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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 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.

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**Example 16.5 Johnson’s Rule at the Morris Machine Co.**

Time (hr) Motor Workstation 1 Workstation 2 M M2 4 5 M3 5 3 M M5 10 8 Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next. 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 M1 and the only job remaining to be scheduled is M4. Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last. Sequence = M2 M1 M4 M5 M3 61

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**Example 16.5 Johnson’s Rule at 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. Workstation M2 (4) M1 (12) M4 (15) M5 (10) M3 (5) Idle—available for further work 5 10 15 20 25 30 Day 35 40 45 50 55 60 65 Idle 2 (22) (16) (8) (3) 1 Gantt Chart for the Morris Machine Company Repair Schedule 88

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**Johnson’s 2 M/c Algorithm**

Job 1 2 3 4 5 6 7 8 A 10 B Schedule 1 2 6 8 7 5 4 3

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**Johnson’s 2 M/c Algorithm Optimal Sequence**

Job 1 2 6 8 7 5 4 3 Total Dur (A) 10 54 Dur(B) 48 Start on A 9 14 20 30 36 46 End on A Start on B 12 22 29 35 41 End on B 50 56 Idle Time

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Homework Find the Optimal Make-span for the following problems using Johnson's Algorithm Problem 1 Job 1 2 3 4 5 6 7 8 9 10 A B Problem 2

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**2 Job m Machine case – Akers Method**

1 2 3 4 5 6 Total Job1 M/C M1 M3 M2 M5 M4 M6 Duration 7 9 33 Job2 8 35

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Operations Scheduling Supplement J Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 01.

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