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7). Consider the following data on jobs waiting to be scheduled on two machines in serial.

Proc Time
Job Machine 1 Machine 2
A 5 8
B 3 9
C 8 7
D 7 2
E 4 6

Using Johnson's Rule to sequence the jobs, what would be the correct sequence for processing the jobs?

11) Consider the following data on jobs waiting to be scheduled on two machines in serial.
Proc Time
Job Machine 1 Machine 2
A 5 2
B 9 3
C 8 7
D 5 4
E 9 6

These jobs are sequenced by a scheduler in the following order: C E D B A. What will be the total flowtime (or makespan) for all of the jobs to be processed on both machines (from start of first job on first machine until completion of last job on second machine)?

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7). Consider the following data on jobs waiting to be scheduled on two machines in serial.

Using Johnson's Rule to sequence the jobs, what would be the correct sequence for processing the jobs?
Solution procedure:
Step 1 Select the SPT (SHORTEST PROCESSING TIME) from the list and identify the job.
Step 2 If the SPT is for the first processing facilities, schedule the corresponding job as early as possible. If it is for the second processing facilities, schedule the job as late as possible.
Step 3 Repeat Steps 2 and 3 until all jobs are scheduled.

SPT= 2 days for Job D . This is on machine 2 . Schedule D as the last job. (Step 2).
- - - D.

In Jobs A,B,C,E SPT = 3 for Job B. This is on machine 1. Schedule B as the first job.
B - - - D.

In jobs A,C, E SPT= 4 for Job E. This is on machine 1. Schedule E as the second job.
B E - - D.

In jobs A,C SPT= 5 for Job A. This is on machine 1. Schedule A as the third job.
B E A - D.

The only job left is C. Schedule it as the fourth job ( the only place left).

Thus the sequence is BEACD

sequence Start day on Machine 1 Process Time on Machine1 End day on Machine 1 Start day on Machine 2 Process Time on Machine2 End day on Machine 2
B 1 3 3 4 9 12
E 4 4 7 13 6 18
A 8 5 12 19 8 26
C 13 8 20 27 7 33
D 21 7 27 34 2 35

11) Consider the following data on jobs waiting to be scheduled on two machines in serial.

These jobs are sequenced by a scheduler in the following order: C E D B A. What will be the total flowtime (or makespan) for all of the jobs to be processed on both machines (from start of first job on first machine until completion of last job on second machine)?

sequence Start day on Machine 1 Process Time on Machine1 End day on Machine 1 Start day on Machine 2 Process Time on Machine2 End day on Machine 2
C 1 8 8 9 7 15
E 9 9 17 18 6 23
D 18 5 22 24 4 27
B 23 9 31 32 3 34
A 32 5 36 37 2 38

Johnson's Rule (n jobs/2 machines case)
Objective: To sequence n jobs through two processing facilities to minimize the makespan (total processing time) given that all jobs follow the same flow pattern through the facilities.
Solution procedure:
Step 1 List the operations time for each job on both processing facilities.
Step 2 Select the SPT (SHORTEST PROCESSING TIME) from the list and identify the job.
Step 3 If the SPT is for the first processing facilities, schedule the corresponding job as early as possible. If it is for the second processing facilities, schedule the job as late as possible.
Step 4 Repeat Steps 2 and 3 until all jobs are scheduled.
Step 5 Compute the makespan.

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