Discussion
Parts P1-P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required for carrying out both the operations for all 7 parts is __________ hours.
| Part No. | Milling (hours) | Polishing (hours) |
|---|---|---|
| P1 | 8 | 6 |
| P2 | 3 | 2 |
| P3 | 3 | 4 |
| P4 | 4 | 6 |
| P5 | 5 | 7 |
| P6 | 6 | 4 |
| P7 | 2 | 1 |
Answer: B
The minimum total completion time is 33 hours.
Two machines in a fixed order is the case solved by Johnson's rule: parts whose milling time is less than their polishing time go first, in increasing order of milling time; the rest go last, in decreasing order of polishing time.
- Milling less than polishing: P3 (3, 4), P4 (4, 6), P5 (5, 7), in that order.
- The rest, by decreasing polishing time: P1 (6), P6 (4), P2 (2), P7 (1).
Sequence P3, P4, P5, P1, P6, P2, P7. Milling ends at 3, 7, 12, 20, 26, 29, 31 hours. Each polishing job starts at the later of its milling end and the previous polishing end:
| Part | Polish start | Polish end |
|---|---|---|
| P3 | 3 | 7 |
| P4 | 7 | 13 |
| P5 | 13 | 20 |
| P1 | 20 | 26 |
| P6 | 26 | 30 |
| P2 | 30 | 32 |
| P7 | 32 | 33 |
The last part finishes polishing at 33 hours. 31 is only the total milling time, which ignores the final part's polishing; no sequence can finish in 30 or 32, since Johnson's rule gives the minimum.
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