Johnson's rule
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. 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.
- 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.
If there are three work centers, Johnson's rules can still be applied if the minimum processing time in the first 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.| Job | Work center A | Work center B |
| A | 3.2 | 4.2 |
| B | 4.7 | 1.5 |
| C | 2.2 | 5.0 |
| D | 5.8 | 4.0 |
| E | 3.1 | 2.8 |
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.