQ 387.298units 388 units Total cost per year, = Material cost Ordering costTC

+ Holding cost

EOQEOQ 2o h

DTC DC C C

Case-1 : ( ) 10000 200at EOQTC

10000 388300 40388 2

( ) = Rs.2015491.959at EOQTC

( ) Rs.2015492at EOQTC

Case-2 : For getting 2% discount 1000units( ) 10000 196at xTC

10000 1000300 401000 2

1000units( ) = Rs.1983000at xTC

Case-3 : For getting 4% discount 2000units( ) 10000 192at xTC

10000 2000300 402000 2

2000units( ) = Rs.1961500at xTC Since, total cost is minimum at lot size of 2000 units. Therefore 4% discount should be accepted and 2000 units to be ordered per lot. Hence, the correct option is (C). Key Point Material cost is included in total cost per year only in volume discount model. i.e., when product has more than one price due to some discount or offer.

Given :

Demand 50 70 75 80 85 Probability 0.15 0.14 0.21 0.20 0.30

Expected demand is given by, 50 0.15 70 0.14 75 0.21

80 0.20 85 0.3 74.55 Hence, the expected demand during lead time is 74.55.

Given : Annual demand of an item ( ) 100000 / yearD Ordering cost ( ) Rs.30/orderoC Handling cost ( ) Rs.1.5/unit/yearhC Economic order quantity,

2 o

h

C DEOQ

C

2 30 100000 20001.5

EOQ

units

Number of order per year,

100000 502000

DN

EOQ

Hence, the total number of economic orders per year to meet the annual demand is 50.

1.18 (C)

1.19 74.55

1.20 50




Given : Production rate of bearing ( ) 12000/dayP Setup cost ( ) Rs.500/production runoC Carrying cost ( ) Rs.0.20/unit/monthhC Consumption rate ( ) 8000/dayr Number of days in one year 300 days Annual demand r Number of days in one year 300 8000D 2400000unit/yearD Economic order quantity,

2 o

h

C D PEOQ

C P r

2 500 2400000 120000.2 12 12000 8000

EOQ

54772.25 unitsEOQ Time period,

54772.25 6.88000

EOQT

r days


Given : Annual demand of a product ( )D = 50000 units Ordering cost ( )oC = Rs.7000/order Economic order quantity ( )EOQ = 10000 units : Method 1 : Number of order

50000 510000

DN

EOQ

At EOQ, Carrying cost/year = Ordering cost/year Carrying cost/year = Number of order Ordering cost/order Carrying cost = 5 7000 Rs.35000 Hence, the annual inventory holding cost is Rs. 35000.

: Method 2 :

02

h

DCEOQ

C

2 50000 700010000hC

Rs.7 /unit/yearhC

Carrying cost /year,

7 100002 2

hCEOQ Rs.35000

Hence, the annual inventory holding cost is Rs. 35000.

Given : Annual demand of rivets (D) = 2000 unit/year Unit cost ( ) Rs.25/unitC

Ordering cost ( ) Rs.100oC /order

Annual carrying cost per unit ( ) 9% of hC C

9 25 Rs.2.25 / unit / year100hC

2 o

h

DCEOQ

C

2 2000 1002.25

EOQ

421.637 422EOQ The cycle length of the order,

422 0.211 year2000

EOQT

D

0.211 365 77.01 daysT Hence, the cycle length of the order will be 77.01 days.

Given : Annual demand of an item ( ) 10000D units Unit cost of item ( ) Rs.100C

1.21 (C)

1.22 35000

1.23 77.01

1.24 2




Holding cost ( ) 0.144 100 Rs.14.4hC /year

Ordering cost ( ) Rs.2000 / orderoC


2 2 10000 200014.4

o

h

DCEOQ

C

1666.67EOQ units The times between two consecutive orders. The cycle length of the order,

1666.67 121210000

EOQT

D

2 monthsT Hence, the time between two consecutive orders to meet the above demand is 2 months.

Given : Annual demand of corn flour ( ) 25000kg/yearD


Carrying cost ( ) 20%hC of unit price

Quantity (kg)

Unit price C = (Rs./kg)

20100hC C

(Rs./unit/year)1-749 70 14

750-1499 65 13 1500 and

above 60 12

For optimal order quantity we have to check total cost for every price category,

Total cost unit cost2 h o

Q DD C C

Q

Case-1 : For 1-749 quantity,

2 2 25000 5000.20 70

o

h

DCEOQ

C

1336.30kgEOQ Here EOQ is not in range, so in 1st category we can order to size of 749 units.

Total cost,

479units749( ) 25000 70 14

2QTC

25000 500749

6479units( ) Rs.1.771 10QTC

Case-2 : For 750-1499 quantity,

2 2 25000 50013

o

h

DCEOQ

C

1386.75kgEOQ EOQ falls on the range, Total cost,

1386.75units1386.75( ) 25000 65 13

2QTC

25000 5001386.75

61386.75units( ) Rs.1.64 10QTC

Case-3 : For range 1500 and above,

2 2 25000 50012

o

h

DCEOQ

C

1443.38 kgEOQ EOQ does not falls on this range, so minimum lot size = 1500 units Total cost at 1500 units,

1500units1500( ) 25000 60 12

2QTC

25000 5001500

61500units( ) Rs.1.517 10QTC

Among these three ranges total cost is minimum at 1500 units. Hence, the optimal order quantity is 1500 kg.

Given : Annual demand of tyre ( ) 9600 units/yearD Holding cost ( ) Rs.16/unit/yearhC


1.25 1500

1.26 (C)





2 o

h

DCEOQ

C

2 9600 75 300 units16

EOQ


Given : Annual demand ( ) 10000D /year

Ordering cost 0( ) Rs.400 /orderC

Holding cost ( ) Rs.24 /valve/yearhC

Case-1 : At order quantity ( ) 400unit/orderQ

1 0( )2 h

D QTC C C

Q

110000 400( ) 400 24

400 2TC

1( ) Rs. 14800TC

Case-2 : At EOQ ,

2 0( ) 2 hTC DC C

2( ) 2 10000 400 24TC

2 min( ) Rs. 13856.4 ( )TC TC

Saving in total cost per year, 1 2( ) ( )TC TC Rs.943.6

Hence, the saving in the total cost of inventory per year will be Rs.943.6.

1.27 943.6

GATE 2020 · BOranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401 1.1 In an ideal inventory...

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Transcript of GATE 2020 · BOranch ffice : Raipur : 79743-90037, Bhopal : 83198-88401 1.1 In an ideal inventory...