The processing sequence for the six jobs shown below using Johnson’s Rule is:
Job
Station 1
Station 2
A 46
B 98
C 105
D 69
E 97
F 1210
Multiple Choice
a-d-f-b-e-c
a-f-d-b-e-c
a-d-f-e-b-c
The correct answer and explanation is :
To apply Johnson’s Rule for sequencing jobs through two workstations (Station 1 and Station 2), we need the processing times for each job at both stations. However, you’ve only provided processing times for one station (presumably Station 1), and there’s no information for Station 2.
To solve the sequencing problem using Johnson’s Rule, we must have processing times for both stations for each job. Here’s how the rule works (with an explanation that assumes both station times are given):
✅ Johnson’s Rule: Step-by-Step Process
Johnson’s Rule is used to minimize total completion time (makespan) for a set of jobs processed on two machines (e.g., Station 1 and Station 2) in the same order.
Steps:
- List all jobs and their processing times on both machines.
- Find the job with the shortest processing time among all jobs across both machines.
- If that shortest time is on Station 1, schedule that job as early as possible.
- If that shortest time is on Station 2, schedule it as late as possible.
- Remove the scheduled job and repeat steps 2–4 for the remaining jobs.
This sequence minimizes idle time and leads to the shortest possible total processing time.
🔍 Your Data Seems Incomplete:
You’ve listed jobs A to F with one column of numbers:
- A: 46
- B: 98
- C: 105
- D: 69
- E: 97
- F: 1210
But these numbers only represent one station. Without the Station 2 times, we can’t accurately apply Johnson’s Rule.
📝 What You Need to Do:
Please provide the processing times for Station 2 for each job, like this:
| Job | Station 1 | Station 2 |
|---|---|---|
| A | 46 | ?? |
| B | 98 | ?? |
| C | 105 | ?? |
| D | 69 | ?? |
| E | 97 | ?? |
| F | 1210 | ?? |
Once both sets of times are given, I can find the correct Johnson’s Rule sequence (and confirm whether a-d-f-b-e-c, etc., is the right answer).
Would you be able to provide the missing Station 2 data?