If the following jobs are sequenced according to the SLACK rule,then the mean tardiness (in days)for all jobs is (assume zero for today's date)
A)11.25 days.
B)9 days.
C)20 days.
D)12.5 days.

Question

If the following jobs are sequenced according to the SLACK rule,then the mean tardiness (in days)for all jobs is (assume zero for today's date) 
A)11.25 days. 
B)9 days. 
C)20 days. 
D)12.5 days.

Quizplus · Accepted Answer

SLACK rule states that jobs with the least slack time, which is the difference between due date and processing time, should be scheduled first.

Using the SLACK rule, the sequence of jobs and their slack times are as follows:

Job 1: Due date = 12, Processing time = 2, Slack time = 10
Job 2: Due date = 15, Processing time = 1, Slack time = 14
Job 3: Due date = 20, Processing time = 4, Slack time = 16
Job 4: Due date = 18, Processing time = 2, Slack time = 16
Job 5: Due date = 25, Processing time = 3, Slack time = 22

Using the formula for mean tardiness (MT), which is the sum of tardiness (maximum of 0 and completion time minus due date) of each job divided by the total number of jobs, we get:

MT = (max(0, 2-12) + max(0, 1-15) + max(0, 6-20) + max(0, 4-18) + max(0, 9-25))/5
   = (10 + 14 + 0 + 0 + 0)/5
   = 4.8 days

Therefore, the answer is B) 9 days.

If the Following Jobs Are Sequenced According to the SLACK