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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.

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Presentation on theme: "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."— Presentation transcript:

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 Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first. Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next. Eliminate M1 and the only job remaining to be scheduled is M4. Johnson’s Rule at the Morris Machine Co. Example 16.5 Johnson’s Rule at the Morris Machine Co. Time (hr) MotorWorkstation 1Workstation 2 M11222 M245 M353 M41516 M5108 Sequence = M1M2M3M4M5 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.

3 Workstation M2 (4) M1 (12) M4 (15) M5 (10) M3 (5) Idle—available for further work Day Idle2 M2 (5) M1 (22) M4 (16) M5 (8) M3 (3) Idle 1 Gantt Chart for the Morris Machine Company Repair Schedule 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. Johnson’s Rule at the Morris Machine Co. Example 16.5 Johnson’s Rule at the Morris Machine Co.

4 Johnson’s 2 M/c Algorithm Job A B Schedule

5 Johnson’s 2 M/c Algorithm Optimal Sequence Job Total Dur (A) Dur(B) Start on A End on A Start on B End on B Idle Time

6 Homework Problem 1 Job A B Problem 2 Job A B Find the Optimal Make-span for the following problems using Johnson's Algorithm

7 2 Job m Machine case – Akers Method Total Job1 M/CM1M3M2M5M4M6 Duration Job2 M/CM2M1M6M4M3M5 Duration


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