1. Find solution of Processing 5 Jobs Through 3 Machines Problem
| Job | 1 | 2 | 3 | 4 | 5 |
| Machine-1 | 8 | 10 | 6 | 7 | 11 |
| Machine-2 | 5 | 6 | 2 | 3 | 4 |
| Machine-3 | 4 | 9 | 8 | 6 | 5 |
Solution:
| Job | 1 | 2 | 3 | 4 | 5 |
|---|
| Machine `M_1` | 8 | 10 | 6 | 7 | 11 |
|---|
| Machine `M_2` | 5 | 6 | 2 | 3 | 4 |
|---|
| Machine `M_3` | 4 | 9 | 8 | 6 | 5 |
|---|
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 8 hour for job 3 on Machine-G. So job 3 will be processed first.
2. The next smallest processing time is 9 hour for job 1,4,5 on Machine-H and for this jobs 10 is smallest on Machine-G. So job 4 will be processed last.
3. The next smallest processing time is 9 hour for job 1,5 on Machine-H and for this jobs 13 is smallest on Machine-G. So job 1 will be processed before job 4.
4. The next smallest processing time is 9 hour for job 5 on Machine-H. So job 5 will be processed before job 1.
5. The next smallest processing time is 15 hour for job 2 on Machine-H. So job 2 will be processed before job 5.
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` |
| 3 | 0 | 0 + 6 = 6 | 6 | 6 + 2 = 8 | 8 | 8 + 8 = 16 | 6 | 8 |
| 2 | 6 | 6 + 10 = 16 | 16 | 16 + 6 = 22 | 22 | 22 + 9 = 31 | 8 | 6 |
| 5 | 16 | 16 + 11 = 27 | 27 | 27 + 4 = 31 | 31 | 31 + 5 = 36 | 5 | - |
| 1 | 27 | 27 + 8 = 35 | 35 | 35 + 5 = 40 | 40 | 40 + 4 = 44 | 4 | 4 |
| 4 | 35 | 35 + 7 = 42 | 42 | 42 + 3 = 45 | 45 | 45 + 6 = 51 | 2 | 1 |
The total minimum elapsed time = 51
Idle time for Machine-1
`=51 - 42`
`=9`
Idle time for Machine-2
`=(6)+(16-8)+(27-22)+(35-31)+(42-40)+(51-45)`
`=6+8+5+4+2+6`
`=31`
Idle time for Machine-3
`=(8)+(22-16)+(40-36)+(45-44)+(51-51)`
`=8+6+4+1+0`
`=19`
This material is intended as a summary. Use your textbook for detail explanation.
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