replacement theory mab ppt

7/31/2019 Replacement Theory MAB PPT

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Replacement TheoryModule 6



replacement

•

The problem of replacement is felt when the jobperforming units such as

• men

• Machine

• Equipments

• Parts etc.. Become less effective or useless due to eithersudden or gradual deterioration in their efficiency, failure orbreakdown

• By replacing them with new ones at frequent intervalsmaintenance and other overhead cost can be reduced



Types of failure

• There are two types of failure• Gradual failure

• Sudden failure



Gradual failure cases

• Increased running costs ( maintenance +operating cost)

• Decrease in productivity

• Decrease in the resale or salvage value



Sudden failure cases

• This type of failure occurs in items aftersome period of giving desired service ratherthan deteriorating while in service



Replacement of items whoserunning cost increases with timeand value of money remains

constant during a period

MODEL 1



ATCn = TC/n

Where TC = C-S+ Σ R(n)Where n = Replacement age of equipment

C = Capital or purchase cost of equipmentS = Scrap (salvage ) value of the equipment at the end of t years

R(n) = Running cost of the equipment

TC = Total CostATC = Average Total Cost

After determining the ATCn find out which year the value of ATCn isminimum which means it is the appropriate time for replacement



E.g.:

1. A firm is considering replacement of a machine,whose cost price is Rs 12,200, and the scrap valueRs 200.The running( maintenance and operating)costs are found from the experience to be as

follows:Year 1 2 3 4 5 6 7 8

Running cost(Rs)

200 500 800 1200 1800 2500 3200 4000

When the machine should be replaced?



Soln.Year ofservice

n

Runningcost R(n)

(Rs)

Cumulativerunning cost

ΣR(n)(Rs)

Depreciation cost

C-S

(Rs)

Total Cost

TC

(Rs)

Average Cost

ATCn

(Rs)

1 200 200 12000 12200 12000

2 500 700 12000 12700 6350

3 800 1500 12000 13500 45004 1200 2700 12000 14700 3675

5 1800 4500 12000 16500 3300

6 2500 7000 12000 19000 3167

7 3200 10200 12000 22200 3171

8 4000 14200 12000 26200 3275



MODEL 2

Replacement policy for items whoserunning cost increases with time but

value of money changes withconstant rate during the period



100

100+r d=

Where d is the discount rate or depreciation valuer is the rate of change

n



E.g.:• Let the value of the money be assumed to be 10 per

cent per year and suppose that machine A isreplaced after every 3 years where as machine B isreplaced after every 6 years. the yearly cost (In Rs)of both the machines are given as under:

Year 1 2 3 4 5 6

MachineA

1000 200 400 1000 200 400

MachineB

1700 100 200 300 400 500

Determine which machine should be purchased?



The discounted cost (present worth) at 10 percent ratefor machine A and machine B is given below

Discounted cost of Machine A

Year Discounted cost at 10% rate (Rs)

Cost present worth

1 1000 1*1000 1000.00

2 200 200* ( 100/(100+10) 181.82

3 400 400*(100/100+10)2 330.56

=0.9091

Total Rs 1512.38

Hence the average yearly cost of machine A is 1512.38/3=Rs 504.13



Discounted cost of machine B

Year Discounted cost at 10% rate(Rs)

cost Present Worth1 1700 1700*1 1700.00

2 100 100*0.9091 90.91

3 200 200*0.8264 165.28

4 300 300*0.7513 225.395 400 400*0.6830 273.20

6 500 500*0.6209 310.45

Total Rs 2765.23

The average yearly cost of machine B is 2765.23/6=Rs 460.87



• With the data on average yearly cost of bothmachines , the apparent advantage is in purchasingmachine B .but the periods for which the costs areconsidered are different .

• There fore , let us first calculate total present worthof machine A for 6 years

• Total present worth=1000+200*0.9091+400*0.8264+1000*0.7513+200*0.6830+400*0.6209=Rs 2648.64

• Which is less than the total present worth ofmachine B .

• Thus machine A should be purchased

replacement theory mab ppt

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