Model Answer
0 min readIntroduction
Line balancing is a critical aspect of operations management, aiming to distribute workload evenly across workstations to minimize bottlenecks and maximize efficiency. In manufacturing environments, it ensures that no single machine or process becomes a constraint on overall production. Effective line balancing reduces work-in-progress inventory, shortens lead times, and lowers production costs. This problem presents a classic scenario where applying a sequencing rule, such as Johnson’s Rule, can optimize the processing order of jobs across two machines to achieve a balanced workload and minimize total completion time.
Applying Johnson’s Rule for Line Balancing
Johnson’s Rule is a simple dispatching rule used to minimize the makespan (total completion time) in a two-machine flow shop. The rule states:
- For jobs with shorter processing times on Machine 1, schedule them earlier.
- For jobs with shorter processing times on Machine 2, schedule them later.
Let's apply this rule to the given jobs:
Step 1: Identify the shortest processing time for each job.
We already have the processing times in the given table. We need to compare the processing times on Machine 1 and Machine 2 for each job.
Step 2: Prioritize Jobs based on Johnson’s Rule.
We will create two lists: one for jobs where Machine 1 processing time is shorter, and another for jobs where Machine 2 processing time is shorter.
- Machine 1 Shorter: Jobs A (2.5 vs 1.5), C (1.1 vs 3.25), F (1.25 vs 4.0)
- Machine 2 Shorter: Jobs B (3.6 vs 2.0), D (2.25 vs 2.75), E (3.75 vs 1.8)
Step 3: Sequence the Jobs.
The sequence will be: Jobs with shorter Machine 1 times, followed by jobs with shorter Machine 2 times. Within each list, jobs are arranged in ascending order of their processing times on the respective machine.
Therefore, the sequence is: C, F, A, E, B, D
Step 4: Calculate Completion Times (Optional, but demonstrates understanding)
We can calculate the completion times for each job to verify the effectiveness of the sequence. This is not explicitly asked for, but strengthens the answer.
| Job | Machine 1 Start | Machine 1 Finish | Machine 2 Start | Machine 2 Finish | Total Time |
|---|---|---|---|---|---|
| C | 0 | 1.1 | 1.1 | 4.35 | 4.35 |
| F | 1.1 | 2.35 | 2.35 | 6.35 | 6.35 |
| A | 2.35 | 4.85 | 4.85 | 6.35 | 6.35 |
| E | 4.85 | 8.6 | 8.6 | 10.4 | 10.4 |
| B | 8.6 | 12.2 | 12.2 | 14.2 | 14.2 |
| D | 12.2 | 14.45 | 14.45 | 17.2 | 17.2 |
The total completion time for all jobs is 17.2 hours.
Limitations
Johnson’s Rule is optimal for two-machine flow shops. For more than two machines, more complex algorithms are required. It also assumes that jobs are processed in the same order on all machines, which may not always be the case.
Conclusion
In conclusion, applying Johnson’s Rule to the given job processing times results in the optimal sequence of C, F, A, E, B, D. This sequence minimizes the makespan and ensures a more balanced workload across the two machines. While this rule is specifically designed for two-machine flow shops, it provides a valuable framework for understanding and addressing line balancing challenges in manufacturing operations. Further optimization might be possible with more sophisticated techniques for multi-machine scenarios.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.