GATE ME 2022 Set 2 — Question 41
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Industrial Engineering → Production Planning & Control → Scheduling & Job Sequencing
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Question
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 | 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 |
Correct answer
(B) 33
Solution
Using Johnson's Rule for sequencing jobs on 2 machines:
1.Min time is 1 hr (P7 on Polishing) P7 is last.
2.Next min is 2 hr (P2 on Polishing) P2 is second last.
3.Next min is 3 hr (P3 on Milling) P3 is first.
4.Next min is 4 hr (P4 on Milling) P4 is second.
5.Next min is 4 hr (P6 on Polishing) P6 is third last.
6.Next min is 5 hr (P5 on Milling) P5 is third.
7.Remaining is P1.
Optimal Sequence: P3 - P4 - P5 - P1 - P6 - P2 - P7Calculation of completion time:- P3: Milling (0-3), Polishing (3-7)
- P4: Milling (3-7), Polishing (7-13)
- P5: Milling (7-12), Polishing (13-20)
- P1: Milling (12-20), Polishing (20-26)
- P6: Milling (20-26), Polishing (26-30)
- P2: Milling (26-29), Polishing (30-32)
- P7: Milling (29-31), Polishing (32-33)
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