Lab # 1
Lab # 1
Lab # 1
Title:
Replacement Theory
Objectives:
The objective of this lab is to solve replacement theory problems using MS Excel.
Apparatus:
MS Excel
Background:
The replacement theory is concerned with the situations that arise when some items such as
machines, electric light bulbs, computers, etc. need replacement due to their decreased
efficiency, failure or break-down. Such decreased efficiency or complete breakdown may either
be gradual or suddenly. The replacement problem arises primarily because of the following
reasons:
• Gradual failure
• Sudden failure.
Gradual Failure:
Gradual failure is progressive in nature, i.e., as the life of an item increases, its operational
efficiency also deteriorates. This results in:
• Increase in running (maintenance and operating) costs.
• Decrease in its productivity.
• Decrease in the resale or salvage value.
Sudden Failure:
This type of failure occurs in items after some period of desired service rather than deterioration
while in service. The period of desired service is not constant but follows some frequency
distribution. Sudden failure may be progressive, retrogressive, or random in nature.
• Progressive failure - If the probability of failure of an item increases with the increase
in its life, then such a failure is called progressive failure. For example, light bulbs and
tubes fail progressively.
• Retrogressive failure - If the probability of failure at the beginning of the life of an item
is more but as time passes the chances of its failure become less, then such failure is
said to be retrogressive.
• Random failure - In this type of failure, the constant probability of failure is associated
with items that fail due to random causes but not related to age. For example, vacuum
tubes in air-born equipment have been found to fail at a rate independent of the age of
the tube.
The replacement situations may be placed into the following two main categories:
• Replacement of capital equipment that deteriorates with time, e.g., machine tools, buses
in transport organization, planes, etc.
• Individual or group replacement of items that fail completely, e.g., light bulbs, tubes,
etc.
Here the term ‘failure’ will be considered in the context of replacement decisions.
So, we want perform the replacement theory problems in excel solver in order to get the desired
results.
Problem 1
Activity:
The cost of a machine is Rs. 6100/- and its scrap value is Rs. 100/- The maintenance cost found
from experience are as follows:
Years 1 2 3 4 5 6 7 8
Maintenance cost 100 250 400 600 900 1200 1600 2000
Solution:
Discussion:
So, the machine should be replaced at the end of the 6th year because average annual
replacement cost is least after 6 years which is Rs.1575/-.
Problem 2
Activity:
A machine owner finds from his past records that the costs per year of maintaining a machine
whose purchase price is Rs. 6000 are as given below:
Years 1 2 3 4 5 6 7 8
Maintenance cost 1000 1200 1400 1800 2300 2800 3400 4000
Cost Resale Price 3000 1500 750 375 200 200 200 200
Solution:
Discussion:
So, the machine should be replaced at the end of the 5th year because average annual
replacement cost is least after 5 years which is Rs.2700/-.
Problem 3
Activity:
A firm is considering replacing equipment whose first cost is 1920, whose scrap value is
negligible at the end of any year. Based on experience, it is found that maintenance cost is zero
during the first year, and it increases by Rs. 100 every year thereafter (if the interest rate is 0%).
Solution:
Discussion:
So, the machine should be replaced at the end of the 6th year because average annual
replacement cost is least after 6 years which is Rs.570/-.
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