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case_16_2__1_.docx
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Case 16-2 “School’s Out Forever . . .”
Alice Cooper
Brent Bonnin begins his senior year of college filled with excitement and a twinge of fear. The
excitement stems from his anticipation of being done with it all—professors, exams, problem
sets, grades, group meetings, all-nighters . . . The list could go on and on. The fear stems from the fact
that he is graduating in December and has only four months to find a job.
Brent is a little unsure about how he should approach the job search. During his
sophomore and junior years, he had certainly heard seniors talking about their strategies for
finding the perfect job, and he knows that he should first visit the Campus Career Planning Center to
devise a search plan.
On September 1, the first day of school, he walks through the doors of the Campus
Career PlanningCenter and meets Elizabeth Merryweather, a recent graduate overflowing with
energy and comforting smiles. Brent explains to Elizabeth that since he is graduating in
December and plans to begin work in January, he wants to leave all of November and December open for
interviews. Such a plan means that by October 31 he has to have all his preliminary materials, such as
cover letters and résumés, submitted to the companies where he wants to work.
Elizabeth recognizes that Brent has to follow a very tight schedule, if he wants to meet
his goal within the next 60 days. She suggests that the two of them sit down together and decide the major
milestones that need to be completed in the job search process. Elizabeth and Brent list the 19 major
milestones. For each of the 19 milestones, they identify the other milestones that must be accomplished
directly before Brent can begin this next milestone. They also estimate the time needed to complete each
milestone. The list is shown below.
In the evening after his meeting with Elizabeth, Brent meets with his buddies at the
college coffee house to chat about their summer endeavors. Brent also tells his friends about the meeting
he had earlier with Elizabeth. He describes the long to-do list he and Elizabeth developed and says that he
is really worried about keeping track of all the major milestones and getting his job search organized. One
of his friends reminds him of the cool management science class they all took together in the first
semester of Brent’s junior year and how they had learned about some techniques to organize large
projects. Brent remembers this class fondly since he was able to use a number of the methods he studied
in that class in his last summer job.
a. Draw the project network for completing all milestones before the interview process. If
everything stays on schedule, how long will it take Brent until he can start with the interviews? What are
the critical steps in the process?
b. Brent realizes that there is a lot of uncertainty in the times it will take him to complete
some of the milestones. He expects to get really busy during his senior year, in particular
since he is taking a demanding course load. Also, students sometimes have to wait quite a
while before they get appointments with the counselors at the career center. In addition to
the list estimating the most likely times that he and Elizabeth wrote down, he makes a list
of optimistic and pessimistic estimates of how long the various milestones might take.
How long will it take Brent to get everything done under the worst-case scenario? How
long will it take if all his optimistic estimates are correct?
c. Determine the mean critical path for Brent’s job search process. What is the variance of
the project duration?
d. Give a rough estimate of the probability that Brent will be done within 60 days.
e. Brent realizes that he has made a serious mistake in his calculations so far. He cannot
schedule the career fair to fit his schedule. Brent read in the campus newspaper that the
fair has been set 24 days from today on September 25th. Draw a revised project network
that takes into account this complicating fact.
f. What is the mean critical path for the new network? What is the probability that Brent
will complete his project within 60 days?
0
S TART
A
Register
onlin e
2
G
Atten d mock
inter view
B
C
Attend
5
orientation
W rite initial
7
r esu me
D
F
4
E
Search
Intern et
10
Attend company
25
sessions
H
Review
industry
Sub mit
initial resu me 2
7
I
Meet resume
expert
1
J
Revise
resume
4
L
K
S earch
jobs
Attend
caree r fair
5
M
Decide
jobs
N
3
O
Bid
1
3
W rite cover
10
le tters
P
Submit cover
4
letters
Q
Re vise cover
letters
4
S
R
Drop
FINIS H
0
2
Mail
6
START
A
Regist er
online
2
B
C
A ttend
orientation
W rite initial
resume
G
Attend moc k
int erview
5
0
T
D
Dum my
7
F
10
H
Review
industry
4
24
E
Search
Inte rnet
Submit
initial re sume
7
2
I
Mee t resume
expert
1
J
L
Revise
resum e
4
Attend
care er fair
1
K
Search
jobs
5
M
Decide
jobs
N
3
O
Bid
3
W rite cove r
letters
10
Submit cover
letters
4
Revise cover
letters
4
P
Q
S
R
Drop
FINISH
0
2
Mail
6
Attend
company
sessions
25
Reliable Construction Company Project
•
The Reliable Construction Company has just made the winning bid of $5.4
million to construct a new plant for a major manufacturer.
•
The contract includes the following provisions:
–
–
A penalty of $300,000 if Reliable has not completed construction within 47 weeks.
A bonus of $150,000 if Reliable has completed the plant within 40 weeks.
Questions:
1.
2.
3.
4.
5.
6.
7.
8.
How can the project be displayed graphically to better visualize the activities?
What is the total time required to complete the project if no delays occur?
When do the individual activities need to start and finish?
What are the critical bottleneck activities?
For other activities, how much delay can be tolerated?
What is the probability the project can be completed in 47 weeks?
What is the least expensive way to complete the project within 40 weeks?
How should ongoing costs be monitored to try to keep the project within budget?
McGraw-Hill/Irwin
16.1
© The McGraw-Hill Companies, Inc., 2013
Activity List for Reliable Construction
Activity
Activity Description
Immediate
Predecessors
Estimated
Duration (Weeks)
A
Excavate
—
2
B
Lay the foundation
A
4
C
Put up the rough wall
B
10
D
Put up the roof
C
6
E
Install the exterior plumbing
C
4
F
Install the interior plumbing
E
5
G
Put up the exterior siding
D
7
H
Do the exterior painting
E, G
9
I
Do the electrical work
C
7
J
Put up the wallboard
F, I
8
K
Install the flooring
J
4
L
Do the interior painting
J
5
M
Install the exterior fixtures
H
2
N
Install the interior fixtures
K, L
6
McGraw-Hill/Irwin
16.2
© The McGraw-Hill Companies, Inc., 2013
Reliable Construction Project Network
START
A
Activity C ode
0
A. Excavate
2
B. Foundation
C. Rough wall
B
D. Roof
4
E. Exterior plumbing
C
F. Interior plumbing
10
G. Exterior siding
H. Exterior painting
D
E
6
4
I
I. Electrical work
7
J. Wallboard
K. Flooring
L. Interior painting
G
F
7
5
M. Exterior fixtures
N. Interior fixtures
J
H
9
K
M
4
L
5
2
N
McGraw-Hill/Irwin
8
FINISH
0
16.3
6
© The McGraw-Hill Companies, Inc., 2013
The Critical Path
•
A path through a network is one of the routes following the arrows (arcs) from
the start node to the finish node.
•
The length of a path is the sum of the (estimated) durations of the activities
on the path.
•
The (estimated) project duration equals the length of the longest path through
the project network.
•
This longest path is called the critical path. (If more than one path tie for the
longest, they all are critical paths.)
McGraw-Hill/Irwin
16.4
© The McGraw-Hill Companies, Inc., 2013
The Paths for Reliable’s Project Network
Path
Length (Weeks)
Start A B C D G H M Finish
2 + 4 + 10 + 6 + 7 + 9 + 2 = 40
Start A B C E H M Finish
2 + 4 + 10 + 4 + 9 + 2 = 31
Start A B C E F J K N Finish
2 + 4 + 10 + 4 + 5 + 8 + 4 + 6 = 43
Start A B C E F J L N Finish
2 + 4 + 10 + 4 + 5 + 8 + 5 + 6 = 44
Start A B C I J K N Finish
2 + 4 + 10 + 7 + 8 + 4 + 6 = 41
Start A B C I J L N Finish
2 + 4 + 10 + 7 + 8 + 5 + 6 = 42
McGraw-Hill/Irwin
16.5
© The McGraw-Hill Companies, Inc., 2013
Earliest Start and Earliest Finish Times
•
The starting and finishing times of each activity if no delays occur anywhere in
the project are called the earliest start time and the earliest finish time.
–
–
ES = Earliest start time for a particular activity
EF = Earliest finish time for a particular activity
•
Earliest Start Time Rule: ES = Largest EF of the immediate predecessors.
•
Procedure for obtaining earliest times for all activities:
1. For each activity that starts the project (including the start node), set its ES = 0.
2. For each activity whose ES has just been obtained, calculate EF = ES + duration.
3. For each new activity whose immediate predecessors now have EF values, obtain
its ES by applying the earliest start time rule. Apply step 2 to calculate EF.
4. Repeat step 3 until ES and EF have been obtained for all activities.
McGraw-Hill/Irwin
16.6
© The McGraw-Hill Companies, Inc., 2013
ES and EF Times for Reliable Construction
START
D
6 ES = 16
EF = 22
G
ES = 22
7 EF = 29
H
0
ES = 0
EF = 0
A
2
ES = 0
EF = 2
B
4
ES = 2
EF = 6
C
10
ES = 6
EF = 16
E
4
ES = 16
EF = 20
F
I
ES = 16
7 EF = 23
J
8
ES = 20
EF = 25
5
ES = 29
9 EF = 38
K
M
4 ES = 33
EF = 37
L
2 ES = 38
EF = 40
N
McGraw-Hill/Irwin
ES = 25
EF = 33
FINISH
0 ES = 44
EF = 44
16.7
6
5 ES = 33
EF = 38
ES = 38
EF = 44
© The McGraw-Hill Companies, Inc., 2013
Latest Start and Latest Finish Times
•
The latest start time for an activity is the latest possible time that it can start
without delaying the completion of the project (so the finish node still is
reached at its earliest finish time). The latest finish time has the corresponding
definition with respect to finishing the activity.
–
–
LS = Latest start time for a particular activity
LF = Latest finish time for a particular activity
•
Latest Finish Time Rule: LF = Smallest LS of the immediate successors.
•
Procedure for obtaining latest times for all activities:
1. For each of the activities that together complete the project (including the finish
node), set LF equal to EF of the finish node.
2. For each activity whose LF value has just been obtained, calculate LS = LF –
duration.
3. For each new activity whose immediate successors now have LS values, obtain its
LF by applying the latest finish time rule. Apply step 2 to calculate its LS.
4. Repeat step 3 until LF and LS have been obtained for all activities.
McGraw-Hill/Irwin
16.8
© The McGraw-Hill Companies, Inc., 2013
LS and LF Times for Reliable’s Project
START
D
G
6 LS = 20
LF = 26
LS = 0
LF = 0
0
LS = 0
LF = 2
A
2
B
4
LS = 2
LF = 6
C
10
LS = 6
LF = 16
E
4
LS = 16
LF = 20
LS = 26
7 LF = 33
H
9
F
I
LS = 18
7 LF = 25
J
8
LS = 20
LF = 25
5
LS = 33
LF = 42
K
M
4 LS = 34
LF = 38
L
2 LS = 42
LF = 44
N
McGraw-Hill/Irwin
LS = 25
LF = 33
FINISH
0
LS = 44
LF = 44
16.9
6
5
LS = 33
LF = 38
LS = 38
LF = 44
© The McGraw-Hill Companies, Inc., 2013
The Complete Project Network
START
D
G
6 S = (16, 20)
F = (22, 26)
9
S = (0, 0)
F = (0, 0)
S = (0, 0)
F = (2, 2)
A
2
B
4
S = (2, 2)
F = (6, 6)
C
10
S = (6, 6)
F = (16, 16)
E
4
S = (22, 26)
7 F = (29, 33)
H
0
S = (16, 16)
F = (20, 20)
F
5
I
7
J
8
S = (20, 20)
F = (25, 25)
S = (25, 25)
F = (33, 33)
S = (29, 33)
F = (38, 42)
K
M
4 S = (33, 34)
F = (37, 38)
2 S = (38, 42)
F = (40, 44)
N
FINISH
McGraw-Hill/Irwin
S = (16, 18)
F = (23, 25)
6
0 S = (44, 44)
F = (44, 44)
16.10
L
5 S = (33, 33)
F = (38, 38)
S = (38, 38)
F = (44, 44)
© The McGraw-Hill Companies, Inc., 2013
Slack for Reliable’s Activities
McGraw-Hill/Irwin
Activity
Slack (LF–EF)
On Critical Path?
A
0
Yes
B
0
Yes
C
0
Yes
D
4
No
E
0
Yes
F
0
Yes
G
4
No
H
4
No
I
2
No
J
0
Yes
K
1
No
L
0
Yes
M
4
No
N
0
Yes
16.11
© The McGraw-Hill Companies, Inc., 2013
Spreadsheet to Calculate ES, EF, LS, LF, Slack
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
B
Activity
A
B
C
D
E
F
G
H
I
J
K
L
M
N
C
Description
Excavate
Foundation
Rough Wall
Roof
Exterior Plumbing
Interior Plumbing
Exterior Siding
Exterior Painting
Electrical Work
Wallboard
Flooring
Interior Painting
Exterior Fixtures
Interior Fixtures
McGraw-Hill/Irwin
D
Time
2
4
10
6
4
5
7
9
7
8
4
5
2
6
E
ES
0
2
6
16
16
20
22
29
16
25
33
33
38
38
Project Duration
16.12
F
EF
2
6
16
22
20
25
29
38
23
33
37
38
40
44
G
LS
0
2
6
20
16
20
26
33
18
25
34
33
42
38
H
LF
2
6
16
26
20
25
33
42
25
33
38
38
44
44
I
Slack
0
0
0
4
0
0
4
4
2
0
1
0
4
0
J
Critical?
Yes
Yes
Yes
No
Yes
Yes
No
No
No
Yes
No
Yes
No
Yes
44
© The McGraw-Hill Companies, Inc., 2013
The PERT Three Estimate Approach
Most likely estimate (m) = Estimate of most likely value of the duration
Optimistic estimate (o) = Estimate of duration under most favorable conditions.
Pessimistic estimate (p) = Estimate of duration under most unfavorable conditions.
Beta distribution
0
o
m
p
Elapsed time
McGraw-Hill/Irwin
16.13
© The McGraw-Hill Companies, Inc., 2013
Mean and Standard Deviation
An approximate formula for the variance (2) of an activity is
2
p o
6
2
An approximate formula for the mean (m) of an activity is
m
McGraw-Hill/Irwin
o 4m p
6
16.14
© The McGraw-Hill Companies, Inc., 2013
Time Estimates for Reliable’s Project
Activity
o
m
p
Mean
Variance
A
1
2
3
2
1/
B
2
3.5
8
4
1
C
6
9
18
10
4
D
4
5.5
10
6
1
E
1
4.5
5
4
4/
9
F
4
4
10
5
1
G
5
6.5
11
7
1
H
5
8
17
9
4
I
3
7.5
9
7
1
J
3
9
9
8
1
K
4
4
4
4
0
L
1
5.5
7
5
1
M
1
2
3
2
1/
9
N
5
5.5
9
6
4/
9
McGraw-Hill/Irwin
16.15
9
© The McGraw-Hill Companies, Inc., 2013
Pessimistic Path Lengths for Reliable’s Project
Path
Pessimistic Length (Weeks)
Start A B C D G H M Finish
3 + 8 + 18 + 10 + 11 + 17 + 3 = 70
Start A B C E H M Finish
3 + 8 + 18 + 5 + 17 + 3 = 54
Start A B C E F J K N Finish
3 + 8 + 18 + 5 + 10 + 9 + 4 + 9 = 66
Start A B C E F J L N Finish
3 + 8 + 18 + 5 + 10 + 9 + 7 + 9 = 69
Start A B C I J K N Finish
3 + 8 + 18 + 9 + 9 + 4 + 9 = 60
Start A B C I J L N Finish
3 + 8 + 18 + 9 + 9 + 7 + 9 = 63
McGraw-Hill/Irwin
16.16
© The McGraw-Hill Companies, Inc., 2013
Three Simplifying Approximations of PERT/CPM
1. The mean critical path will turn out to be the longest path through the project
network.
2. The durations of the activities on the mean critical path are statistically
independent. Thus, the three estimates of the duration of an activity would
never change after learning the durations of some of the other activities.
3. The form of the probability distribution of project duration is the normal
distribution. By using simplifying approximations 1 and 2, there is some
statistical theory (one version of the central limit theorem) that justifies this as
being a reasonable approximation if the number of activities on the mean
critical path is not too small.
McGraw-Hill/Irwin
16.17
© The McGraw-Hill Companies, Inc., 2013
Calculation of Project Mean and Variance
Activities on Mean Critical Path
Mean
Variance
A
2
1/
B
4
1
C
10
4
E
4
4/
F
5
1
J
8
1
L
5
1
N
6
4/
Project duration
mp = 44
2p = 9
McGraw-Hill/Irwin
16.18
9
9
9
© The McGraw-Hill Companies, Inc., 2013
Probability of Meeting Deadline
2
p=9
d – m p = 47 – 44 = 1
p
3
44
(Mean)
McGraw-Hill/Irwin
47
(Deadline)
16.19
Project duration
(in weeks)
© The McGraw-Hill Companies, Inc., 2013
Spreadsheet for PERT Three-Estimate Approach
B
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Activity
A
B
C
D
E
F
G
H
I
J
K
L
M
N
McGraw-Hill/Irwin
C
D
E
Time Estimates
o
m
p
1
2
3
2
3.5
8
6
9
18
4
5.5
10
1
4.5
5
4
4
10
5
6.5
11
5
8
17
3
7.5
9
3
9
9
4
4
4
1
5.5
7
1
2
3
5
5.5
9
F
On Mean
Critical Path
*
*
*
*
*
*
*
*
16.20
G
H
m
2
4
10
6
4
5
7
9
7
8
4
5
2
6
0.1111
1
4
1
0.4444
1
1
4
1
1
0
1
0.1111
0.4444
I
J
K
Mean Critical
Path
m
44
9
P(T<=d) =
where
d=
0.8413
47
© The McGraw-Hill Companies, Inc., 2013
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