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Job sequencing on 3 machines.

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.

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Job sequencing on 3 machines.

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  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 1Mach 2Mach 3 B 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6

  5. Example: 3 machines One of the conditions is met. Duration (hrs.) Job Mach 1Mach 2Mach 3 A 13 5 9 B 5 3 7 C 6 4 5 D 7 2 6

  6. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 13+5 5+9 B 5+3 3+7 C 6+4 4+5 D 7+2 2+6

  7. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 18 14 B 8 10 C 10 9 D 9 8

  8. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 A 18 14 B 8 10 C 10 9 D 9 8 B goes first.

  9. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10 A 18 14 C 10 9 D 9 8 D goes last.

  10. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10 A 18 14 C 10 9 D 9 8 C goes next-to-last.

  11. Example: 3 machines Duration (hrs.) Job Mach 1+2 Mach 2+3 B 8 10 A 18 14 C 10 9 D 9 8 B goes 3rd-to-last.

  12. Ex: 3 machines: Gantt Chart Duration (hrs.) Job Mach 1 Mach 2 Mach 3 B 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6 Time (hrs.) => B B B

  13. Ex: 3 machines: Gantt Chart Duration (hrs.) Job Mach 1 Mach 2 Mach 3 B 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6 Time (hrs.) => B A B A B A

  14. Ex: 3 machines: Gantt Chart Duration (hrs.) Job Mach 1 Mach 2 Mach 3 B 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6 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 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6 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 5 3 7 A 13 5 9 C 6 4 5 D 7 2 6 43 31 33 37 24 28 5 8 15 18 23 32 B A C D B A C D B A C D

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