1
Presented By:
SONIA
ROLL NO-78
ReplacementTheory
2
WHAT IS REPLACEMENT THEORY?
The replacement problems are concerned with the situations that arise when some time such as machines, equipment's and electric bulbs etc. need replacement due to decreased efficiency, failure or breakdown.
The problem of replacement is to decide best policy to determine an age at which the replacement is more economical instead of continuing at increased cost.
What do we replace?Machinery, Tools,Equipment, Inefficient/Dead Human resource.
3
TYPES OF FAILURE
Two types of failure1. Gradual Failure : Tyres, Break shoes2. Sudden Failure:Progressive Eg: Automobile TubesRetrogressive Eg: Human skills and air craft enginesRandom Eg: Vaccum tubes, Electric Bulbs
4
life
Pro
babili
ty o
f outp
ut
Progressive failure
Retrogressive failure Random failure
5
REPLACEMENT SITUATIONS Due to failure of machine or expected to fail
shortly Availability of new technology.
Why we do Replacement? To minimize the maintenance cost To maximize the effective money utilization To increase efficiency
6
ASSUMPTIONS OF REPLACEMENT THEORY
Quality of output remain constant Replacement and maintenance cost remain
constant. Operational efficiency of equipment remain
constant. There is not any change in the tech of asset
under consideration.
7
REPLACEMENTS OF ITEMS THAT FAILS WITH TIME
When ignoring the changes in the value of money-The item should be replaced when the average annual cost to date becomes equal to the current maintenance cost.
When considering the changes in the value of money-
(a) The machine should be replaced if the next period’s cost is greater than the weighted average of previous cost.(b) The machine should not be replaced if the next period’s cost is less than the weighted average of previous costs.
8
WHAT IS INVOLVED IN CALCULATION?
Y Year
C Purchasing Cost
S Scrap value
R Maintenance Cost
∑R Cum. Maintains cost
C-S Depreciation
TC Total cost
ATC Average Total cost
9
WHAT IS INVOLVED IN CALCULATION?Year
Y Co
st
C Scrap Val
ue
S Running co
st
R Cumulative Running co
st
∑R
Dep
reciation
(C-S)
Total cost
TC Average total cost
ATC
1
2
3
4
5
6
7
8
9
10
Cost-S
crap=M
aintainance costWHAT IS INVOLVED IN CALCULATION?Year
Y Co
st
C Scrap Val
ue
S Running co
st
R Cumulative Running co
st
∑R Dep
reciation
(C-S)
Total cost
TC Average total cost
ATC
1 10 4 5 -
2 10 3 6 11
3
4
5
6
7
8
9
Maintenance value
Cummulaive mantenance
cost is sum of the two
consecutive R values
11
Cost-S
crap=M
aintainance costWHAT IS INVOLVED IN CALCULATION?Year
Y Co
st
C Scrap Val
ue
S Running co
st
R Cumulative Running co
st
∑R Dep
reciation
(C-S)
Total cost
TC Average total cost
ATC
1 10 4 5 -
2 10 3 6 11 7
3
4
5
6
7
8
9
Cost-Scrap value=Depreciation cost
12
TOTAL COST FORMULA
Total cost=[∑ Rn + (C-S)] =Maintainance cost+Depreciation
Average Total Cost =[∑ Rn + (C-S)]/Y
13
Cost-S
crap=M
aintainance costWHAT IS INVOLVED IN CALCULATION?Year
Y Co
st
C Scrap Val
ue
S Running co
st
R Cumulative Running co
st
∑R Dep
reciation
(C-S)
Total cost
TC Average total cost
ATC
1 10 4 5 -
2 10 3 6 11 7 18
3
4
5
6
7
8
9
Total cost=Cumm. Maintenance cost+
depreciation
14
Cost-S
crap=M
aintainance costWHAT IS INVOLVED IN CALCULATION?Year
Y Co
st
C Scrap Val
ue
S Running co
st
R Cumulative Running co
st
∑R Dep
reciation
(C-S)
Total cost
TC Average total cost
AVC
1 10 4 5 -
2 10 3 6 11 7 18 9
3
4
5
6
7
8
9
Average total cost=TC/Year
15
EXAMPLE: SOLVE IT!!!! The cost of a machine is Rs. 6100/- and its
scrap value is Rs. 100/- The maintenance costs found from experience are as follows:
When should the machine be replaced? Solution: let it is profitable to replace the
machiney after n years. N is determined by average of tc
years 1 2 3 4 5 6 7 8
Maintenance cost
100 250 400 600 900 1200 1600
2000
16
Years Purchase price-scrap value
Annual maint. cost
Cum. MC
Total Cost
Avg. annual cost
1 6000 100 100 6100 6100
2 6000 250 350 6350 3175
3 6000 400 750 6750 2250
4 6000 600 1350 7350 1837.50
5 6000 900 2250 8250 1650
6 6000 1200 3450 9450 1575
7 6000 1600 5050 11050 1578
8 6000 2000 7050 13050 1631
The avg. annual cost is minimum Rs. should be replaced after 6 years of use.(1575/-)
17
GRAPH PLOTED FOR TC; R AND S.
18
QUES 2
A machine owner finds from his past records that the costs per year of maintaining a machine whose purchase price is Ks. 6000 are as given below:
Determine at what age is a replacement due? Ans. Capital cost C = 6000/-. Let it be profitable to replace the. machine after n years. Then n should be determined by the minimum value of Tav•
19
SOLUTION
We observe from the table that avg. annual cost is minimum (Rs. 2700/-). Hence the m/c should replace at the end of 5th year.
20
Type B. Replacement of items whose maintenance costs increase with time and value of money also changes with time.
The machine should be replaced if the next period’s cost is greater than weighted average of previous cost. Discount rate [Present worth factor (PWF)
21
QUES 3
Purchase price of a machine is Rs. 3000/— and its running cost is given in the table below. If should be replaced. the discount rate is 0.90. Find at what age the machine
22
SOLUTION V (DISCOUNT RATE) = 0.90
M/c should be replaced at the end of 5th year.
23
II: REPLACEMENT OF ITEMS WHICH FAIL COMPLETELY
24
II: REPLACEMENT OF ITEMS WHICH FAIL COMPLETELY
Types of replacement
1. Individual replacement- Item is replaced after its failure. Eg: Machine tools, Bus, Planes
2. Group replacement – Decision to be taken when the items are to be replaced irrespective of the fact that items have failed or not. Eg: Light bulbs, radio tubes
25
Group replacement is concerned with those items that either work or fail completely. It often happens that a system contains a large no. of identical low cost items that are increasingly liable to failure with age When the value of individual items is so small that cost of keeping records of individual ages cannot be justified. It may be advantageous to replace all items at fixed intervals. Such a policy is called Group replacement.
Individual replacement: Under this policy an item is replaced immediately after its failure
Group replacement: Under this policy, decision is taken as to when all the items must be replaced irrespective of the fact that the item has failed or have not failed, with the provision of that an item fails before optimal time, it may be replaced individually
26
III: OTHER REPLACEMENT PROBLEMS Replacement policy for items whose
maintenance cost increases with time and money value is not constant
Recruitment and promotion problems of employees
Equipment renewal problem
27
THANK YOU
Top Related