Replacement Theory

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ROLL NO-78

ReplacementTheory

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.

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

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Progressive failure

Retrogressive failure Random failure

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

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.

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.

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

WHAT IS INVOLVED IN CALCULATION?Year

C Scrap Val

S Running co

R Cumulative Running co

reciation

Total cost

TC Average total cost

Cost-S

crap=M

aintainance costWHAT IS INVOLVED IN CALCULATION?Year

C Scrap Val

S Running co

∑R Dep

reciation

Total cost

1 10 4 5 -

2 10 3 6 11

Maintenance value

Cummulaive mantenance

cost is sum of the two

consecutive R values

Cost-S

crap=M

C Scrap Val

S Running co

∑R Dep

reciation

Total cost

1 10 4 5 -

2 10 3 6 11 7

Cost-Scrap value=Depreciation cost

TOTAL COST FORMULA

Total cost=[∑ Rn + (C-S)] =Maintainance cost+Depreciation

Average Total Cost =[∑ Rn + (C-S)]/Y

Cost-S

crap=M

C Scrap Val

S Running co

∑R Dep

reciation

Total cost

1 10 4 5 -

2 10 3 6 11 7 18

Total cost=Cumm. Maintenance cost+

depreciation

Cost-S

crap=M

C Scrap Val

S Running co

∑R Dep

reciation

Total cost

1 10 4 5 -

2 10 3 6 11 7 18 9

Average total cost=TC/Year

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

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/-)

GRAPH PLOTED FOR TC; R AND S.

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•

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.

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)

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

SOLUTION V (DISCOUNT RATE) = 0.90

M/c should be replaced at the end of 5th year.

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

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

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

THANK YOU

Replacement Theory

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