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Question
Find the sequence of the following five jobs to be processed on three machines M1 M2, , M3 that will minimize the total elapsed time to complete the tasks . Each job is to be processed in the order M1 - M2 - M3 :
| Jobs | 1 | 2 | 3 | 4 | 5 |
| Machine M1 | 5 | 11 | 5 | 7 | 6 |
| Machine M2 | 1 | 4 | 2 | 5 | 3 |
| Machine M3 | 1 | 5 | 2 | 3 | 4 |
Solution
Min(M1) = 5, Max(M2) = 5, Min(M3) = 1
Min (M1) ≥ Max (M2)
∴ Min(M3) ≥ Max (M2) is satisfied.
G = M1 + M3 and H = M2 + M3
| Jobs | 1 | 2 | 3 | 4 | 5 |
| MG | 6 | 15 | 7 | 12 | 9 |
| MH | 2 | 9 | 4 | 8 | 7 |
∴ The required sequence is
| 2 | 4 | 5 | 3 | 1 |
The table of total elapsed time is as follows:
| Job | Machine (M1) | Machine (M2) | Machine (M3) | |||
| In | Out | In | Out | In | Out | |
| 2 | 0 | 11 | 11 | 15 | 15 | 20 |
| 4 | 11 | 18 | 18 | 23 | 23 | 26 |
| 5 | 18 | 24 | 24 | 27 | 27 | 31 |
| 3 | 24 | 29 | 29 | 31 | 31 | 33 |
| 1 | 29 | 34 | 34 | 35 | 35 | 36 |
Total elapsed time = 36 units.
Idle time for M1 = 2 units
Idle time for M2 = 20 units
Idle time for M3 = 20 units
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