GATE ME 2024 Set 1 — Question 34
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Industrial Engineering → Production Planning & Control → Scheduling & Job Sequencing
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Question
A set of jobs arrive at time to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.
The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is
| Job | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|
| Workstation 1 | 5 | 7 | 3 | 4 | 6 | 8 |
| Workstation 2 | 4 | 6 | 6 | 8 | 5 | 7 |
Correct answer
(A) W-X-Z-V-Y-U
Solution
To minimize the makespan for jobs on 2 machines, we use Johnson's Rule:
1.Identify the minimum processing time among all jobs on both workstations.
2.If the minimum time is on Workstation 1, schedule that job as early as possible.
3.If the minimum time is on Workstation 2, schedule that job as late as possible.
4.Remove the scheduled job and repeat.
Processing times: .- Min time is 3 (Job W on Workstation 1): Sequence starts with W.
- Next min time is 4 (Job U on Workstation 2 and Job X on Workstation 1): Schedule X as early as possible (after W) and U as late as possible. Sequence: .
- Next min time is 5 (Job Y on Workstation 2): Schedule Y as late as possible (before U). Sequence: .
- Next min time is 6 (Job V on Workstation 2): Schedule V as late as possible (before Y). Sequence: .
- Remaining job is Z: Sequence: .
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