GATE 2024 ME – Question 34
A set of jobs $U, V, W, X, Y, Z$ arrive at time $t = 0$ 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.
| Job | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|
| Workstation 1 | 5 | 7 | 3 | 4 | 6 | 8 |
| Workstation 2 | 4 | 6 | 6 | 8 | 5 | 7 |
The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is
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Correct answer: (A) W-X-Z-V-Y-U
Explanation
Johnson's rule gives the sequence with the least makespan for two workstations in series. Jobs whose shortest time is on workstation 1 go first, in increasing order of that time: W (3) and X (4). The remaining jobs, whose shortest time is on workstation 2, go last in decreasing order of that time: Z (7), V (6), Y (5) and U (4). The sequence is W-X-Z-V-Y-U.