Consider the following three jobs that need to be run on two machines in sequence: A (3 1), B (2 2), and C (1 3), where the run times on the first and second machines are given in parenthesis. In what order should the jobs be run to minimize the total time to complete all three jobs?

Johnson's rule is a technique for minimizing idle time while arranging a set of jobs on two workstations. The following are the steps to find out the order of the job:

Step 1: Among the unscheduled jobs, find the one with the least processing time. If two or more jobs are matched, pick one at random.

Step 2: If the shortest processing time is on workstation 1, schedule the associated job as soon as possible; if the shortest processing time is on workstation 2, arrange the corresponding job as late as possible.

Step 3: Dismiss the final scheduled job from further evaluation. Steps 1 and 2 should be repeated until all jobs have been scheduled.

Choose the job with the least operation time. If the first work center has the lowest operation time, then schedule that project first. If the shortest operating time is for the second work center, schedule that job last. Job C is the shortest on Machine I, thus it will be completed first.

Step 3 should be repeated for each remaining work until the schedule is finished. Now, among the remaining jobs, choose the one with the least operating time. Because Job A is the second shortest on Machine II, it will be completed last of the remaining jobs. Because Jobs C and A are no longer available for scheduling, we may infer that the best sequence is as follows:

C-> B-> A