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Johnson’s Rule

Johnson’s Rule. Johnson’s rule : A procedure that minimizes makespan when scheduling a group of jobs on two workstations. Step 1 . Find the shortest processing time among the jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily.

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Johnson’s Rule

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  1. Johnson’s Rule • Johnson’s rule: A procedure that minimizes makespan when scheduling a group of jobs on two workstations. • Step 1. Find the shortest processing time among the jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily. • Step 2. If the shortest processing time is on workstation 1, schedule the corresponding job as early as possible. If the shortest processing time is on workstation 2, schedule the corresponding job as late as possible. • Step 3. Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.

  2. Time (hr) Motor Workstation 1 Workstation 2 M1 12 22 M2 4 5 M3 5 3 M4 15 16 M5 10 8 Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first. Shortest time is 3 hours at workstation 2, so schedule job M3 last. Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last. Eliminate M1 and the only job remaining to be scheduled is M4. Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next. Example 16.5Johnson’s Ruleat the Morris Machine Co. Sequence = M2 M1 M4 M5 M3

  3. Workstation M2 M1 M4 M5 M3 Idle—available 1 Gantt Chart for the Morris Machine Company Repair Schedule (4) (12) (15) (10) (5) for further work M2 M1 M4 M5 M3 2 Idle Idle (5) (22) (16) (8) (3) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Day Example 16.5Johnson’s Ruleat the Morris Machine Co. The schedule minimizes the idle time of workstation 2 and gives the fastest repair time for all five motors. No other sequence will produce a lower makespan.

  4. Johnson’s 2 M/c Algorithm

  5. Johnson’s 2 M/c AlgorithmOptimal Sequence

  6. Homework Find the Optimal Make-span for the following problems using Johnson's Algorithm

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