Question

Six jobs (1, 2, 3, 4, 5, 6) undergo drilling, followed by reaming operation. The time required for each operation is given as \[ \begin{array}{|c|c|c|} \hline \text{Job} & \text{Drilling (min)} & \text{Reaming (min)} \\ \hline 1 & 30 & 40 \\ 2 & 30 & 15 \\ 3 & 60 & 40 \\ 4 & 20 & 25 \\ 5 & 35 & 28 \\ 6 & 45 & 70 \\ \hline \end{array} \] The sequence of processing the jobs, using the Johnson’s rule, is

• A. 4 – 1 – 6 – 3 – 5 – 2
• B. 4 – 6 – 1 – 5 – 3 – 2
• C. 2 – 1 – 6 – 3 – 5 – 4
• D. 2 – 1 – 3 – 6 – 5 – 4

Hint:

Use Johnson's rule for minimizing total completion time in two-machine scheduling problems by selecting jobs with the shortest operation time in either of the two processes.

Answer 1

The Correct Option is A

- Johnson's rule is used for minimizing makespan in two-machine flow shop scheduling. According to this rule, we need to create two lists: one for the jobs with the shortest drilling time and the other for the shortest reaming time. We then use the rule to determine the job order by selecting the shortest job and alternating between drilling and reaming.
- By applying Johnson's rule, the optimal sequence of jobs is \(4 - 1 - 6 - 3 - 5 - 2\).