Page 214 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 10: Sequencing Problems and Replacement Theory

10.5 Consideration of Money Value for Investments on Machines or Notes
Equipments

10.5.1 Replacement Policy Decisions

Replacement policy for items whose maintenance cost increases with time and the money value
changes with constant rate. If the maintenance cost increases with time and the money value
decreases with constant rate, the replacement policy will be:
1. Replace if the next period’s cost is greater than the weighted average cost of the previous
period.

2. Do not replace if next period’s cost is less than the weighted average cost of the previous
period.

How to select the Best Machine?

1. Weighted average cost of each machine is to be computed.
st
nd
2. If the weighted average cost of X [1 machine] is less than X [2 machine] then choose X .
1 2 1
3. If the weighted average cost of X is greater than X than choose machine B.
1 2
4. If the weighted average cost of X and X are equal then both the machines are good.
1 2
Notations used:
n = Year of replacement
R = Running cost
n
V = Present worth factor(PWF)
n–1
n–1
R V = The running costs at discounted rates
n
n–1
R V = Cumulative running costs at discounted rates
n
TC = Total Cost – Capital Cost + R V n–1
n
WAC = Weighted average cost
= 


Example: The following table has the details of 2 machines A and B:

Year Cost at the beginning of the year
Machine A Machine B
1 900 1,400
2 600 100
3 700 700

Find the cost pattern for each machine when money is worth 10% per year and find which
machine is less costly.
Solution:
1. If the future value of money is not considered, then the decision as to which machine is
best is arrived at by comparing the total outlay of both machines which is worked out as
under:

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