Job sequencing on 3 machines.

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Presentation transcript:

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.

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

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

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

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 13 5 9 B 5 3 7 C 6 4 5 D 7 2 6

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

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

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

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

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

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

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

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

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

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

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 31 33 43 24 28 37 5 8 15 18 23 32 B A C D B A C D B A C D