Question
A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence – first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below. If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is
Job A B C D E F G H Turning (minutes) 2 4 8 9 7 6 5 10 Grinding (minutes) 6 1 3 7 9 5 2 4
| Job | A | B | C | D | E | F | G | H |
| Turning (minutes) |
2 | 4 | 8 | 9 | 7 | 6 | 5 | 10 |
| Grinding (minutes) |
6 | 1 | 3 | 7 | 9 | 5 | 2 | 4 |
If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is
Options :
A-E-D-F-H-C-G-B
A-D-E-F-H-C-G-B
G-E-D-F-H-C-A-B
B-G-C-H-F-D-E-A
Answer :
A-E-D-F-H-C-G-B
Solution :
By Johnson’s rule of sequencing
1) Mark the minimum time consuming operation for each process
| Turning (x) | Grinding (y) | |
| A | 2 | 6 |
| B | 4 | 1 |
| C | 8 | 3 |
| D | 9 | 7 |
| E | 7 | 9 |
| F | 6 | 5 |
| G | 5 | 2 |
| H | 10 | 4 |
2) It is mentioned in problem to first process turning operation.
Perform that job in machine x which has minimum time consumption.
It is A – E
3) If minimum time is force y then perform that activity from last
Here B is minimum & performed at last.
Final sequence is :
A – E – D – F – H – C – G – B
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