What is the optimum job sequence for the jobs listed below using Johnson's Rule?
A)e-g-f-d
B)d-g-f-e
C)d-f-g-e
D)e-d-f-g
E)f-e-d-g

Question

What is the optimum job sequence for the jobs listed below using Johnson's Rule? 
A)e-g-f-d 
B)d-g-f-e 
C)d-f-g-e 
D)e-d-f-g 
E)f-e-d-g

Quizplus · Accepted Answer

Johnson's rule is used to minimize the makespan, which is the total time required to complete all the jobs. Based on the processing time of each job on Machine A and B, we can compute the following completion times:

Job D: A=2, B=2, C1=2, C2=4
Job E: A=6, B=6, C1=8, C2=6
Job F: A=1, B=3, C1=9, C2=11
Job G: A=3, B=1, C1=10, C2=12

We start by selecting the job with the minimum completion time on either of the machines. In this case, job F has the minimum completion time on Machine A. Therefore, we schedule job F first. Next, we look for the job with the minimum completion time on the other machine (Machine B). In this case, job D has the minimum completion time on Machine B. Therefore, we schedule job D last. 
The remaining two jobs, E and G, have identical completion times on both machines at 6 and 12. We break the tie by looking at the processing time of each job on Machine A and schedule the job with the shorter processing time first. In this case, job E has a shorter processing time on Machine A than job G (6 vs. 3). Therefore, we schedule job E second, and job G third.
Therefore, the optimum job sequence is: 
C) d-f-g-e

What Is the Optimum Job Sequence for the Jobs Listed