- 20 Marks
Question
The management of a bank observed that the disruption of the bank ATM services was due to the age of the machines. Data on ATM failure is as follows:
| Year after replacement | 1 | 2 | 3 |
|---|---|---|---|
| Cumulative % of failures | 30% | 75% | 100% |
It was further observed that 1,000 units of these machines are in use nationwide and they can be replaced collectively for N5 million per machine. If replaced individually, they cost N30 million per machine.
You are required to calculate:
a.
i. Average machine life (2 Marks)
ii. Average number of replacements per year (2 Marks)
iii. Cost of individual replacement per year (2 Marks)
iv. Cost of mass replacement at the end of the year (12 Marks)
b. Determine the best replacement strategy (2 Marks)
Answer
Calculation of percentage of failure
a (i) Average machine life
The total cost of group replacement is therefore:
Since the lowest average cost of N14,000 million is obtained in the first year of mass
replacement, it is optimal to have a mass replacement at the end of year one.
The best replacement strategy is the mass replacement since the cost of mass replacement (that is
N14,000 million relatively lower than the cost of individual replacement (that is N15,390
million)
- Tags: ATM Services, Cost Analysis, Machine Life, Replacement Theory, Strategy
- Level: Level 1
- Topic: Operations Research
- Series: MAY 2015
- Uploader: Kwame Aikins