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N-Jobs 3 Machine Case

Johnson’s algorithm in regard to sequencing jobs can be further extended for using n jobs through 3 machine case. This can be done with the following conditions-

  1. The least processing time for a task on machine M3 is equal to or higher than that of the processing time for an analogous task on M2 machine.
  2. The utmost operation time for a task carried out on a machine M1 is higher than or equal to the highest operation time for a similar task on the M2 machine.

Assumptions

While following the above conditions, there are certain assumptions which need to be made. These presuppositions are-

  1. The operation time for each task on machines – M1, M2, M3, is known.
  2. Each of these jobs is operated on all the above three machines. These are first processed in the chronological order- first on M1, then on M2 and finally on M3.
  • Passing of tasks is strictly prohibited.

In this process, two dummy machines M1 ’ and M3 ’ are presumed in such a way that the operation time of tasks in regard to these machines can be easily calculated.

A job’s processing time on M1 ’ = Total processing time of  (M1 + M2 )

A job’s processing time on M2 ’ = Total processing time of  (M2 + M1 )

Johnson’s algorithm in regard to sequencing jobs is then applied on M1 ’ and M2 ’ for deriving the most advantageous sequencing of tasks.

Students can have a better understanding of these machines and the processing time of tasks once they start practicing some problems based on the same. Refer to the examples and keep the above conditions and assumptions in mind.

 

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