Please show all work. Partial Answer Key: 3. Average flow time: SPT = 16, EDD =
ID: 464339 • Letter: P
Question
Please show all work.
Partial Answer Key:
3. Average flow time: SPT = 16, EDD = 17.333, CR = 20.167
The following jobs are waiting to be processed at the machine center. They are ready to be scheduled today, which is day 20 (day 20 is a work day). Complete the following table. (Show your supporting calculations. Which dispatching rule has the best score for flow time? Which dispatching rule has the best score for utilization metric? Which dispatching rule has the best score for lateness? In other words, number of days till due date for job A = 25 - 20 + 1 = 6.Explanation / Answer
Consider Starting Date is 20, thus job due date for activity A = Date job is due - Starting date + 1
Job
Processing time
Date job is due
Job Due date
A
5
25
6
B
3
30
11
C
4
32
13
D
6
28
9
E
8
34
15
F
6
32
13
Shortest Processing Time (SPT) priority rule:
According to SPT rule the jobs are sequenced according to the processing time, the highest priority is assigned to job with shortest processing time.
Job Sequence by SPT: B-C-A-D-F-E
SPT Rule
Job Sequence
Processing time
Work Begins
Flow Time
Job Due date
Job Lateness
a
b
c = a +b
d
e
B
3
0
3
11
0
C
4
3
7
13
0
A
5
7
12
6
6
D
6
12
18
9
9
F
6
18
24
13
11
E
8
24
32
15
17
Total
32
64
96
43
Average
10.67
16
7.17
Measure of effectiveness of Priority Rule:
a. Average flow time = (total flow time/number of jobs)
Average flow time by SPT rule = 96/5 = 16
b. Utilization metric = Total processing time/total flow time
Utilization metric by SPT rule= 32/96 =33.33%
c. Average number of jobs in system = Total Flow time/Total Processing time
Average number of jobs in system by SPT rule = 96/32 = 3 jobs
d. Average job lateness = Total job lateness/number of jobs
Average job lateness by SPT rule = 43/5 = 7.17
Earliest Due Date (EDD) Priority Rule:
According to EDD rule the jobs are sequenced according to the job due date, the highest priority is assigned to job with earliest due date.
Job Sequence: A-D-B-C-F-E
EDD Rule
Job Sequence
Processing time
Work Begins
Flow Time
Job Due date
Job Lateness
a
b
c = a +b
d
e
A
5
0
5
6
0
D
6
5
11
9
2
B
3
11
14
11
0
C
4
14
18
13
0
F
6
18
24
13
11
E
8
24
32
15
17
Total
32
72
104
67
30
Average
12.00
17.33
11.17
5.00
Measure of effectiveness of Priority Rule:
a. Average flow time = (total flow time/number of jobs)
Average flow time by EDD rule = 104/5 = 17.33
b. Utilization metric = Total processing time/total flow time
Utilization metric by EDD rule= 32/104 =30.76%
c. Average number of jobs in system = Total Flow time/Total Processing time
Average number of jobs in system by EDD rule = 104/32 = 3.25 jobs
D*. Average job lateness = Total job lateness/number of jobs
Average job lateness by EDD rule = 30/5 = 5.00
Critical ratio Priority rule:
Critical ratio (CR) is computed as follows:
CR = (Due date –current time)/Processing time
Job
Processing time
Date job is due
Current Time
CR
Priority order
A
5
25
20
1
1
B
3
30
20
3.33
6
C
4
32
20
3
5
D
6
28
20
1.33
2
E
8
34
20
1.75
3
F
6
32
20
2
4
According to CR rule, the highest priority is given to job with lowest CR.
Sequence: A-D-E-F-C-B
CR Rule
Job Sequence
Processing time
Work Begins
Flow Time
Job Due date
Job Lateness
A
b
c = a +b
d
e
A
5
0
5
6
0
D
6
5
11
9
2
E
8
11
19
15
4
F
6
19
25
13
12
C
4
25
29
13
0
B
3
29
32
11
0
Total
32
89
121
67
18
Average
14.83
20.17
11.17
3.00
Measure of effectiveness of Priority Rule:
a. Average completion time = (total flow time/number of jobs)
Average completion time by CR rule = 121/5 = 20.17
b. Utilization metric = Total processing time/total flow time
Utilization metric by CR rule= 32/121 =26.44%
c. Average number of jobs in system = Total Flow time/Total Processing time
Average number of jobs in system by CR rule = 121/32 = 3.78 jobs
d. Average job lateness = Total job lateness/number of jobs
Average job lateness by CR rule = 18/5 = 3.00.
ANSWER
a.
SPT
EDD
CR
Average flow time
16
17.33
20.17
Average Lateness
7.17
5.00
3.00
Average no. of Jobs
3
3.25
3.78
Utilization
33.33%
30.76%
26.44%
b.
the lowest flow time is 16 days, SPT has the best score for flow time.
c.
The highest score for utilization metric is for sequencing by SPT rule. Thus, SPT rule has best score for utilization metric.
d.
Lowest average lateness is 3.00, CR has best score for lateness.
Job
Processing time
Date job is due
Job Due date
A
5
25
6
B
3
30
11
C
4
32
13
D
6
28
9
E
8
34
15
F
6
32
13
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