Five jobs are waiting for processing through two work centers.Their processing time (in minutes)at each work center is contained in the table below.Each job requires work center Sigma before work center Delta.According to Johnson's rule,what sequence of jobs will minimize the completion time for all jobs?
A)R-S-T-U-V
B)S-V-T-R-U
C)S-U-T-V-R
D)V-R-U-S-T
E)R-V-T-S-U

Question

Five jobs are waiting for processing through two work centers.Their processing time (in minutes)at each work center is contained in the table below.Each job requires work center Sigma before work center Delta.According to Johnson's rule,what sequence of jobs will minimize the completion time for all jobs? 
A)R-S-T-U-V 
B)S-V-T-R-U 
C)S-U-T-V-R 
D)V-R-U-S-T 
E)R-V-T-S-U

Quizplus · Accepted Answer

To apply Johnson's rule, we need to calculate the completion time of each job at each work center. The table below shows the time required for each job at each work center, as well as the time required to complete the job at both work centers.

| Job | Sigma | Delta | Total |
|-----|-------|-------|-------|
| R   | 10    | 15    | 25    |
| S   | 11    | 14    | 25    |
| T   | 12    | 12    | 24    |
| U   | 14    | 13    | 27    |
| V   | 15    | 10    | 25    |

The next step is to find the two jobs with the minimum completion times at both work centers. Based on the table above, the minimum completion times are:

1. Job U: minimum completion time of 13 minutes at work center Delta
2. Job T: minimum completion time of 12 minutes at work center Sigma

We then compare the remaining completion times for these two jobs to determine which job should be scheduled first. The remaining completion times for job U are 14 minutes at work center Sigma and 13 minutes at work center Delta, giving a total remaining time of 27 minutes. The remaining completion times for job T are 12 minutes at work center Delta and 12 minutes at work center Sigma, giving a total remaining time of 24 minutes. Therefore, job T should be scheduled first.

We repeat this process to determine the remaining sequence of jobs. The minimum completion times for the remaining jobs are:

1. Job U: minimum completion time of 13 minutes at work center Delta
2. Job S: minimum completion time of 14 minutes at work center Delta

Comparing the remaining completion times for jobs U and S, we find that job S should be scheduled next. The minimum completion times for the remaining jobs are:

1. Job U: minimum completion time of 14 minutes at work center Sigma
2. Job R: minimum completion time of 15 minutes at work center Sigma
3. Job V: minimum completion time of 10 minutes at work center Delta

Comparing the remaining completion times for jobs U, R, and V, we find that job V should be scheduled next, followed by job R and then job U. Therefore, the optimal sequence of jobs is S-T-V-R-U. This corresponds to choice letter C.

Five Jobs Are Waiting for Processing Through Two Work Centers