question archive The normal cost of the spare part is birr100 when the spare part is not available, the cost of rush purchase and the cost of down time of machine is birr1000, determine the optimum number of spare parts to be stocked for failure rate of spare part of a machine shown in the table
The normal cost of the spare part is birr100 when the spare part is not available, the cost of rush purchase and the cost of down time of machine is birr1000, determine the optimum number of spare parts to be stocked for failure rate of spare part of a machine shown in the table
Subject:Operations ManagementPrice:4.87 Bought7
The normal cost of the spare part is birr100 when the spare part is not available, the cost of rush purchase and the cost of down time of machine is birr1000, determine the optimum number of spare parts to be stocked for failure rate of spare part of a machine shown in the table.
Number of failures
Probability (P)
0
0.4
1
0.2
2
0.25
3
0.15
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Answer:
The optimum quantity of spare parts to be ordered = 3
Step-by-step explanation
Normal cost of the spare par or Cost of overstocking, Co = 100
Cost of a rush purchase and the cost of machine's downtime or cost of underage, Cu = 1,000
Critical Ratio = Cu/ Co + Cu
CR = 1,000/(100 + 1,000) = 0.91
Cumulative probability for a number of failures 'x' = sum of probability of all failures less than or equal to 'x'
The optimal order of spare parts for which the minimum cost is incurred is for the minimum number of failures for which the cumulative probability > = Critical Ratio
Thus, the optimum quantity of spare parts to be ordered = 3
PFA
