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Question
A machine operator has to perform two operations, turning and threading on 6 different jobs. The time required to perform these operations (in minutes) for each job is known. Determine the order in which the jobs should be processed in order to minimize the total time required to complete all the jobs. Also find the total processing time and idle times for turning and threading operations.
| Job | 1 | 2 | 3 | 4 | 5 | 6 |
| Time of turning | 3 | 12 | 5 | 2 | 9 | 11 |
| Time for threading | 8 | 10 | 9 | 6 | 3 | 1 |
Solution
| Job | 1 | 2 | 3 | 4 | 5 | 6 |
| Time of turning | 3 | 12 | 5 | 2 | 9 | 11 |
| Time for threading | 8 | 10 | 9 | 6 | 3 | 1 |
Observe that Min (turning, threading) = 1, which corresponds to job 6 on threading machine.
Therefore, job 6 is placed last in sequence.
| 6 |
Then the problem reduces to
| Job | 1 | 2 | 3 | 4 | 5 |
| Time of turning | 3 | 12 | 5 | 2 | 9 |
| Time for threading | 8 | 10 | 9 | 6 | 3 |
Now, Min (turning, threading) = 2, which corresponds to job 4 on turning machine
∴ Job 4 is placed first in sequence.
| 4 | 6 |
Then the problem reduces to
| Job | 1 | 2 | 3 | 5 |
| Time of turning | 3 | 12 | 5 | 9 |
| Time for threading | 8 | 10 | 9 | 3 |
Now, Min (turning, threading) = 3, which corresponds to job 1 on turning and job 5 on threading.
∴ Job 1 is placed second and job 5 is placed second last.
| 4 | 1 | 5 | 6 |
Then the problem reduces to
| Job | 2 | 3 |
| Time of turning | 12 | 5 |
| Time for threading | 10 | 9 |
Now, Min (turning, threading) = 5, which corresponds to job 3 on turning.
∴ Job 3 is placed third on sequence and job 2 on remaining.
∴ Optimal solution is
| 4 | 1 | 3 | 2 | 5 | 6 |
Total elapsed time
| Job | Turning | Threading | ||
| In | Out | In | Out | |
| 4(2, 6) | 0 | 2 | 2 | 8 |
| 1(3, 8) | 2 | 5 | 8 | 16 |
| 3(5, 9) | 5 | 10 | 16 | 25 |
| 2(12, 10) | 10 | 22 | 25 | 35 |
| 5(9, 3) | 22 | 31 | 35 | 38 |
| 6(11, 1) | 31 | 42 | 42 | 43 |
∴ Total elapsed time = 43 mins
Idle time for turning = 43 – 42 = 1 min
Idle time for threading = 2 + 4 = 6 mins.
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