This document discusses optimal replacement strategies for assets that deteriorate over time. It explains that the optimal replacement period is determined by minimizing the average total cost, which includes running costs, salvage value, and new equipment costs. An example is provided of calculating these costs for an asset over 8 years to determine the optimal replacement year, which is the year with the lowest average total cost. Replacement should occur when maintenance costs exceed average costs or when average total costs are minimized.

1. Operations Research
MBA-024

2. REPLACEMENT PROBLEM
UNIT IV

3. Replacement of Assets that
Deteriorate with Time
• If the scrap value of the equipment is zero
(depreciation cost is not given), replace the
equipment when the maintenance cost becomes
greater than the current average cost.
• If the resale value (depreciation cost) is given
along with the maintenance cost and the cost of
equipment, then the optimal replacement period
is determined by the minimum value of the
average cost to date.

4. Example:
The following table gives the running costs per
year and resale values of a certain equipment
whose purchase price is Rs. 65,000. At what year is
the replacement due optimally:
Year: 1 2 3 4 5 6 7 8
Running 14 15 17 20 24 28 33 39

5. Yea
r
Runnin
g
Cost
Salvag
e
Value
1 14,000 40,000
2 15,000 30,000
3 17,000 22,000
4 20,000 17,000
5 24,000 13,000
6 28,000 10,000
7 33,000 10,000
8 39,000 10,000

6. Yea
r
Runnin
g
Cost
Cumulati
ve
Running
Salvag
e
Value
1 14,000 14,000 40,000
2 15,000 29,000 30,000
3 17,000 46,000 22,000
4 20,000 66,000 17,000
5 24,000 90,000 13,000
6 28,000 1,18,000 10,000
7 33,000 1,51,000 10,000
8 39,000 1,90,000 10,000

7. Yea
r
Runnin
g
Cost
Cumulati
ve
Running
Salvag
e
Value
Cost
of
New
1 14,000 14,000 40,000 25,000
2 15,000 29,000 30,000 35,000
3 17,000 46,000 22,000 43,000
4 20,000 66,000 17,000 48,000
5 24,000 90,000 13,000 52,000
6 28,000 1,18,000 10,000 55,000
7 33,000 1,51,000 10,000 55,000
8 39,000 1,90,000 10,000 55,000

8. Yea
r
Runnin
g
Cost
Cumulati
ve
Running
Salvag
e
Value
Cost
of
New
Total
Cost1 14,000 14,000 40,000 25,000 39,000
2 15,000 29,000 30,000 35,000 64,000
3 17,000 46,000 22,000 43,000 89,000
4 20,000 66,000 17,000 48,000 1,14,000
5 24,000 90,000 13,000 52,000 1,42,000
6 28,000 1,18,000 10,000 55,000 1,73,000
7 33,000 1,51,000 10,000 55,000 2,06,000
8 39,000 1,90,000 10,000 55,000 2,45,000

9. Yea
r
Runnin
g
Cost
Cumulati
ve
Running
Salvag
e
Value
Cost
of
New
Total
Cost
Average
Cost1 14,000 14,000 40,000 25,000 39,000 39,000.00
2 15,000 29,000 30,000 35,000 64,000 32,000.00
3 17,000 46,000 22,000 43,000 89,000 29,666.67
4 20,000 66,000 17,000 48,000 1,14,000 28,500.00
5 24,000 90,000 13,000 52,000 1,42,000 28,400.00
6 28,000 1,18,000 10,000 55,000 1,73,000 28,833.33
7 33,000 1,51,000 10,000 55,000 2,06,000 29,428.57
8 39,000 1,90,000 10,000 55,000 2,45,000 30,625.00

10. Yea
r
Runnin
g
Cost
Cumulati
ve
Running
Salvag
e
Value
Cost
of
New
Total
Cost
Average
Cost1 14,000 14,000 40,000 25,000 39,000 39,000.00
2 15,000 29,000 30,000 35,000 64,000 32,000.00
3 17,000 46,000 22,000 43,000 89,000 29,666.67
4 20,000 66,000 17,000 48,000 1,14,000 28,500.00
5 24,000 90,000 13,00 52,000 1,42,00 28,400.0
6 28,000 1,18,000 10,000 55,000 1,73,000 28,833.33
7 33,000 1,51,000 10,000 55,000 2,06,000 29,428.57

11. Replacement of Assets which Fail
Suddenly