36
76) Use the information in the table and sequence the six jobs using the critical ratio algorithm. Calculate
the average flow times and average lateness. All jobs arrived at time zero and are ready at time zero.
Job
Production
Time
Due Date
A
10
20
B
15
25
C
17
22
D
20
31
E
16
20
F
20
24
Answer:
Job
Date
Received
Prod
Time
Due
Date
Critical
Ratio
Order
Flow
time
Late
A
0
10
20
2
sixth
98
78
B
0
15
25
1.67
fifth
88
63
C
0
17
22
1.29
third
53
31
D
0
20
31
1.55
fourth
73
42
E
0
16
20
1.25
second
36
16
F
0
20
24
1.2
first
20
0
TOTAL
98
368
230
AVERAGE
61.33
38.33
37
77) Use the information in the table and sequence the six jobs using the slack per remaining operation
algorithm. Calculate the average flow times and average lateness. All jobs arrived at time zero and are
ready at time zero.
Job
Production
Time
Due Date
A
10
20
B
15
25
C
17
22
D
20
31
E
16
20
F
20
24
Answer:
Job
Date
Received
Prod
Time
Due
Date
Slack
Order
Flow
time
Late
A
0
10
20
10
fifth
83
63
B
0
15
25
10
sixth
98
73
C
0
17
22
5
third
53
31
D
0
20
31
11
fourth
73
42
E
0
16
20
4
first
16
0
F
0
20
24
4
second
36
12
TOTAL
98
359
221
AVERAGE
59.83
36.83
38
Copyright © 2019 Pearson Education, Inc.
J.3 Flow Shop Scheduling
1) Johnson’s rule is a procedure that minimizes makespan in scheduling a group of jobs on two
workstations.
2) Janice decides to minimize the average flow time of the pastas using Johnson’s rule. Which pasta
occupies the middle position of her schedule?
A) Liguria
B) Farfalle
C) Manicotti
D) Penne
3) Janice decides to minimize the average flow time of the pastas using Johnson‘s rule. How much idle
time does the Roller/Former machine experience?
A) none
B) 8 minutes
C) 12 minutes
D) 16 minutes
4) Janice uses Johnson’s rule to schedule her pasta production. When is the Manicotti done on the Roller?
A) 22 minutes
B) 14 minutes
C) 31 minutes
D) 43 minutes
5) Janice uses Johnson’s rule to schedule her pasta production. What is the average flow time of her seven
pastas?
A) 81 minutes
B) 77 minutes
C) 73 minutes
D) 69 minutes
6) Janice uses Johnson’s rule to schedule her pasta production. How long will it take her to complete the
seven pastas?
A) one hour and fifty two minutes
B) one hour and forty three minutes
C) two hours and two minutes
D) one hour and fifty eight minutes
Table J.14
Gable Bakery has five cake orders to be processed today. Each cake has to go through the baking and
decorating processes. The baking and decorating times are estimated as follows:
7) Use the information in Table J.14. In what sequence should the orders be processed to minimize the
total processing time?
A) 5-3-1-4-2
B) 3-5-4-1-2
C) 3-5-1-4-2
D) 5-1-4-3-2
8) Use the information in Table J.14. If all cakes are to be picked up at 11:00 a.m., what is the latest time
that Gable should start making these cakes?
A) 8:00 a.m.
B) 8:30 a.m.
C) 9:00 a.m.
D) 9:30 a.m.
Table J.15
Consider the following problem in which four jobs that arrived this morning are to be processed on two
machines. They start with the cutting machine and then go to the painting machine. The following
processing times are available (in hours):
Cutting
Painting
5
4
8
3
3
2
10
9
9) Use the information in Table J.15. If the SPT rule is used to determine the sequence at the cutting
machine and the same sequence is also used at the painting machine, what is the makespan through both
machines?
A) fewer than or equal to 32 hours
B) greater than 32 hours but fewer than or equal to 34 hours
C) greater than 34 hours but fewer than or equal to 36 hours
D) greater than 36 hours
10) Use the information in Table J.15. What is the makespan through both machines if Johnson’s rule is
used?
A) fewer than or equal to 30 hours
B) greater than 30 hours but fewer than or equal to 32 hours
C) greater than 32 hours but fewer than or equal to 34 hours
D) greater than 34 hours
Table J.16
Five jobs are currently waiting to be processed. Each job has to go through Machine 1 first and then
Machine 2 before it is completed. The processing times (in hours) for the five jobs on each machine are:
Machine 1
Machine 2
3
5
7
1
5
7
6
8
4
2
11) Use the information in Table J.16. What is the makespan through both machines if the SPT rule is used
to determine the sequence at Machine 1 and the same sequence is also used at Machine 2?
A) fewer than or equal to 27 hours
B) greater than 27 hours but fewer than or equal to 28 hours
C) greater than 28 hours but fewer than or equal to 29 hours
D) greater than 29 hours
12) Use the information in Table J.16. What is the makespan through both machines if Johnson’s rule is
used?
A) fewer than or equal to 26 hours
B) greater than 26 hours but fewer than or equal to 27 hours
C) greater than 27 hours but fewer than or equal to 28 hours
D) greater than 28 hours
Table J.17
A company must take on seven new projects. Each project has a planning stage and a design stage, and
the planning stage must be completed before the design stage can begin. Also, two project teams are
available to work on these projects: Team 1 works only on planning stages of projects, and Team 2 works
only on design stages of projects. The times to complete the project stage, in days, are shown in the
following table.
Team 1
9
12
8
10
4
11
2
13) Using the information in Table J.17 and Johnson’s rule, what is the sequence of projects that minimizes
makespan?
A) C-A-D-G-E-F-B
B) C-A-D-B-G-F-E
C) G-E-C-A-D-F-B
D) G-E-F-B-D-A-C
14) Using the information in Table J.17 and Johnson’s rule, on which day will project F be completed?
A) day 33 or earlier
B) day 33-day 36
C) day 37-day 40
D) day 41 or later
15) Using the information in Table J.17 and Johnson’s rule, what is the makespan for these seven jobs?
A) 58 days or greater
B) greater than or equal to 55 days but less than 58 days
C) greater than or equal to 52 days but less than 55 days
D) less than 52 days
16) Using the information in Table J.17 and Johnson’s rule, how much idle time does Team 2 have from
the start of the first project through completion of the seventh?
A) 2 days
B) 3 days
C) 4 days
D) 5 days
17) Using the information in Table J.17 and Johnson’s rule, develop a schedule that minimizes makespan
for these seven jobs. Assume that job C could be neatly split into two equal parts, each having half of the
processing time on each machine as the full job C. Using your original sequence, but splitting job C, what
is the makespan for the seven jobs?
A) between 58 and 59 days
B) between 56 and 57 days
C) between 55 and 56 days
D) between 57 and 58 days
18) Using the information in Table J.17 and Johnson’s rule, develop a schedule that minimizes makespan
for these seven jobs. Assume that job C could be neatly split into two equal parts, each having half of the
processing time on each machine as the full job C. Using your original sequence, but splitting job C, what
is the reduction in makespan for the seven jobs?
A) The schedule with job C split is almost a day longer.
B) The schedule with job C split is almost 2 days shorter.
C) The schedule with job C split is almost 2 days longer.
D) There is no difference between the makespan for the original schedule and that made with job C split
into two halves.
19) ________ is a procedure that minimizes makespan in scheduling a group of jobs on two workstations.
20) Consider the following problems in which four jobs must each be processed on two machines starting
with Machine A and then going to Machine B. The following processing times are available (in hours):
Job
Processing
Time
Machine A
Processing
Time
Machine B
A
1
5
B
8
2
C
3
9
D
7
7
What is the minimum makespan for this group of jobs? Depict it graphically using a Gantt chart.
21) Lee Beedo, a hip bachelor in Edmond, has a date for Saturday night and finds himself without a thing
to wear. Faced with the daunting task of doing enough laundry to fully accessorize during his night out,
Lee has sorted his clothes into loads according to fabric and color. Based on his vast experience doing
laundry, Lee knows how long each load will take in both the washer and the dryer. He glances at his
watch; it is now 2:00 p.m. and he has to have the last load dry by 8:30 p.m. to be there in time. Help Lee
develop a schedule that will enable him to make his date on time and depict that schedule using a Gantt
chart. Can he make it and, if so, by how much?
Load
Wash Time
(hrs.)
Dry Time (hrs.)
Polyesters
0.50
0.75
Leathers
2.00
1.50
Whites
0.75
1.25
Unmentionables
1.00
1.25
Silks
0.50
0.25
1
Polyesters
0.0
0.50
0.50
1.25
2
Whites
0.50
1.25
1.25
2.50
4
Leathers
2.25
4.25
4.25
5.75
5
Silks
4.25
4.75
5.75
6.00
22) Consider this list of jobs that have just arrived and are ready for processing. They all require
processing first on machine 1 and then on machine 2. Both machines are now idle. Develop a schedule
that minimizes makespan and calculate this makespan time. Now assume that each job can be split into
two jobs, each having half the duration on both machine 1 and machine 2. Using the original sequence
that minimized average flow time, calculate the flow times for all split jobs What is the effect of this new
schedule on the average flow time for these split jobs?
Machine 1
14
11
16
12
22
13
10
8
Job
Machine 1
Machine 2
Done 1
Done 2
8
8
13
8
21
7
10
12
18
33
2
11
12
29
45
6
13
15
42
60
3
16
14
58
74
5
22
9
80
89
4
12
8
92
100
1
14
6
106
112
The average flow time is 66.75.
49
Splitting each task into equal halves (Job 1 becomes Job 1a and Job 1b, and so forth) results in this
schedule:
Machine 1
Done 1
4
4
4
8
5
13
5
18
5.5
23.5
5.5
29
6.5
35.5
6.5
42
8
50
8
58
11
69
11
80
6
86
6
92
7
99
7
106
50
Copyright © 2019 Pearson Education, Inc.
J.4 Labor-Limited Environments
1) Acme has an overabundance of machinery available, but most of the workforce has called in sick after
the local team’s devastating loss on Monday Night Football. This scheduling problem is a labor-limited
environment.
2) Training workers on a variety of machines and tasks decreases flexibility of operations and leads to
labor-limited environments.
3) An example of a labor-assignment rule would be to assign personnel to the workstation with the job
that has the earliest due date.
4) Of the following examples for labor-assignment rules, which of the following is least likely to be
utilized:
A) assign personnel to the workstation with the job that has been in the system for the shortest amount of
time.
B) assign personnel to the workstation with the most jobs waiting to be processed.
C) assign personnel to the workstation with the largest standard work content.
D) assign personnel to the workstation with the job that has the earliest due date.