replacement_theory ppt slide in python .

slide on replacement theory

1. Replacement Theory
Dr. Sourabh Singha Roy

2. Replacement Theory
•The problem of replacement is felt when the job
performing units such as
•men
•Machine
•Equipments
•Parts etc.. Become less effective or useless due to either sudden
or gradual deterioration in their efficiency, failure or breakdown
•By replacing them with new ones at frequent intervals
maintenance and other overhead cost can be reduced

3. Types of failure
•There are two types of failure
•Gradual failure
•Sudden failure

4. Gradual failure cases
•Increased running costs ( maintenance +
operating cost)
•Decrease in productivity
•Decrease in the resale or salvage value

5. Sudden failure cases
•This type of failure occurs in items after some
period of giving desired service rather than
deteriorating while in service

6. Objectives:
•The objective of replacement is to decide the
best policy in determining a time at which the
replacement is most economical, instead of
continuing at an increased cost. The main
objective of replacement is to direct the
organization in maximizing its profit ( or
minimizing the cost).

7. MODEL 1
Replacement of items whose running cost
increases with time and value of money
remains constant during a period

8. ATC
n = TC/n
Where TC = C-S+ ΣR(n)
Where n = Replacement age of equipment
C = Capital or purchase cost of equipment
S = Scrap (salvage ) value of the equipment at the end of t years
R(n) = Running cost of the equipment
TC = Total Cost
ATC = Average Total Cost
After determining the ATC
nfind out which year the value of ATCn is
minimum which means it is the appropriate time for replacement

9. E.g.:
1.A firm is considering replacement of a machine, whose cost
price is Rs 12,200, and the scrap value Rs 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)
20050080012001800250032004000
When the machine should be replaced?

10. Solution
Year of
service
n
Running
cost R(n)
(Rs)
Cumulative
running 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 4500
4 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

11. MODEL 2
Replacement policy for items whose
running cost increases with time but
value of money changes with
constant rate during the period

12. 100
100+r
d=
Where d is the discount rate or depreciation value
r is the rate of change
n

13. E.g.:
•Let the value of the money be assumed to be 10 per cent
per year and suppose that machine A is replaced after
every 3 years where as machine B is replaced after every
6 years. the yearly cost (In Rs) of both the machines are
given as under:
Year 1 2 3 4 5 6
Machine
A
1000 200 400 1000 200 400
Machine
B
1700 100 200 300 400 500
Determine which machine should be purchased?

14. The discounted cost (present worth) at 10 percent rate for
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
TotalRs 1512.38
Hence the average yearly cost of machine A is 1512.38/3=Rs 504.13

15. Discounted cost of machine B
Year Discounted cost at 10% rate(Rs)
cost Present Worth
1 1700 1700*1 1700.00
2 100 100*0.9091 90.91
3 200 200*0.8264 165.28
4 300 300*0.7513 225.39
5 400 400*0.6830 273.20
6 500 500*0.6209 310.45
TotalRs 2765.23
The average yearly cost of machine B is 2765.23/6=Rs 460.87

16. •With the data on average yearly cost of both machines ,
the apparent advantage is in purchasing machine B .but
the periods for which the costs are considered are
different .
•There fore , let us first calculate total present worth of
machine A for 6 years
•Total present worth
=1000+200*0.9091+400*0.8264+1000*0.7513+200*0.68
30+400*0.6209=Rs 2648.64
•Which is less than the total present worth of machine B .
•Thus machine A should be purchased