Johnson's Rule

Johnson's Rule is a sequencing method in Intro to Industrial Engineering for ordering jobs on two machines so the total completion time, or makespan, is as small as possible.

What is Johnson's Rule?

Johnson's Rule is a two-machine scheduling algorithm used in Intro to Industrial Engineering to decide the best order for a set of jobs moving through a job shop or flow shop. Its goal is to minimize makespan, which is the total time needed to finish every job.

The rule works by looking at each job's processing time on Machine 1 and Machine 2, then placing jobs according to the smallest times. If a job is shorter on Machine 1 than on Machine 2, it belongs as early as possible in the sequence. If a job is shorter on Machine 2, it belongs as late as possible.

That basic idea sounds simple, but it solves a real scheduling problem: machines can sit idle while waiting for jobs to arrive, or jobs can pile up behind a busy machine. Johnson's Rule reduces that wasted time by arranging jobs so the flow through the two machines is smoother.

A common way to apply it is to make a list of all jobs, find the smallest remaining processing time, and place that job either at the front or the back of the sequence depending on which machine has the smaller time. Then you repeat the process until every job is placed. The final order is the sequence you would follow on the shop floor or in a scheduling problem.

Here is a compact example. Suppose Job A takes 2 hours on Machine 1 and 7 on Machine 2, Job B takes 6 and 3, and Job C takes 4 and 5. Job A goes near the front because its Machine 1 time is smaller, Job B goes near the back because its Machine 2 time is smaller, and Job C fits in the remaining middle position. The result is not random, it is built to keep the two-machine system moving with less waiting.

Johnson's Rule applies cleanly only when every job follows the same two-machine route. If the problem adds a third machine, you usually need a different method or a transformation of the data before scheduling.

Why Johnson's Rule matters in Intro to Industrial Engineering

Johnson's Rule shows how industrial engineering turns a messy production question into a clear decision procedure. Instead of guessing which job should go first, you use processing-time data to build a sequence that lowers the total completion time for the whole batch.

That matters because scheduling affects machine idle time, work-in-process inventory, and how late finished jobs reach the next step in a process. In a job shop, even a small change in order can create a bottleneck at one machine and leave the other one waiting. Johnson's Rule gives you a structured way to compare orders instead of relying on intuition.

It also connects directly to bigger ideas in the course. When you study job shop scheduling, bottleneck analysis, or makespan, Johnson's Rule is one of the first concrete methods that shows how optimization works in practice. It is simple enough to do by hand in class, but the logic behind it is the same logic used in more advanced scheduling tools.

You will also see why the assumptions matter. The rule is powerful because it fits a specific environment, two machines in series with jobs following the same route. Once the setup changes, the same rule may no longer produce the best schedule, which is a good reminder that industrial engineering methods depend on the system you are modeling.

How Johnson's Rule connects across the course

Makespan

Johnson's Rule is built to minimize makespan, so these two terms almost always show up together. Makespan is the total time from the start of the first job to the finish of the last job, and Johnson's Rule is one method for shrinking that span in a two-machine schedule.

Flow Shop Scheduling

Johnson's Rule is a special case of flow shop scheduling. In a flow shop, every job follows the same machine order, and Johnson's Rule gives you an efficient sequence when that flow shop has exactly two machines.

Job Shop Scheduling

Job shop scheduling covers a wider set of routing problems, often with different job paths and more flexible machine use. Johnson's Rule is simpler than most job shop methods, so it is useful for seeing the basic logic of sequencing before the problems get more complex.

Bottleneck Analysis

Johnson's Rule can reduce waiting around a bottleneck by choosing an order that keeps both machines busy more evenly. If one machine is much slower than the other, sequencing alone may not fix the problem, but it can still make the bottleneck less damaging.

Is Johnson's Rule on the Intro to Industrial Engineering exam?

A scheduling problem will usually give you processing times for several jobs on two machines and ask for the sequence that minimizes completion time. Your job is to apply the rule correctly, not just name it. You sort jobs by the shortest processing times, place jobs with smaller Machine 1 times at the front, place jobs with smaller Machine 2 times at the back, and then write the final sequence in order.

You may also need to explain why that order makes sense in terms of idle time or makespan. A common mistake is putting every short job first, even when the rule says some of them belong at the end because their smaller time is on Machine 2. Another mistake is trying to use Johnson's Rule when the problem has three machines and no reduction has been given. If the setup is not two machines in series, pause before applying it.

Johnson's Rule vs Flow Shop Scheduling

Johnson's Rule is not the same thing as flow shop scheduling. Flow shop scheduling is the broader scheduling setup where every job follows the same machine order, while Johnson's Rule is a specific method for finding the best sequence in a two-machine flow shop.

Key things to remember about Johnson's Rule

• Johnson's Rule is a two-machine sequencing method that orders jobs to minimize makespan.

• Jobs with a smaller processing time on Machine 1 go toward the front, and jobs with a smaller processing time on Machine 2 go toward the back.

• The rule is designed to reduce idle time and keep the two-machine system moving smoothly.

• It works best in a flow shop where every job follows the same two-machine path.

• If the problem has more than two machines, you usually need a different scheduling method.

Frequently asked questions about Johnson's Rule

What is Johnson's Rule in Intro to Industrial Engineering?

Johnson's Rule is a sequencing algorithm for two-machine scheduling problems. You use it to arrange jobs so the total time to finish all of them, called makespan, is as small as possible.

How do you apply Johnson's Rule?

List each job's processing time on both machines, then find the smallest time among the remaining jobs. If that smallest time is on Machine 1, place the job at the front of the sequence. If it is on Machine 2, place it at the back.

Is Johnson's Rule the same as flow shop scheduling?

No. Flow shop scheduling is the problem setup, where all jobs move through machines in the same order. Johnson's Rule is one method for solving a very specific version of that problem with exactly two machines.

Can Johnson's Rule be used for three machines?

Not directly in the basic form. The rule is made for two-machine systems, so a three-machine problem usually needs another approach unless your instructor gives a special reduction or simplification.