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प्रश्न
There are found jobs to be completed. Each job must go through machines M1 , M2 , M3 in the order M1 - M2 - M3. Processing time in hours is given below. Determine the optimal sequesnce and idle time for machine M1 .
| Jobs | A | B | C | D |
| M1 | 5 | 8 | 7 | 3 |
| M2 | 6 | 7 | 2 | 5 |
| M3 | 7 | 8 | 10 | 9 |
उत्तर
Given ,
| Jobs | A | B | C | D |
| M1 | 5 | 8 | 7 | 3 |
| M2 | 6 | 7 | 2 | 5 |
| M3 | 7 | 8 | 10 | 9 |
Here Min. (M1) = 3 , Min. (M3) = 7 . Max.(M2) = 7 Min. (M3) ≥ Max.(M2)
∴ The problem can be converted into
2 machine , 4 jobs problem.
Let G = M1 + M2 , H = M2 + M3
| A | B | C | D | |
| G | 11 | 15 | 9 | 8 |
| H | 13 | 15 | 12 | 14 |
Here Min . (Gi1 , Hi2 ) = 8
corresponding to machine G , job D.
∴ job D is processed first.
| D |
The problem now reduced to 2 machines , 3 job problem.
Now Min. (Gi1 , Hi2 ) = 9 , corresponding to machine G , job C
∴ job C is processed second.
| D | C |
Here Min . (Gi1 , Hi2 ) = 11 , corresponding to machine G , job A.
∴ job A is processed third.
| D | C | A |
The optimal sequence of jobs is obtained as follows :
| D | C | A | B |
| Job | `"M"_1` | `"M"_2` | `"M"_3` | |||
| Time in | Time out | Time in | Time out | Time in | Time out | |
| D | 0 | 3 | 3 | 8 | 8 | 17 |
| C | 3 | 10 | 10 | 12 | 17 | 27 |
| A | 10 | 15 | 15 | 21 | 27 | 34 |
| B | 15 | 23 | 23 | 30 | 34 | 42 |
The minimum elapsed time = 42 hrs.
Ideal time for `M_1` = 42 – 23 = 19 hrs.
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