1. Job sequencing on 3 machines.
Two conditions for a easy solution:
1. The smallest duration on machine #1 is at least as great as the largest duration on machine #2.
2. The smallest duration on machine #3 is at least as great as the largest duration on machine #2.

2. Conditions for an easy solution:
T1,smallest >= T2,largest
AND/OR
T3,smallest >= T2,largest

3. The easy solution: how-to...
Add: T1 + T2 & T2 + T3
Use these sums to do Johnson’s rule.

4. Example: 3 machines Duration (hrs.) Job Mach 1 Mach 2 Mach 3 B 5 3 7

5. Example: 3 machines Duration (hrs.) Job Mach 1 Mach 2 Mach 3 A 13 5 9
One of the conditions is met.
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 A B C D

6. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 13+5 5+9

7. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 18 14

8. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 18 14
B goes first.

9. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10
D goes last.

10. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10
C goes next-to-last.

11. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10
B goes 3rd-to-last.

12. Ex: 3 machines: Gantt Chart
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 B A C D
Time (hrs.) => B B B

13. Ex: 3 machines: Gantt Chart
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 B A C D
Time (hrs.) => B A B A B A

14. Ex: 3 machines: Gantt Chart
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 B A C D
Time (hrs.) => B A C B A C B A C

15. Ex: 3 machines: Gantt Chart
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 B A C D
Time (hrs.) => B A C D B A C D B A C D

16. Ex: 3 machines: Gantt Chart
Duration (hrs.)
Job Mach 1 Mach 2 Mach 3 B A C D 31 33 43 24 28 37 5 8 15 18 23 32 B A C D B A C D B A C D