Find solution of Processing 6 Jobs Through 3 Machines Problem
| Job | 1 | 2 | 3 | 4 | 5 | 6 |
| Machine-1 | 8 | 3 | 7 | 2 | 5 | 1 |
| Machine-2 | 3 | 4 | 5 | 2 | 1 | 6 |
| Machine-3 | 8 | 7 | 6 | 9 | 10 | 9 |
Solution:
| Job | 1 | 2 | 3 | 4 | 5 | 6 |
|---|
| Machine `M_1` | 8 | 3 | 7 | 2 | 5 | 1 |
|---|
| Machine `M_2` | 3 | 4 | 5 | 2 | 1 | 6 |
|---|
| Machine `M_3` | 8 | 7 | 6 | 9 | 10 | 9 |
|---|
Since any of condition `min{T_(1j)} >= max{T_(ij)}` and/or `min{T_(mj)} >= max{T_(ij)}`, for j=2,3,...,m-1 is satisfied.
So given problem can be converted to 2-machine problem.
Machine-G
Machine-H
1. The smallest processing time is 4 hour for job 4 on Machine-G. So job 4 will be processed first.
2. The next smallest processing time is 6 hour for job 5 on Machine-G. So job 5 will be processed after job 4.
3. The next smallest processing time is 7 hour for job 2,6 on Machine-G and for this jobs 15 is largest on Machine-H. So job 6 will be processed after job 5.
4. The next smallest processing time is 7 hour for job 2 on Machine-G. So job 2 will be processed after job 6.
5. The next smallest processing time is 11 hour for job 1 on Machine-G. So job 1 will be processed after job 2.
6. The next smallest processing time is 11 hour for job 3 on Machine-H. So job 3 will be processed last.
According to Johanson's algorithm, the optimal sequence is as below
| Job | `M_1`
In time | `M_1`
Out time | `M_2`
In time | `M_2`
Out time | `M_3`
In time | `M_3`
Out time | Idle time
`M_2` | Idle time
`M_3` |
| 4 | 0 | 0 + 2 = 2 | 2 | 2 + 2 = 4 | 4 | 4 + 9 = 13 | 2 | 4 |
| 5 | 2 | 2 + 5 = 7 | 7 | 7 + 1 = 8 | 13 | 13 + 10 = 23 | 3 | - |
| 6 | 7 | 7 + 1 = 8 | 8 | 8 + 6 = 14 | 23 | 23 + 9 = 32 | - | - |
| 2 | 8 | 8 + 3 = 11 | 14 | 14 + 4 = 18 | 32 | 32 + 7 = 39 | - | - |
| 1 | 11 | 11 + 8 = 19 | 19 | 19 + 3 = 22 | 39 | 39 + 8 = 47 | 1 | - |
| 3 | 19 | 19 + 7 = 26 | 26 | 26 + 5 = 31 | 47 | 47 + 6 = 53 | 4 | - |
The total minimum elapsed time = 53
Idle time for Machine-1
`=53 - 26`
`=27`
Idle time for Machine-2
`=(2)+(7-4)+(19-18)+(26-22)+(53-31)`
`=2+3+1+4+22`
`=32`
Idle time for Machine-3
`=(4)+(53-53)`
`=4+0`
`=4`
This material is intended as a summary. Use your textbook for detail explanation.
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