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The following table shows jobs to be processed at a machine. Determine the processing sequence that will minimize total number of late jobs.   Job Processing Time (days) Due Date (days)   A 3   4    B 2   5    C 5 10   D 2 11   E 4 13   F 9 20

Question

The following table shows jobs to be processed at a machine. Determine the processing sequence that will minimize total number of late jobs.   Job Processing Time (days) Due Date (days)   A 3   4    B 2   5    C 5 10   D 2 11   E 4 13   F 9 20

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Solution

To minimize the total number of late jobs, we should sequence the jobs in increasing order of their due dates. This is known as the Earliest Due Date (EDD) rule.

Here are the steps to determine the processing sequence:

  1. Arrange the jobs in ascending order of their due dates.

    Job Processing Time (days) Due Date (days)

    A 3 4

    B 2 5

    C 5 10

    D 2 11

    E 4 13

    F 9 20

  2. The sequence of jobs according to the EDD rule is: A, B, C, D, E, F.

  3. Now, calculate the completion time for each job by adding the processing time of the current job to the completion time of the previous job.

    Job Processing Time (days) Due Date (days) Completion Time (days)

    A 3 4 3

    B 2 5 5

    C 5 10 10

    D 2 11 12

    E 4 13 16

    F 9 20 25

  4. Determine if a job is late by comparing its due date with its completion time. If the completion time is greater than the due date, then the job is late.

    Job Processing Time (days) Due Date (days) Completion Time (days) Late

    A 3 4 3 No

    B 2 5 5 No

    C 5 10 10 No

    D 2 11 12 Yes

    E 4 13 16 Yes

    F 9 20 25 Yes

So, the sequence that will minimize the total number of late jobs is A, B, C, D, E, F, with 3 jobs (D, E, F) being late.

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