Johnson’s Rule: An Effective Technique for Job Sequencing

In the realm of operations research and production planning, Johnson’s rule stands as a prominent method for optimizing the sequencing of jobs in a two-machine or two-work-center environment. This rule aims to minimize the makespan, which refers to the total time required to complete all jobs, and simultaneously reduce idle time between the two work centers.

Key Facts

  1. Objective: Minimize the makespan and reduce idle time between two work centers.
  2. Application: Johnson’s rule is used in sequencing problems where a number of jobs need to be processed by a finite number of machines.
  3. Conditions: To apply Johnson’s rule, the following conditions must be met:
    • Job times must be known and constant for each job at each work center.
    • Job times must be independent of the job sequence.
    • All jobs must follow the same two-setup work sequence.
    • Job priorities cannot be used.
  4. Steps involved in Johnson’s rule:
    • List all jobs and their processing times on each machine.
    • Select the job with the shortest processing time.
    • If the shortest time is on the first machine, schedule the job first. If it’s on the second machine, schedule it last.
    • Repeat the process for the remaining jobs, working towards the center of the sequence.
  5. Example: Consider a scenario with five jobs and two machines. Using Johnson’s rule, the optimal sequence of processing the jobs would be J4, J3, J1, J2, and J5.
  6. Benefits: Johnson’s rule helps in minimizing the total elapsed time and idle time, leading to improved efficiency in job scheduling.

Objectives of Johnson’s Rule

The primary objectives of Johnson’s rule are threefold:

    1. Minimizing MakespanThe rule seeks to determine a job sequence that results in the shortest possible makespan, thereby reducing the overall production time.

 

    1. Minimizing Idle TimeBy optimizing the job sequence, Johnson’s rule aims to minimize idle time on both machines, ensuring efficient utilization of resources.

 

  1. Minimizing Flow TimeThe rule also considers the flow time, which is the time interval between the start of the first job and the completion of the last job. Minimizing flow time improves production efficiency and throughput.

Conditions for Applying Johnson’s Rule

To successfully apply Johnson’s rule, several conditions must be met:

    • Constant Job TimesThe processing time for each job at each work center must be known and constant. This assumption ensures that the rule can accurately predict the impact of job sequencing on the overall production schedule.

 

    • Independent Job TimesThe processing times of jobs must be independent of the job sequence. This means that the order in which jobs are processed does not affect their individual processing times.

 

    • Identical Job SequenceAll jobs must follow the same two-setup work sequence. This condition implies that the order of operations for each job is fixed and cannot be altered.

 

  • No Job PrioritiesJohnson’s rule assumes that all jobs have equal priority. This means that the sequencing decision is based solely on processing times and not on job importance or urgency.

Steps Involved in Johnson’s Rule

The application of Johnson’s rule involves a systematic four-step process:

    1. Listing Jobs and Processing TimesBegin by listing all jobs and their respective processing times at each work center. This information provides the foundation for the sequencing decision.

 

    1. Identifying the Shortest Processing TimeDetermine the job with the shortest processing time. This job is the starting point for the sequencing process.

 

    1. Scheduling the JobBased on the shortest processing time, schedule the job accordingly. If the shortest time is associated with the first work center, schedule the job first. Conversely, if the shortest time is associated with the second work center, schedule the job last.

 

  1. Repeating the ProcessOnce a job is scheduled, repeat steps 2 and 3 for the remaining jobs. Continue this process, working towards the center of the job sequence, until all jobs are scheduled.

Benefits of Johnson’s Rule

Johnson’s rule offers several notable benefits in job sequencing problems:

    • Minimized Total Elapsed TimeBy optimizing the job sequence, Johnson’s rule effectively reduces the total elapsed time required to complete all jobs, leading to improved production efficiency.

 

    • Reduced Idle TimeThe rule helps minimize idle time on both machines, ensuring that resources are utilized efficiently. This reduction in idle time contributes to increased productivity and cost savings.

 

  • Simplified SchedulingJohnson’s rule provides a straightforward and systematic approach to job sequencing, making it easy to implement and manage. This simplicity facilitates efficient scheduling and reduces the risk of errors.

Conclusion

Johnson’s rule stands as a valuable tool in the field of operations research, enabling the optimization of job sequencing in two-machine or two-work-center environments. By minimizing makespan, reducing idle time, and simplifying scheduling, Johnson’s rule contributes to improved production efficiency, reduced costs, and enhanced productivity.

References

    1. Johnson, S. M. (1954). Optimal Two- and Three-Stage Production Schedules With Set-up Time Included. Naval Research Logistics Quarterly, 1(1), 61–68. https://doi.org/10.1002/nav.3800010110

 

    1. Morton, T. E., & Pentico, D. W. (2001). Heuristic Scheduling Systems: With Applications to Production Systems and Project Management. Springer Science & Business Media.

 

  1. Johnson’s Rule. (n.d.). Kewhl.Tripod.Com. Retrieved November 22, 2022, from https://kewhl.tripod.com/johnson.htm

FAQs

What is Johnson’s rule?

Johnson’s rule is a method for optimizing the sequencing of jobs in a two-machine or two-work-center environment. It aims to minimize the makespan (total completion time) and reduce idle time between the two work centers.

What are the objectives of Johnson’s rule?

The objectives of Johnson’s rule are threefold: minimizing makespan, minimizing idle time, and minimizing flow time (the time interval between the start of the first job and the completion of the last job).

What conditions must be met to apply Johnson’s rule?

To successfully apply Johnson’s rule, several conditions must be met: job times must be known and constant, job times must be independent of the job sequence, all jobs must follow the same two-setup work sequence, and job priorities cannot be used.

What are the steps involved in Johnson’s rule?

Johnson’s rule involves a four-step process: listing jobs and processing times, identifying the shortest processing time, scheduling the job, and repeating the process for the remaining jobs, working towards the center of the job sequence.

What are the benefits of using Johnson’s rule?

Johnson’s rule offers several benefits, including minimized total elapsed time, reduced idle time, simplified scheduling, and improved production efficiency.

Can Johnson’s rule be applied to more than two machines or work centers?

Johnson’s rule is specifically designed for two-machine or two-work-center environments. For more complex scenarios, other scheduling techniques may be more appropriate.

How does Johnson’s rule handle jobs with different processing times at different work centers?

Johnson’s rule considers the processing times of jobs at each work center when determining the optimal job sequence. It selects the job with the shortest processing time, regardless of which work center it belongs to.

What are some limitations of Johnson’s rule?

Johnson’s rule assumes that job times are known and constant, which may not always be the case in real-world scenarios. Additionally, it does not consider job priorities or the possibility of machine breakdowns or other disruptions.

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