3. The Pohl Pool Company has six jobs waiting to be processed through its liner

Question

3. The Pohl Pool Company has six jobs waiting to be processed through its liner department. Processing can start immediately. Total Remaining Processing Time (Days) Due Date (Days from Now Total Remaining Number of Operation:s Job 13 4 10 12 a. If the slack per operation scheduling rule is used, in what order would the jobs be started? b. What is the mean lateness (in days) of the sequence calculated in question a? c. What is the mean tardiness (in days) of the sequence calculated in question a? d. What is the average number of job in the system using the sequence in question a?

Explanation / Answer

) Lets calculate slack per operation of each job first
Slack per operation = (Due date - Total remaining time) / Total remaining operations
Job Total remaining time Due date Total remaining operations Slack per operation
A 6 11 2 2.5
B 9 13 2 2
C 4 6 3 0.66
D 7 10 3 1
E 7 12 3 1.67
F 3 6 1 3
As per the Slack per operation scheduling rule, Lesser the slack per operation, higher the priority.
So in the ascending order of slack per operation, the scheduling order of jobs would be C-D-E-B-A-F
b. To find the mean lateness, refer to the below table. To calculate lateness, we start the operations in the order found above and calculate how delayed every operation is with respect to the due date.
Lateness = Due date - (Start time +Processing time)
The (start time + processing time) of preceding activity would be the start time of following activity
Mean lateness = Total lateness / Number of operations
Sequence Start Time Processing time Due time Lateness
C 0 4 6 -2
D 4 7 10 1
E 11 7 12 6
B 18 9 13 14
A 27 6 11 22
F 33 3 6 30
TOTAL 71
MEAN 11.833
c. To find the mean tardiness, refer to the below table. Tardiness is similar to lateness except for the fact that if lateness comes out to be negative, then tardiness is taken as zero
Tardiness = Due date - (Start time +Processing time) ; If this comes out to be negative then it should be taken as 0
The (start time + processing time) of preceding activity would be the start time of following activity
Mean tardiness = Total tardiness / Number of operations
Sequence Start Time Processing time Due time Tardiness
C 0 4 6 0
D 4 7 10 1
E 11 7 12 6
B 18 9 13 14
A 27 6 11 22
F 33 3 6 30
TOTAL 73
MEAN 12.167
d. As per the scheduling rule used in question a, the average number of jobs in the system at a point of time would be one

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