Practice Problem: Chapter 15, Short Term Scheduling
Problem 1:
Assume that Susan is a sorority pledge coordinator with four jobs and only three pledges.
The table below gives the expected time for each pledge to do each job.
Job 1
Job 2
Job 3
Job 4
Alice
4
9
3
8
Barbara
7
8
2
6
Jennifer
3
4
5
7
If she wishes to minimize the time taken, to whom should she assign which job?
Problem 2:
A custom furniture shop has the five jobs below to be done and they are unsure how to
sequence them through the shop.
Job
Days to Finish
Date Promised
(in Days from Today)
A
2
5
B
8
8
C
6
12
D
4
10
E
1
4
Compare the effect of the scheduling methods (a) FCFS (first come, first served), (b)
EDD (earliest due date), and (c) SPT (smallest processing time).
1
Problem 3:
A firm has the following six jobs waiting to be processed:
Job
Hours to Process
Time Due
#407
2
7
#281
8
16
#306
4
4
#429
10
17
#038
5
15
#998
12
18
Develop the appropriate sequencing for these jobs using the Critical Ratio criteria.
Problem 4:
Our furniture manufacturer has the following five jobs that must go through the two work
centers in the table below:
Job
Hours Required
Varnishing (Center 1)
Painting (Center 2)
R
4
5
S
17
7
T
14
12
U
9
2
V
11
6
What is the appropriate sequence for these jobs?
2
ANSWERS
Problem 1:
First, begin with the following assignment table:
Job 1
Job 2
Job 3
Job 4
Alice
4
9
3
8
Barbara
7
8
2
6
Jennifer
3
4
5
7
Dummy
0
0
0
0
Note: The “dummy” must be added because we have four jobs and only three people.
Solve this table for the set of assignments giving the minimum total job time.
Your final table should look like:
Job 1
Job 2
Job 3
Job 4
Alice
0
4
0
3
Barbara
4
4
0
2
Jennifer
0
0
3
3
Dummy
1
0
2
0
The set of optimal assignments would then be:
Alice – Job 1
Barbara – Job 3
Jennifer – Job 2
Dummy – Job 4
Note that Job 4 does not get done since it is assigned to the “Dummy.”
3
Problem 2:
(a)
FCFS
Sequence
Process Time
Flow Time
Due Date
Lateness
A
2
2
5
0
B
8
10
8
2
C
6
16
12
4
D
4
20
10
10
E
1
21
4
17
TOTALS
21
69
Average completion time = 69/5 = 13.8 days
Average number of jobs in the system = 69/21 = 3.29 jobs
Average lateness = 33/5 = 6.6 days
Utilization = 21/69 = 30.4%
4
33
(b)
EDD
Sequence
Process Time
Flow Time
Due Date
Lateness
E
1
1
4
0
A
2
3
5
0
B
8
11
8
3
D
4
15
10
5
C
6
21
12
9
TOTALS
21
51
17
Average completion time = 51/5 = 10.2 days
Average number of jobs in the system = 51/21 = 2.43 jobs
Average lateness = 17/5 = 3.4 days
Utilization = 21/51 = 41.2%
(c)
SPT
Sequence
Process Time
Flow Time
Due Date
Lateness
E
1
1
4
0
A
2
3
5
0
D
4
7
10
0
C
6
13
12
1
B
8
21
8
13
TOTALS
21
45
5
14
Average completion time = 45/5 = 9 days
Average number of jobs in the system = 45/21 = 2.14 jobs
Average lateness = 14/5 = 2.8 days
Utilization = 21/45 = 46.7%
Problem 3:
Job
Hours to Process
Time Due
Computed Critical Ratio
#407
2
7
7/2 = 3.5
#281
8
16
16/8 = 2.0
#306
4
4
4/4 = 1.0
#429
10
17
17/10 = 1.7
#038
5
15
15/5 = 3.0
#998
12
18
18/12 = 1.5
Critical Ratio Sequence
Critical Ratio
#306
1.0
#998
1.5
#429
1.7
#281
2.0
#038
3.0
#407
3.5
6
Problem 4:
7