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1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
 Year Resale Value Cost of spares Cost of labour 1 2 3 4 5 42,000 30,000 20,400 14,400 9,650 4,000 4,270 4,880 5,700 6,800 14,000 16,000 18,000 21,000 25,000

Determine the optimum period for replacement of the machine.

Solution:
The data collected in running a machine,

 Year Resale Value Cost of spares Cost of labour 1 2 3 4 5 42,000 30,000 20,400 14,400 9,650 4,000 4,270 4,880 5,700 6,800 14,000 16,000 18,000 21,000 25,000

The costs of spares and labour, together, determine the running cost

The running costs and resale price of the machine in successive years

 Year Resale Value Running Cost 1 2 3 4 5 42,000 30,000 20,400 14,400 9,650 18,000 20,270 22,880 26,700 31,800

In order to determine the optimal time n when the machine should be replaced, we first calculate the average cost per year during the life of the machine,

 Yearn(1) Running CostR(n)(2) Cummulative Running CostSigma R(n)(3) Resale ValueS(4) Depritiation CostC-S(5)=60,000-(4) Total CostTC(6)=(3)+(5) Average Total CostATC_n(7)=(5)/(1) 1 18,000 18,000 18000 = 0 + 18000(3) = Previous(3) + (2) 42,000 18,000 18000 = 60000 - 42000(5)=60000-(4) 36,000 36000 = 18000 + 18000(6)=(3)+(5) 36,000 36000 = 36000 / 1(7)=(5)/(1) 2 20,270 38,270 38270 = 18000 + 20270(3) = Previous(3) + (2) 30,000 30,000 30000 = 60000 - 30000(5)=60000-(4) 68,270 68270 = 38270 + 30000(6)=(3)+(5) 34,135 34135 = 68270 / 2(7)=(5)/(1) 3 22,880 61,150 61150 = 38270 + 22880(3) = Previous(3) + (2) 20,400 39,600 39600 = 60000 - 20400(5)=60000-(4) 100,750 100750 = 61150 + 39600(6)=(3)+(5) 33,583.33 33583.33 = 100750 / 3(7)=(5)/(1) 4 26,700 87,850 87850 = 61150 + 26700(3) = Previous(3) + (2) 14,400 45,600 45600 = 60000 - 14400(5)=60000-(4) 133,450 133450 = 87850 + 45600(6)=(3)+(5) 33,362.5 33362.5 = 133450 / 4(7)=(5)/(1) 5 31,800 119,650 119650 = 87850 + 31800(3) = Previous(3) + (2) 9,650 50,350 50350 = 60000 - 9650(5)=60000-(4) 170,000 170000 = 119650 + 50350(6)=(3)+(5) 34,000 34000 = 170000 / 5(7)=(5)/(1)

The calculations in table show that the average cost is lowest during the 4^(th) year (Rs 33,362.5).

Hence, the machine should be replaced after every 4^(th) years, otherwise the average cost per year for running the machine would start increasing.

This material is intended as a summary. Use your textbook for detail explanation.
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