science

Johnson's rule

Johnson's rule is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Johnson's rule rather than just read about it. In short: In operations research, Johnson's rule, named for Selmer M. Johnson, is a method of scheduling jobs in two work centers.

Key takeaways

Johnson's rule belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johnson's rule to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johnson's rule from memory before moving on to harder problems.

Reference excerpt

In operations research, Johnson's rule, named for Selmer M. Johnson, is a method of scheduling jobs in two work centers. Its primary objective is to find an optimal sequence of jobs to reduce makespan (the total amount of time it takes to complete all jobs). It also reduces the amount of idle time between the two work centers. The method minimizes the makespan in the case of two work centers. Furthermore, the method finds the shortest makespan in the case of three work centers if additional constraints are met.

Algorithm The technique requires several preconditions:

The time for each job must be invariant with respect to when it is done. Job times must be independent of the job sequence. All jobs must be processed in the first work center before going through the second work center. All jobs are equally prioritised. Johnson's rule is as follows:

List the jobs and their times at each work center. Select the job with the shortest activity time. If that activity time is for the first work center, then schedule the job first. If that activity time is for the second work center then schedule the job last. Break ties arbitrarily. Eliminate the shortest job from further consideration. Repeat steps 2 and 3, working towards the center of the job schedule until all jobs have been scheduled. Given significant idle time at the second work center (from waiting for the job to be finished at the first work center), job splitting may be used. If there are three work centers, Johnson's rules can still be applied if the minimum processing time in the first (and/or the third) work center is not less than the maximum processing time in the second work center. If so, one can create two virtual work center then apply Johnson's rules like for the two work center case.

Example Each of five jobs needs to go through work center A and B. Find the optimum sequence of jobs using Johnson's rule.

So, the jobs must be processed in the order C → A → D → E → B, and must be processed in the same order on both work centers.

Implementation

Notes

References Morton, Thomas; Pentico, David W. (2001-07-20). Heuristic Scheduling Systems: With Applications to Production Systems and ... - Thomas Morton, David W. Pentico - Google Książki. ISBN 9780471578192. Retrieved 2012-09-26. j

Further reading William J Stevenson, Operations Management 9th Edition, McGraw-Hill/Irwin, 2007

Worked examples

Example 1 — a first encounter with Johnson's rule

Start with the simplest possible case. Write down what Johnson's rule claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johnson's rule before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johnson's rule ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johnson's rule

In research: Johnson's rule appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johnson's rule in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johnson's rule is common in secondary-school and first-year university syllabi. It links to neighbouring topics Operations research, Production planning, so understanding it makes those chapters shorter.
In everyday life: Look for Johnson's rule outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Johnson's rule in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johnson's rule means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johnson's rule out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johnson's rule in simple terms?

In operations research, Johnson's rule, named for Selmer M. Johnson, is a method of scheduling jobs in two work centers.

Why does Johnson's rule matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johnson's rule?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johnson's rule.