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) none of the above

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) none of the above

Quizplus · Accepted Answer

To apply Johnson's rule, we need to first calculate the "completion time" for each job at each work center by adding up the processing times.

Job | Work Center Sigma | Work Center Delta | Total Completion Time
--- | --- | --- | ---
R | 3 | 7 | 10
S | 9 | 6 | 15
T | 6 | 8 | 14
U | 2 | 5 | 7
V | 5 | 4 | 9

Next, we need to identify the shortest total completion times at both work centers. For work center Sigma, the shortest times are U and R (both take 2 minutes). For work center Delta, the shortest times are V and R (both take 4 minutes). Since R appears in both lists, it must be the first and last job in the sequence (as it requires both work centers).

Next, we can compare U and V to see which comes first in the sequence. U has a total completion time of 7 and V has a total completion time of 9, so U comes before V.

Finally, we need to choose between S and T to come in third in the sequence. S has a total completion time of 15 and T has a total completion time of 14, so T comes before S.

Therefore, the optimal sequence is: R-U-T-V-S.

Five Jobs Are Waiting for Processing Through Two Work Centers