Johnson’s Rule in Production Planning and Control

Johnson’s Rule is a sequencing heuristic used in Operations Management to minimize the total elapsed time (makespan) for processing a set of jobs through two machines arranged in a fixed order.

It was developed by S. M. Johnson in 1954 and is widely applied in flow shop scheduling problems.

📌 Problem Setting (Two-Machine Flow Shop)

• There are n jobs

• Each job must be processed on:

  • Machine 1 (M1) first

  • Then Machine 2 (M2)

• Processing times are known and deterministic

• Objective: Minimize total completion time (makespan)

📌 Johnson’s Rule – Algorithm Steps

1. List all jobs with their processing times on M1 and M2.

2. Find the smallest processing time among all remaining jobs (consider both machines).

3. If the smallest time belongs to:

   • Machine 1 → Schedule that job as early as possible.

   • Machine 2 → Schedule that job as late as possible.

4. Remove that job from the list.

5. Repeat until all jobs are scheduled.

📌 Logic Behind the Rule

• Jobs that are faster on Machine 1 should start early to prevent idle time on Machine 2.

• Jobs that are faster on Machine 2 should be delayed to avoid bottlenecks.

• The rule balances machine utilization and reduces waiting time.