Scheduling n Jobs × 3 Machines using Jackson's Rule

For sequencing and scheduling n jobs on three machines, Jackson proposed a simple rule by which the n × 3 is converted to n × 2 model for preparing the sequence. And then schedule may be prepared as usually for the three machines individually either by time chart or Gantt chart.

For converting the n × 3 to n × 2 the given problem has to satisfy one or both of the following conditions.

Condition 1

The minimum process time among all the jobs to be performed on first machine is greater than or equal to the maximum process time among the jobs to be performed on second machine.

Condition 2

The minimum process time among all the jobs to be performed on third machine is greater than or equal to the maximum process time among the jobs to be performed on second machine.

(In other words the maximum of second machine is greater than or equal to the minimum of first or/and third machine timings).

If one or both of the above conditions is/are satisfied the 3 × n sequencing problem is converted to 2 × n sequencing problem by adding the job timings of first machine with the corresponding job timings of second machine to make as first work center and similarly adding job timings of second machine with their respective job timings of third machine to make it as second work center. Now, the sequencing is made for the two work centers with these new timings according to Johnson's rule.

After finding the sequence, the Gantt chart and time chart calculations are done by considering three machines with the timings given in the original problem.