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Model-1.1
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1. A firm is considering the replacement of a machine, whose cost price is Rs 12,200 and its scrap value is Rs 200. From experience the running (maintenance and operating) costs are found to be as follows:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | | Running Cost | 200 | 500 | 800 | 1,200 | 1,800 | 2,500 | 3,200 | 4,000 |
When should the machine be replaced?
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Model-1.2
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1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
| Year | 1 | 2 | 3 | 4 | 5 |
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| Resale Value | 42,000 | 30,000 | 20,400 | 14,400 | 9,650 |
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| Cost of spares | 4,000 | 4,270 | 4,880 | 5,700 | 6,800 |
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| Cost of labour | 14,000 | 16,000 | 18,000 | 21,000 | 25,000 |
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Determine the optimum period for replacement of the machine.
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Model-1.3
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1. Machine A costs Rs 45,000 and its operating costs are estimated to be Rs 1,000 for the first year
increasing by Rs 10,000 per year in the second and subsequent years.
Machine B costs Rs 50,000 and operating costs are Rs 2,000 for the first year, increasing by Rs 4,000 in the second and subsequent years.
If at present we have a machine of type A, should we replace it with B? if so when?
Assume that both machines have no resale value and their future costs are not discounted.
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Model-2
Replacement policy for items whose running cost increases with time but value of money changes constant rate during a period
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1. An engineering company is offered a material handling equipment A. It is priced at
Rs 60,000 includeing cost of installation. The costs for operation and maintenance are estimated to be
Rs 10,000 for each of the first five years, increasing every year by Rs 3,000 in the sixth and subsequent years.
The company expects a return of 10 percent on all its investment. What is the optimal replacement period?
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
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| Running Cost | 10,000 | 10,000 | 10,000 | 10,000 | 10,000 | 13,000 | 16,000 |
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2. A company is buying mini computers. It costs Rs 5 lakh, and its running and maintenance costs are Rs 60,000
for each of the first five years, increasing by Rs 20,000 per year in the sixth and subsequent years.
If the money is worth 10 percent per year, What is the optimal replacement period?
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Model-3
Group replacement policy
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1. A computer contains 10,000 resistors. When any resistor fails, it is replaced. The cost of replacing a resistor
individually is Rs 1 only. If all the resistors are replaced at the same time, the cost per resistor would be
reduced to 35 paise. The percentage of surviving resistors say S(t) at the end of month t and the probability
of failure P(t) during the month t are as follows:
| t | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
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| P(t) | 0 | 0.03 | 0.07 | 0.20 | 0.40 | 0.15 | 0.15 |
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What is the optimal replacement plan?
2. The following mortality rates have been observed for a certain type of fuse:
| t | 0 | 1 | 2 | 3 | 4 | 5 |
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| P(t) | 0 | 0.05 | 0.10 | 0.20 | 0.40 | 0.25 |
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There are 1,000 fuses in use and it costs Rs 5 to replace an individual fuse. If all fuses were replaced
simultaneously it would cost Rs 1.25 per fuse. It is proposed to replace all fuses at fixed intervals of time,
whether or not they have burnt out, and to contiune replacing burnt out fuses as they fail. At what time
intervals should the group replacement be made? Also prove that this optimal policy is superior to the straight
forward policy of replacing each fuse only when it fails.
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