If the following jobs are sequenced according to the LPT rule then the mean tardiness (in days)for all jobs is (assume zero for today's date)
A)62 days.
B)12.4 days.
C)15.5 days.
D)25 days

Question

If the following jobs are sequenced according to the LPT rule then the mean tardiness (in days)for all jobs is (assume zero for today's date) 
A)62 days. 
B)12.4 days. 
C)15.5 days. 
D)25 days

Quizplus · Accepted Answer

The LPT (largest processing time) rule sequences jobs in decreasing order of their processing times. The job sequence and their respective processing times and due dates are:

Job D: processing time = 20 days, due date = 24 days
Job C: processing time = 15 days, due date = 33 days
Job E: processing time = 12 days, due date = 44 days
Job A: processing time = 10 days, due date = 55 days
Job B: processing time = 8 days, due date = 60 days

Using LPT rule, the job sequence will be D-C-E-A-B. Using this sequence, we can calculate the tardiness for each job as follows:

Job D tardiness = max(0, 26 - 24) = 2
Job C tardiness = max(0, 28 - 33) = 0
Job E tardiness = max(0, 24 - 44) = 0
Job A tardiness = max(0, 37 - 55) = 0
Job B tardiness = max(0, 57 - 60) = 0

Total tardiness = 2 + 0 + 0 + 0 + 0 = 2
Mean tardiness = total tardiness / number of jobs = 2 / 5 = 0.4 days

Therefore, the best choice is B, with a mean tardiness of 0.4 days, or 12.4 days rounded to the nearest integer.

If the Following Jobs Are Sequenced According to the LPT