Replacement Theory In Quantitative Analysis

1. Presented By-
Name : Vilas Bhagwan Adole.
Roll No.: MMS B-01
Specialization: Operations Management.

2. Meaning
Equipments and machines used in industries and in
military deteriorate with time, as a result of which their
efficiency decreases and in turn increases their
maintenance cost.
Hence, there arises a need to formulate a
replacement policy which would enable us in deciding
the age at which the replacement of the old equipment
by new one is most economical than continuation of
old equipment at an increased maintenance cost.

3. Need for Replacement Theory
 The item that has become inefficient with passage
of Time.
The item requires more cost for its maintenance as
age increases.
The item doesn't deteriorate with time but suddenly
fails.
A better/ more efficient design of machine/
equipment has become available in the market.

4. O.R. Methodology of solving replacement problems:
 Identify the items to be replaced & their failure
mechanism
Mechanism
Gradual
Failure
Sudden
Failure
 On the basis of Data
Cost
Depreciation Maintenance

5. Companies Using Replacement theory:-
 Manufacturing – Machine tools, Automotive.
 Construction – Renovation.
 Electronic – Electric parts.
 Service Industries – Retrenchment.

6. Optimum period for Replacement :-

7. Example
The running costs per year and resale values of a
certain equipment whose purchase price is Rs. 6500/-
At what year is the replacement due optimally?
Year 1 2 3 4 5 6 7 8
Running
cost
140
0
1500 1700 2000 2400 2800 3300 3900
Resale
cost
400
0
300
0
220
0
1700 1300 1000 1000 1000

8. Solution

9. Notations used
C – (Capital) Cost of Equipment.
S(t) – Scrap (or Resale) Value.
R(t) – Running (or Maintenance) Cost.
∑R(t) – Cumulative Running Cost.
T – Total Cost.
TA – Average Total Cost

10. Rules of Problem
The Optimum Replacement is calculated according to the
following rules:-
I. If the scrap value of equipment is zero i.e. The
depreciation cost is not given, then replace the
equipment when the maintenance cost become greater
then the current average cost.
II. If you are given the resale value/depreciation cost, the
maintenance cost & the cost of equipment, then the
optimum replacement period is determined by the
minimum value of the average cost to date.