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?
1 Problem 2: Five jobs are to be done at custom furniture shop:
Job Days Date Promised to Finish (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).
2 Problem 3: The following six jobs are waiting to be processed:
Job Hours Time to Due Process
#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.
3 Problem 4: Five jobs go through two work centers, as shown below:
Job Hours Required
Varnishing Painting (Center 1) (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?
4 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
5 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.”
Problem 2: (A)
FCFS
Sequence Process Flow Due Lateness Time Time Date
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 33
Average completion time 69 / 5 13.8 days
Average number of jobs in the system 69 / 21 3.28 jobs Average lateness 33 / 5 6.6 days
Utilization 21/ 69 30.4%
6 (B)
EDD
Sequence Process Flow Due Lateness Time Time Date
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
Utilization 21/ 51 41.2%
(C)
SPT
Sequence Process Flow Due Lateness Time Time Date
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 14
7 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 Time Computed Process Due 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
8 Critical Critical Ratio Ratio Sequence
#306 1.0
#998 1.5
#429 1.7
#281 2.0
#038 3.0
#407 3.5
Problem 4:
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