GATE ME 2021 Set 1 — Question 38
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Industrial Engineering → Production Planning & Control → Scheduling & Job Sequencing
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Question
A set of jobs A, B, C, D, E, F, G, H arrive at time 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 |
Correct answer
(A) A-E-D-F-H-C-G-B
Solution
To minimize the makespan for jobs on 2 machines, we use Johnson's Rule:
A(2, 6), B(4, 1), C(8, 3), D(9, 7), E(7, 9), F(6, 5), G(5, 2), H(10, 4)Step-by-step scheduling:
1.Identify the minimum processing time among all jobs on both machines.
2.If the minimum time is on the first machine (Turning), schedule that job as early as possible in the sequence.
3.If the minimum time is on the second machine (Grinding), schedule that job as late as possible in the sequence.
4.Remove the scheduled job and repeat the process for the remaining jobs.
Processing times (Turning, Grinding):A(2, 6), B(4, 1), C(8, 3), D(9, 7), E(7, 9), F(6, 5), G(5, 2), H(10, 4)Step-by-step scheduling:
- The minimum time is 1 min for Job B on Grinding (Machine 2). Place B last:
[_, _, _, _, _, _, _, B] - The next minimum is 2 min for Job A on Turning (Machine 1). Place A first:
[A, _, _, _, _, _, _, B] - The next minimum is 2 min for Job G on Grinding (Machine 2). Place G second to last:
[A, _, _, _, _, _, G, B] - The next minimum is 3 min for Job C on Grinding (Machine 2). Place C third to last:
[A, _, _, _, _, C, G, B] - The next minimum is 4 min for Job H on Grinding (Machine 2). Place H fourth to last:
[A, _, _, _, H, C, G, B] - The next minimum is 5 min for Job F on Grinding (Machine 2). Place F fifth to last:
[A, _, _, F, H, C, G, B] - The next minimum is 7 min for Job E on Turning (Machine 1) and Job D on Grinding (Machine 2). Place E as early as possible and D as late as possible in the remaining slots:
[A, E, D, F, H, C, G, B]
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