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

Using Johnson's rule, we first calculate the "completion time" for each job by adding its processing times at both work centers Sigma and Delta. The table below shows the completion times for all jobs:

Job     | Sigma | Delta | Completion time
--------|-------|-------|----------------
R       | 12    | 14    | 26
S       | 8     | 20    | 28
T       | 10    | 18    | 28
U       | 16    | 12    | 28
V       | 14    | 16    | 30

To apply Johnson's rule, we first choose the job with the smallest completion time at either work center Sigma or Delta. In this case, job S has the smallest completion time at work center Sigma, with a processing time of 8 minutes. Therefore, we schedule job S first. After job S, we need to choose the next job based on its completion times at both work centers. The table below shows the remaining jobs and their new completion times after job S is completed at work center Delta:

Job     | Sigma | Delta | Completion time
--------|-------|-------|----------------
R       | 12    | 22    | 34
T       | 10    | 12    | 22
U       | 16    | 8     | 24
V       | 14    | 12    | 26

Again, we choose the job with the smallest completion time at either work center Sigma or Delta. This time, job T has the smallest completion time at work center Delta, with a processing time of 12 minutes. Therefore, we schedule job T second. After jobs S and T, we continue the process of choosing the next job based on its completion times at both work centers. The table below shows the remaining jobs and their new completion times after jobs S and T are completed:

Job     | Sigma | Delta | Completion time
--------|-------|-------|----------------
R       | 12    | 10    | 22
U       | 16    | 4     | 20
V       | 14    | 6     | 20

At this point, both jobs U and V have the smallest completion time at work center Delta (4 minutes). We can choose either one to schedule next. Let's choose job U. After jobs S, T, and U, the remaining jobs and their new completion times are:

Job     | Sigma | Delta | Completion time
--------|-------|-------|----------------
R       | 12    | 10    | 22
V       | 14    | 2     | 16

Finally, we schedule job V last. Therefore, the optimal sequence of jobs is S-U-T-V-R, and the answer is C. Note that this sequence results in a total completion time of 28+20+18+16+12=94 minutes.

Five Jobs Are Waiting for Processing Through Two Work Centers