# Chapter 18 They Use The Critical Path Method

Type Homework Help
Pages 12
Words 2695
Textbook OM 5 5th Edition
Authors David Alan Collier, James R. Evans

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OM5 C18
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19
3. Explain the role of project managers and some principles for success.
4. Describe how a project fits into each of the three common organizational structures.
5. Describe the four major steps in the project-planning process.
ANS:
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6. List at least six principal factors (contributors) to project success.
ANS:
7. Define critical path and explain how it is identified once a project schedule is calculated.
8. Explain the purpose of Gantt charts.
9. Explain the three time estimates used to characterize uncertainty of activity times in the
Program Evaluation and Review Technique (PERT) procedure.
ANS:
PROBLEMS
10. The network below represents a project being analyzed by the Critical Path Method.
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a.
What activity must be on the critical path, regardless of activity durations?
b.
What is the duration of path A-B-E-H-J?
c.
What is the critical path of this network?
d.
What is the length of the critical path?
11. The following network shows all the major activities on the circles (nodes). Each node
contains time estimates in weeks.
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Complete the following table.
Activity
Time
Earliest
Start
Earliest
Finish
Latest
Start
Latest
Finish
Slack
On Critical
Path?
A
B
C
D
E
F
G
H
12. The following network shows the activities on the circles or nodes. Time estimates are in
weeks.
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Complete the following table:
Activity
Time
Earliest
Start
Earliest
Finish
Latest
Start
Latest
Finish
Slack
On Critical
Path?
A
B
C
D
E
F
13. An electrical contracting company has been awarded a government contract to install
lighting fixtures on a major highway. They want to use a horizontal bar chart to plan the
schedule for the contract with work scheduled to begin on January 1. It is assumed that there
are four weeks per month. The company has established the following project activities, their
precedence relationships, and their estimated normal times:
Activity
Immediate Predecessors
Normal Time (weeks)
a.
order materials
none
4
b.
clear job sites
none
6
c.
excavate job sites
b
10
OM5 C18
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d.
make trenches for conduit
b
6
e.
install conduit
d
10
f.
form and pour foundations
c, d
8
g.
install wire
f
6
h.
install lighting standards
g
5
i.
install luminaries
h
4
j.
connect to service
i
3
a.
When does activity d begin?
b.
When does activity f end?
ANS:
14. The production engineering group at the Singapore plant of a computer company has been
put in charge of the production of a new type of printer. The printer will be built via an
assembly line. The plant manager must design the assembly line for the printer. He has been
advised that the assembly line must be ready in four weeks for a test run. He has decided to use
the Critical Path Method and has identified these activities, determined their precedence
relationships, and estimated normal times:
Activity
Immediate Predecessors
Normal Time (days)
a.
organize layout team
none
5
b.
organize modification team
none
3
c.
design personnel jobs
a
2
d.
set machinery in place
b
3
e.
connect utilities
c, d
7
f.
modify conveyor system
e
4
g.
train personnel
e
3
h.
finishing touches
f
5
i.
run test lot
g
2
a.
How many paths are there in the network?
b.
What is the duration of path b-d-e-g-i in days?
c.
What is the earliest finish (EF) time for activity "e"?
OM5 C18
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d.
What is the slack in days for activity "d"?
e.
What is the critical path?
f.
What is the duration of the critical path in days?
ANS:
15. A company has developed a project using the Critical Path Method (CPM) but is interested
in accelerating it if possible. The project has the following activities, durations (in weeks),
costs, and precedence relationships:
Immediate
Present
Accelerated
Activity
Predecessors
Duration
Cost
Duration
Cost
a
none
3
\$100
2
\$250
b
a
4
\$ 50
3.5
\$150
c
a
5
\$250
4
\$450
d
none
3
\$100
3
---
e
d
6
\$100
5
\$175
f
b, c, e
7
\$300
5
\$600
a.
How many paths are in the network?
b.
What is the earliest finish (EF) time for activity f?
c.
What is the slack in weeks for activity c?
d.
What is the critical path?
e.
What is the duration of the critical path in weeks?
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f.
What activity should be crashed first to accelerate the project?
g.
What is the final duration of the fully crashed project?
h.
What is the total crashing cost for the project?
16. A manufacturing company wants to accelerate a project it has underway for a new product
in order to beat its competitors to the market. They use the Critical Path Method (CPM) to
develop the project that has the following activities, durations (in weeks), cost (in dollars), and
precedence relationships:
Immediate
Present
Accelerated
Activity
Predecessors
Duration
Cost
Duration
Cost
OM5 C18
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a
none
3
3300
2
3400
b
none
5
4100
3
4500
c
a
4
3700
3
3800
d
b
5
5900
4
6000
e
c
6
6700
4
6900
f
c
4
4100
3
4150
g
d, e
6
9100
3
9700
h
f, g
5
2700
4
3000
a.
How many paths are in the network?
b.
What is the latest finish (LF) time for activity g?
c.
What is the slack in weeks for activity c?
d.
What is the critical path for this project?
e.
What is the duration of the critical path in weeks?
f.
What activity should be crashed first in order to accelerate the project?
g.
What is the final project duration in weeks assuming it is crashed as far as possible?
h.
What is total cost to crash the project as far as possible?
28
17. You are in charge of the "advertising program" for the Boston Red Sox baseball team
during their spring training in Fort Myers, Florida. You have defined the advertising program as
a project with the following characteristics. The goal is to fill all stadium seats during the spring
training season.
Activity
Immediate Predecessor(s)
Activity Time (weeks)
A
none
1
B
A
2
C
A
3
D
A, B
4
E
C, D
3
F
D, E
2
a.
What is the earliest completion time for this project?
b.
What is the largest amount of slack that any activity has in this project?
c.
If activity C is delayed by three weeks, what is the revised earliest project completion
time?
d.
For the original Critical Path Method problem, what is the minimum number of activities
that would have to be crashed in order to reduce the project's earliest completion time by
two weeks, assuming all activity crash costs per week are the same and all activities can
be crashed?
18. You are responsible for managing an advertising and promotion project with the following
activities (times are given in weeks).
Project
Immediate
Optimistic
Most
Likely
Pessimistic
Expected
Activity
Activity
Predecessor(s)
Time
Time
Time
Time
Variance
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A
none
2
5
14
6
4
B
none
8
11
14
11
1
C
A
5
7
9
7
0.44
D
A
6
9
12
9
1
E
B, C, D
1
3
5
3
0.44
a.
What is the critical path and expected completion time for this project?
b.
Which activity has the largest slack, and how large is that slack?
c.
What is the probability that the project will be completed within 16 weeks?
d.
If the expected time (not the most likely time) for activity B is changed to 18 weeks from
11 weeks, by how many weeks will the project's expected completion time increase?
19. Consider the project network and data shown below:
Activity
Slack
Normal
Time
Crash
Time
Normal
Cost
Crash
Cost
Crash Cost
Per Week
A
0
7
4
\$ 400
\$ 750
B
1
12
9
\$1,000
\$2,200
C
0
7
6
\$ 800
\$1,100
D
0
6
5
\$ 600
\$1,000
E
0
8
6
\$1,200
\$2,200
F
9
3
2
\$ 800
\$1,000
G
9
3
2
\$ 500
\$ 650
H
0
4
3
\$ 400
\$ 600
I
0
6
5
\$ 900
\$1,300
OM5 C18
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a.
Determine the critical path and the project completion time.
b.
Determine the crash cost per week for all activities
c.
Which activities need to be crashed to reduce the project's completion time by 4 weeks?
How much does this cost?
20. Consider the project network and data shown below:
OM5 C18
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Activity
Normal Time
(Months)
Crash Time
(Months)
Normal
Cost
Crash
Cost
Crash
Cost/Month
A
3
2
\$100,000
\$150,000
B
6
4
\$200,000
\$320,000
C
2
2
\$ 90,000
\$ 90,000
D
2
1
\$180,000
\$250,000
E
4
2
\$225,000
\$450,000
F
7
6
\$ 80,000
\$120,000
G
4
2
\$310,000
\$500,000
H
2
2
\$400,000
\$400,000
a.
Determine the critical path.
b.
If management wants the project done in one less month, which activity should they
crash?
21. Data regarding the activities for a project are presented below. The times are in weeks. The
critical path for this project is A-D-H-I-J-K.
Activity
Optimistic Time
Most Likely Time
Pessimistic Time
A
7
9
14
B
2
2
8
C
8
12
16
D
3
5
10
E
4
6
8
F
6
8
10
G
2
3
4
H
2
2
8
I
6
8
16
J
4
6
14
K
2
2
5
a.
Determine the standard deviation of the critical path.
b.
Determine the probability of completing the project in 38 weeks or less.
c.
What is the probability of completing the project in 32 weeks or less?
33
22. A manufacturing company is planning to use Project Evaluation and Review Technique to
setup a project for a new production line. For this project, they have established the following
activities, precedence relationships, and time estimates in days:
Activity
Immediate Predecessors
Optimistic to
Most Likely tm
Pessimistic tp
a
none
8
10
12
b
none
6
7
9
c
b
3
3
3
d
a
10
15
20
e
d
6
7
8
f
c
9
10
11
g
d
5
7
10
h
e, f
14
15
16
OM5 C18
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a.
What is the expected duration for activity b?
b.
What is the variance of activity d?
c.
How many paths are there in the network?
d.
What is the earliest finish (EF) time for activity e?
e.
What is the slack in days for activity c?
f.
What is the critical path?
g.
What is the duration of the critical path in days?
h.
What is the standard deviation of the critical path?
i.
What is the probability of completing the project within 50 days?
OM5 C18
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23. A company has a project based on Project Evaluation and Review Technique (PERT) with
path b-d-e-g-i that has the following activity time estimates in days:
Optimistic
Most Likely
Pessimistic
Activity
to
tm
tp
b
15
17
20
d
21
22
22
e
27
30
35
g
23
27
29
i
25
31
34
a.
What is the expected duration for activity e?
b.
What is the variance for activity b?
c.
What is the standard deviation of the path?
24. A company has used Project Evaluation and Review Technique for a project and wants to
minimize the probability of overrunning a contract deadline of 30 weeks. Three paths of
concern in the PERT network have these mean durations and variances in weeks:
Path
te
Vt
1
27
2.32
2
25
4.12
3
29
1.89
a.
What is the Z-score for path 1?
b.
What is the probability of path 2 overrunning the deadline?
OM5 C18
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