Overview1) Overview – The continued discussion of project implem.docx

Overview
1) Overview – The continued discussion of project
implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a
project action plan into an operating timetable.” A schedule is
important because each project is unique in its own way. The
basic process is to identify all tasks and sequential relationships
between them, that is, which tasks must precede or succeed
others. There are a number of benefits to the creation and use of
these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and
controlling the project.
b) It can be used to determine a start and end date for every
project task.
c) It identifies so-called critical activities that, if delayed will
delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT
and CPM are the most commonly used approaches to project
scheduling. Both were introduced in the 1950s. PERT has been
primarily associated with R&D projects, while CPM with
construction projects. Today PERT is not used much since
project management software generates CPM style networks.
The primary difference between them is that PERT uses
probabilistic techniques to determine task durations, while CPM
relies on a single duration estimate for each task. Both
techniques identify the critical path (tasks that cannot be
delayed without delaying the project) and associated float or
slack in the schedule. In 2005 the Project Management Institute
(PMI) deemed it necessary to change the names of these
techniques. According to PMI, PERT is called ADM/PERT
(Arrow Diagram Method) and CPM is PDM/CPM (Precedence
Diagramming Method).
a) Terminology – Following are the key terms associated with
the development and use of networks:

i) Activity – A specific task or set of tasks that have a start and
end, and consume resources.
ii) Event – The result of completing one or more activities.
Events don’t use resources.
iii) Network – The arrangement of all activities and events in
their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two
events in a network.
v) Critical – Activities, events or paths which, if delayed, will
delay the completion of the project.
To construct a network the predecessors and successors of each
activity must be identified. Activities that start the network will
have no predecessor. Activities that end the network will have
no successor. Regardless of the technique used, it is a good
practice to link the activities with no other predecessor to a
START milestone. Those without any successor should be
linked to an END milestone. PDM/CPM networks identify the
activities as nodes in the network, called the Activity on Node
(AON) network. The arrows in between the nodes depict the
predecessor/successor relationships among the activities. The
ADM/PERT method, on the other hand, uses Activity on Arrow
(AOA) networks. Here the nodes represent events and the
arrows represent the actual activities.
b) Constructing the Network, AON Version – The text
illustrates the development of a simple AON network. All the
major project management software packages will generate this
type of network.
c) Constructing the Network, AOA Version – The AOA network
has some development rules that make it somewhat more
difficult to construct than the AON network. The primary rule is
that any given activity must have its source in one and only one
node. As a result, some network relationships can only be
depicted with the use of a “dummy” activity. This is an activity
that has no duration and consumes no resources. Its sole
purpose is to indicate a precedence relationship. The text uses
various figures to illustrate the use of dummy activities.

d) Gantt (Bars) Charts and Microsoft® Project (MSP) – The
most familiar tool for depicting project schedules is the Gantt
chart, invented by Henry L. Gantt in 1917. The activities are
depicted as horizontal bars with their length proportional to
their duration. This method results in an easy to read graphical
depiction of the project schedule. Gantt charts can be difficult
to maintain if there are large changes in the project schedule.
Tools like Microsoft® Project (MSP) will automatically draw
the Gantt chart as a byproduct of the network entered by the
user. The disadvantage of the Gantt chart is that it typically
does not depict the network relationships.
e) An Important Aside on Estimating Activity Times – It is
important that the duration of each of the tasks in a project is
honestly estimated. The deadlines should be set as close to the
actual deadline needed to ensure proper buy-in from everyone
throughout the project. As is the norm with many project
managers, the deadlines are set earlier than what is required and
the workers overestimate the deadlines to ensure task
completions and delivery, both of which lead to serious errors
in the long run of a major project.
f) Solving the Network – The text illustrates the development
and solving an AON network based on the project detailed in
Table 8-1.
g) Calculating Activity Times – The sample project in the text
has three duration estimates for each activity: optimistic (a),
most likely (m) and pessimistic (b). Optimistic and pessimistic
are defined as the durations that represent 99 percent certainty.
In other words the actual duration of an activity will be less
than the optimistic or greater than the pessimistic only one
percent of the time. Then, the expected time (TE) is found with
the formula:
TE = (a + 4m + b)/6
where:
a = optimistic time estimate
b = pessimistic time estimate
m = most likely time estimate, the mode

This formula is based on the beta statistical distribution. In
spite of a flurry of discussion in the 1980s the assumptions used
to derive this formula have stood the test of time. Along with
TE, the variance of the durations can be calculated as:
and the standard deviation as:
h) Critical Path and Time – Using the example network, the text
describes the concept of the critical path. For simple projects,
the critical path can be found by determining the longest path
through the network.
i) Slack (aka, Float) – In the previous section, the earliest
possible dates for each activity were determined. By starting the
analysis at the end of the network and working through it
backwards, the latest possible dates for each activity can be
determined. The difference between the early dates and the late
dates is float or slack. Activities on the critical path have zero
float.
j) Precedence Diagramming – The Precedence Diagram Method
allows for additional relationships to be established between
activities. They are:
i) Finish to Start – The successor activity cannot begin until the
predecessor finishes. This is the most common relationship
ii) depicted in networks.
iii) Start to Start – The successor activity cannot begin until the
predecessor begins.
iv) Finish to Finish – The successor activity cannot finish until
the predecessor activity finishes.
v) Start to Finish – The successor activity cannot finish until
the predecessor activity starts. This relationship is rarely used.
In addition to these relationships, PDM allows for leads and
lags which is the introduction of a specific time period between

the linked activities. For example, in a Start to Start
relationship with five days of lag, the successor activity cannot
begin until five days after the predecessor starts. The critical
path and slack calculation resulting from these relationships can
be complicated and counter intuitive.
k) Once again, Microsoft® Project – The text illustrates the use
of MSP for calculating the most likely project duration using
the PERT method.
l) Exhibits Available from Software, a Bit More MSP – The text
illustrates the types of outputs available from MSP.
m) Uncertainty of Project Completion Time – The chance of
completing a project within a given time period can be
calculated. The project activities are assumed to be statistically
independent and the variance of a set of activities is equal to the
sum of the variances of the individual activities comprising the
set. Then the chance of meeting a particular project duration can
be calculated as:
where:
D = the desired project completion time
µ = the critical time of the project, the sum of the TEs for
activities on the critical path
= the variance of the critical path, the sum of the variances
of activities on the critical path
Z = the number of standard deviation of a normal distribution
(the standard normal deviate)
The weakest element of this technique is that it is difficult to
account for the possibility that other paths through the network
may become critical due to variation in their duration.
Simulation techniques using tools like Crystal Ball® or Risk +®
can be used to better model this situation.

n) Toward Realistic Time Estimates – The traditional PERT
method uses optimistic and pessimistic duration estimates at the
99% confidence level. The calculations can be adjusted for
lower confidence levels that estimators may be more
comfortable in predicting such as 90 or 95%.
4) Risk Analysis Using Simulation With Crystal Ball® – Tools
like Crystal Ball® can be used to model the project and
determine the likelihood of completion within a certain time.
Since Crystal Ball® works with Microsoft® Excel, the project
network must be modeled in the spreadsheet. This involves
creating cells that calculate the early and late dates for each
activity. Then a distribution (commonly triangular) with the
appropriate parameters can be assigned to each duration.
Finally, Crystal Ball® runs its simulation and the results are
displayed.
a) Traditional Statistics or Simulation? – With the advent of
inexpensive and easy to use tools, simulation is the
recommended way to model uncertainty in project durations.
Both methods require the development of three durations for
each activity. The simulation method, however, does a much
better job of handling the possibility that the critical path will
shift due to variation in durations of activities. This issue can
be analyzed with traditional statistics, but it takes considerable
manual effort on the part of an analyst.
5) Using These Tools – The text gives an example of the use of
the tools on a specific project.
Teaching Tips
The authors correctly applaud the advent of many user-friendly
and powerful project management tools available for PCs. They
have performed a great service by integrating the use of tools
like Microsoft® Project into the subject matter. My experience
in teaching these tools, however, reminds me of the story about
IBM’s new programming language. The story goes that IBM, in
their marketing campaign for their new language, said that the
language was so easy to use that it would virtually eliminate the
position of a programmer. Anybody would be able to use this

language to easily create computer programs. The punch line is
that the new language was FORTRAN, a 1960’s era product
long ago supplanted by other “user-friendly” products. Even
today, with all the marvelous tools we have available, the
position of a programmer has not disappeared. The point of all
this is that in the classroom students will have a wide range of
skills and abilities that may or may not be applicable to
Microsoft® Project and similar tools. My experience is that it is
unreasonable to expect students to pick up MSP and use it
successfully based solely on the printed examples in the text.
Unfortunately, even students who claim to be experienced in the
use of the tool often know how to draw a Gantt chart and little
else. This is due to three reasons:
· MSP on the surface may look like a fancy spreadsheet, but
“under the hood” it’s is a very complex tool. Many of its
processes are dependent on complex algorithms, controlled by a
seemingly endless series of settings with mysterious titles.
· The training provided by most organizations ranges between
non-existent and abominable. If there is training, it’s usually
administered by someone who has never managed a project and
doesn’t understand much more than the student he/she is
teaching. One of my very computer literate colleagues will
probably become homicidal, if he is forced to go to yet another
training session that concentrates on issues vital to the PM like
changing the color of the fonts. In my twenty years of both
managing projects and teaching project management, I have
encountered just one person who is both an accomplished user
of MSP on actual projects and a capable instructor.
· MSP training, if it exists, is usually done out of context. It is
taught as a standalone computer tool, without any of the
concepts of project management to put its use in the proper
perspective.
The opportunity then, for any project management instructor, is
to provide both the concept and meaningful tools training in one
package. Ideally, lectures on concept should be alternated with
lab sessions using the tool. If this is not possible then, at a

minimum, the instructor must set aside class time to
demonstrate the key elements of MSP needed to complete the
homework problems. Then, a week later, be prepared for the
questions and frustrations that will erupt from the class.
A good reference case for this chapter follows:
Ivey cases:
9A97D001 Note on Introduction to Project Management. An
introduction to projects with a simple AON problem.
9A97D002 Gadget Toy Company. A simple AON problem that
also introduces Microsoft Project (MSP).
9A95D015 H.M.S. Pinafore. A moderately longer AOA
problem.
9A98D020 Procter & Gamble Canada: Dayquil Sampling
Operations. A realistic problem based on an actual summer
intern’s experience involving a quick decision on a new product
line that requires a number of tasks to be executed.
University of Virginia Darden case: UVA-OM-0803 Tastee Snax
Cookie Company. A straightforward, but more involved network
problem.
Material Review Questions
Question 1:
Activity: Activities have a start and end, and consume
resources.
Event: Events do not consume resources. Typically, events
designate the start or the completion of an activity or a path
Path: A path traces the predecessor-successor relationships that
exist among a set of interconnected activities and events. The
boundaries of a path use a starting event and a completion event
to designate the path’s endpoints.
Dummy Activity: Dummy activities are tasks of zero duration
that have no resources assigned to them. They are used to
maintain predecessor/successor relationships in AOA networks.
Question 2:
Activities along the critical path cannot be delayed without
delaying the completion of the project.

Question 3:
Gantt Chart: The Gantt chart compares planned and actual
progress for the detailed tasks in a project.
Master Schedule: The Gantt chart format (bars to represent
progress over time) may be used to display data regarding the
master project schedule, but the master schedule is oriented
towards overall management of the project and will only focus
on the major project tasks. For example, the Gantt view in MS-
Project can be filtered to only show summary tasks at a
particular level of the WBS hierarchy.
Question 4:
Total slack vs. free slack:
Total slack is the difference between the calculated earliest
finish time of the very last activity and the project’s required
completion time.
Free slack is the time an activity can be delayed without
affecting the start time of any successor activity.
So, the total slack deals with the relationship between the
current activity and the total project completion time, while free
slack relates to the next activity.
Question 5:
The authors of the text have suggested that PERT and CPM are
very similar. Therefore, the terms PERT and CPM have been
used interchangeably in the textbook, when basic educational
concepts of a project schedule is explained. The following
guidelines are suggested with regard to when to use each type of
scheduling technique discussed in this chapter.
1) PDM/CPM should be used when the control of costs
associated with expediting work is an important concern. PDM
networks should be used when the project requires the use of
leads and lags between activities. PDM is easier to draw than
ADM, is used in most project software applications, and tends
to be preferred when CPM is used.
2) ADM/PERT should be used when the activity times are
estimated using probability distributions in order to evaluate the
range of uncertainty around the expected project duration. ADM

networks should be used, when it is desirable to show
completion events as a part of the scheduling network, though
nothing prevents the use of START and FINISH events in a
PDM/CPM network.
3) The Gantt chart is a useful tool for displaying the schedule
regardless of what method is used to derive it. The Gantt chart
can be used directly to develop small project schedules. A less-
known approach: GERT should be used when the project plan is
complex enough to require loop backs and/or the use of multiple
probability distributions associated with branching options in
the relationships between activities.
Question 6:
AON (activity on node) places the activities or tasks on a
rectangle (node), whereas the AOA places the activities on
arrows connecting nodes. Typically the AON provides more
information per activity in the diagram itself because more
information can be placed on the node itself (start time, finish
time, etc).
Question 7:
Simulation requires the project schedule to be modeled
mathematically, which happens to be a by-product of any of the
network scheduling techniques. Once the model is established,
simulation involves inputting appropriately distributed random
numbers into the independent variables and analyzing the
resulting distribution of the dependent variables (those
calculated by the model). To make the result meaningful,
hundreds if not thousands of trials are run, to build a
statistically significant output distribution. Once the output
distribution is established, probabilities of various outcomes
can be calculated.
Question 8:
Networks are drawn from the left to the right. Arrowheads
indicate the direction of flow in the network. The flow
designates the precedence relationships between activities in the
network.
Question 9:

Late start time: Given the precedence relationships in a
network, this is the latest time that an activity can begin without
extending the time required to complete the entire project.
Early start time: Given the precedence relationships in a
network, this is the earliest time that an activity can begin. In
order to begin, all predecessor constraints must have been
satisfied.
Early finish time: Given the precedence relationships in a
network and the activities duration, this is the earliest time that
an activity can be completed if all predecessor constraints are
satisfied.
Question 10:
The critical path is determined by performing the “forward
pass” and “backward pass” calculations. Float is calculated by
subtracting the early dates from the late dates, specifically the
early start from the late start or the early finish from the late
finish. If an activity has zero float, then it is on the critical
path. Any delay in an activity along the critical path would
extend the project’s completion date.
Question 11:
Slack is important for two reasons: 1) Slack tells us that we can
be a bit more forgiving about delays on paths with slack,
whereas our primary attention should be focused on the critical
path. 2) If we need additional resources for some reason (such
as a delay on the critical path), the first place to look is at the
resources on paths with slack in case they might be available for
use.
Class Discussion Questions
Question 12:
The network diagram could serve as a rough process flowchart
showing the steps in a manufacturing cycle. The direct and
indirect costs for each step could be identified and scheduled
for each iteration of the total manufacturing cycle. However, the
basic networks are not sophisticated enough to capture costs
associated with variables such as production yields, rework loop

backs, and branching logic commonly associated with control
points to assure quality.
Question 13:
1) Benefits:
a) Illustrates task interdependencies
b) Establishes the sequence of activities (precedence)
c) Highlights critical and near-critical paths and their tasks
d) Highlights activities that contain float
2) Disadvantages:
a) Emphasizes time at the expense of other dimensions of
project success
b) Large networks are difficult to print in a convenient format
and they may require significant wall space to view the entire
network
c) As the network technique becomes more complex, its
effectiveness as a control tool is reduced
Question 14:
This is a good question to kick off a lively class discussion.
There are no black and white answers to this question, but here
are a couple thoughts:
· It’s easy to become obsessed by the use of even more
sophisticated tools and lose sight of the big picture. Project
management tools are only useful if they help projects achieve
their cost, schedule, and scope goals. Just because a tool is
more sophisticated doesn’t mean that it will yield a better result
for the business.
· Organizations have to clearly articulate the goals of a project,
put together some kind of a plan, and then meticulously monitor
its execution. Many organizations gloss over the monitoring
part because they believe it smacks of micro-management. In
spite of what Dilbert thinks, managers must have a mechanism
for knowing where their project is every day. This allows
corrective action to be taken before the problem grows beyond
recovery. This attention to detail is boring and repetitive, but
it’s far more fundamental to the success of the project than the
sophistication of the simulation tools used to model the plan.

Question 15:
Both methods are of significant value because they force the PM
to consider the relationships among the project activities. Then
using these relationships, both methods produce a schedule for
those activities. In addition, both methods can be used for
analysis of variances and problems when the schedule is
executed.
Question 16:
There are many ways to deal with uncertainty. The most
common in the scheduling process are:
1) Adding buffer or padding to the duration of each activity
2) Adding buffer to the overall project schedule
3) Developing schedules based on a range of activity durations
4) Calculating probabilities of completion using statistical or
simulation techniques
5) Taking specific actions to reduce the uncertainty in duration
for some or all the activities
Question 17:
The “free slack” as it is called, is the slack along a path in the
project and is the minimum of all the slacks on that path. Thus,
if the path of interest is A-B-C and the slacks on A and B are 3
each, while the slack on C is 2, the free slack on the path is 2.
Question 18:
Activity times are generally estimated in a manner similar to
budgets. For example, they can be individually estimated by the
participants or calculated based on time estimates from earlier
projects.
Question 19:
Yes and no. Critical path activities deserve closer scrutiny. If
critical activities run late the project is sure to be late. In a
situation where scant resources have to be allocated to help late
activities recover, the critical path activities would get the
resources before the noncritical path activities.
This, however, does not absolve the PM from monitoring the
noncritical path items. Items off the noncritical path may feed
the critical path, so if they are late they could delay the project

indirectly. Also if noncritical path activities get late enough
then the critical path may shift to them, again delaying the
entire project.
Question 20:
I’m not aware of any network relationship that can’t be built
through some combination of the PDM relationships with leads
and lags. As the text points out, the relationships can become
quite complicated, which leads to anomalies in the critical path.
Questions for Project Management in Practice
Replacing the Atigun Section of the TransAlaska Pipeline
Question 21:
Probably work was done underground in order to avoid wildlife
like grizzly bears.
Question 22:
Petroleum engineers built a bypass system, which was used to
divert the oil flow temporarily, for repairs without interrupting
it.
Question 23:
The environment for this project was very hostile. In addition to
limited sunlight (3 hours per day), temperatures were as low as
–60 degrees during winter. Unless robots could be used, shifts
were likely to be limited to the time one could withstand the
temperatures and still avoid frostbites.
Designing and Delivering a Rush Vehicle for War
Question 24:
For the first billion dollar contract, the army paid around
$450,000 per vehicle and about $590,000 per vehicle for the
second order. The high price can be attributed to the ultra-
efficient schedule followed by the manufacturing company. The
company maintained tight schedules and efficient problem-
solution relay mechanisms to provide a quality solution within
the short time-frame for the army. Producing a car is never such
a critical problem. A highly efficient and tight schedule is not
necessary to produce a car. Producing a rush vehicle for a war is
entirely different than producing a car for, say, the general

public. The situation and its relative importance definitely
demand a premium price.
Question 25:
Need is the mother of invention. Never before the military
encountered such a situation where they needed a new type of
vehicle specialized for the situation. The tight schedule
demanded a different approach of parallel production to
development, which is not a norm with the military equipment
industry and to which Oshkosh adopted seamlessly.
Question 26:
This new approach may hinder the development of new
components. The time-frame of such projects is so small that
rarely a firm would be able to develop and test new components.
Another weakness could be the inefficient testing that could
result from fast prototypes to productions, which in turn would
increase the price of the end-product.
Hosting the Annual Project Management Institute Symposium
Question 27:
One unique aspect of this project is its length. The Gantt chart
shows that planning for the symposium began more than four
years before the event and continued for a year after. This
means that several symposia are continuously in the planning
process throughout the United States.
Question 28:
The symposium took place in September 1992 and the
supporting project completed in April of 1993.
Question 29:
The activities after completion of the symposium are tasks
associated with project closeout work. This would include tasks
related to contract closeout and administrative closeout, and
creation of a project archive and a summary report of lessons
learned. For this project, closeout lasted approximately 6
months. This question points out the importance of establishing
a common understanding of when any project is actually done.
The answer may not be obvious, and it can come back to bite
the PM when he/she least expects it.

Election Returns within Three Hours
Question 30:
While each of the two thrusts had its own difficulties, I believe
that the integration of each citizen’s records with their
respective biometric data was a more difficult task. The primary
reason for this is that the capturing of pertinent information of
each and every citizen involved is a humungous task, which is
only possible with a dedicated team of professionals since it is a
continuing effort spanning many years. The development and
integration of tools needed for this task and their subsequent
successful use is highly commendable.
Question 31:
It is indeed difficult but not impossible for other countries to
replicate this system. The only problems these countries would
encounter would be the efficient handling of such a long
project, that will span years since counting and integrating each
and every citizen on the face of the country is a monstrous task,
and can only be accomplished through thoughtful leadership and
thorough planning. I believe that sooner or later every
developed nation would think of building and customizing a
system like this as a necessity.
Question 32:
The developed nations could easily ignore the technological
aspects of this establishment. Many developed nations already
have the necessary technological infrastructure that is used in
this system. Other nations could ignore the biometric fingerprint
integration of each and every citizen and proceed with simple
establishment of a database through valid birth and death
records, which are mostly present in every country now. This
would be very important in achieving faster returns through fast
development.
Problems
NOTE: Many of the AON graphics in this solutions set depict
the start day of the successor activity to be the same day as the

completion of the predecessor. This is consistent with the
presentation in the text. It is not consistent with the result that
would be obtained using Microsoft® Project, where the start
day of the successor is always the next working day after the
completion of the predecessor.
Problem 1:
Problem 2:
Problem 3:
1) The arrows cannot form a loop such as the one shown
between nodes 2, 3, and 5.
2) The dummy arrow between nodes 6 and 7 is not required
because 6 precedes 5 and 5 precedes 7.
3) Nodes 8 and 9 do not have successors, so it appears that this
network has two final termination nodes. This is not a
conventional diagramming technique. An arrow from 8 should
point to 9.
Problem 4:
a) The critical path is B-E-G.
b) 23 work periods.
Problem 5:
Initial PDM Diagram
Adjusted PDM Diagram

Problem 6:
PDM Diagram 6a
PDM Diagram 6b
Problem 7:
Figure 7a is the AOA diagram.
Figure 7b is the AON diagram.
Problem 8:
Please see note about network depiction preceding Problem 1
a) The critical path activities are A, C, E, and G.
b) The project’s duration is 22 days.
c) Yes. Activity B can be delayed by one day without delaying
the completion of the project.
Problem 9:
Task
a
m
b
Expected
Variance
Std Dev.
A
6.5
7.5
14.5
8.5
1.78
1.33
B

8.5
10.5
12.5
10.5
0.44
0.67
C
2.5
3.5
4.5
3.5
0.11
0.33
D
6.5
7.5
8.5
7.5
0.11
0.33
E
5.5
5.5
9.5
6.2
0.44
0.67
F
5.5
7.5
9.5
7.5
0.44
0.67
G
4.5

6.5
8.5
6.5
0.44
0.67
H
2.5
3.5
3.5
3.3
0.03
0.17
Desired Duration
Expected Project Duration
Sum of Variances Critical Path
Z
Probability
21
24.7
2.77
–2.2
a) 1.4%
22
24.7
2.77
–1.6

b) 5.5%
25
24.7
2.77
0.2
c) 57.9%
Problem 10:
a) The critical path is AC CB BE EF.
b) The only event with slack is “D” at 3 days.
c) If “D” were the final event in the network, then the critical
path would be AC CB BD.
d) The following spreadsheet excerpt illustrates the calculation
of the probability of completion in 14 days:
Task
a
m
b
Expected
Variance
Std Dev.
AB
3
6
9
6.0
1.00
1.00
AC
1
4
7
4.0

1.00
1.00
CB
0
3
6
3.0
1.00
1.00
CD
3
3
3
3.0
0.00
0.00
CE
2
2
8
3.0
1.00
1.00
BD
0
0
6
1.0
1.00
1.00
BE
2
5
8
5.0
1.00

1.00
DF
4
4
10
5.0
1.00
1.00
DE
1
1
1
1.0
0.00
0.00
EF
1
4
7
4.0
1.00
1.00
Desired Duration
Sum of Variances Critical Path
Z
Probability
14

16.0
4.00
–1
15.9%
e) If CD slips to six days the critical path is unchanged, but
slack on D is reduced. If CD slips to seven days, then there are
two critical paths: AC CB BE EF and AC CD DF. If CD slips to
eight days then the critical path shifts to AC CD DF and the
project duration extends to 17 days.
Problem 11:
Figure 8.11 shows duration on the arrow in matching the “(i,j)”
notation used to define the problem’s source data.
b) The critical path is A, D, C, E, F, G, H, and J.
c) The completion time is 43 days.
Problem 12:
Figure 8.12a shows the PDM network for the data from Table A
of Problem 8-12 assuming that the data were applied as shown
in Figure 8.12b.
1) The critical path is 2, 3, 4, 5, 7, 8, and 9.
2) The slack for activity 1 is 11.7 days. The slack for activity 6
is 4 days.
2) The following table shows the calculation of the expected
completion time:
Activity
a
m
b
Expected
1
8
10
13
10.2
2
5

6
8
6.2
3
13
15
21
15.7
4
10
12
14
12.0
5
11
20
30
20.2
6
4
5
8
5.3
7
2
3
4
3.0
8
4
6
10
6.3
9
2
3

4
3.0
66.4
Problem 13:
Figure 8.13 shows the network for problem 13.
1) The critical path is A, B, E, I, L, M, N, and P.
2) The completion time is 75 months.
Problem 14:
Figure 8.14a shows the original network diagram for problem
14.
s
m
2
A
B
C
E

G
H
F
D
A
B
C
E
G
H
F
D
Start
A
B
C
D
E
End
F
G
H
A
B
C
D
1
3

3
4
3
E
8
F
2
4
6
5
G
10
H
11
1
9
J
3
I
8
6
2
0
10
7
3
28
18
13
37
36
43
43
37
41
28

18
13
7
3
0
17
(
)
(
)
6
/
2
2
a
b
-
=
s
s
s
2
=
(
)
s
m
m
2
/
-
=
D
Z
Ensure to read the entire document

A radar project is in the processes of being authorized, and you
have been requested to develop a
schedule. Assume that the start date is 7 July 2014 with a
normal schedule (i.e., five-day work weeks)
and no holidays. An activity defined as a 5 week activity
requires 5 work weeks x 5 work days per
work week = 25 work days. However, when calculating a
completion date, a 5 week activity equates
to 5 calendar weeks x 7 calendar days per calendar week = 35
calendar days.
Without using any computer-based scheduling tools, provide the
following scheduling diagrams and
information for the project listed below.
1.
AON (Activity on Node) Network diagram using the most likely
duration from
the table below. The network should only use and show defined
precedence relationships.

Indicate the critical path and calculate the duration of the
project. The AON diagram should
show the task predecessors and the ES, EF, LS, LF times in a
manner similar to (see attached).
Note, however, that you are requested to draw the
diagram with Most Likely Durations, and thus you may omit the
expected time and variance
shown inside each box in the text’s figure. Also note that
network diagrams show durations,
not calendar days.
2.
Gantt schedule chart (a bar chart of the schedule) using the most
likely duration.
In contrast to the previous display, calendar time should be
represented on the time axis of a
Gantt chart.
The graphic part of the Gantt chart to be at a level of detail
similar to the chart shown in
(see attachmented). You do not need to provide the
columns (duration, start, finish, etc.) seen on the left part of the
figure. The Y axis should
only list the task names or ids corresponding to the bars on the

Gantt chart. The time axis
can be shown in months to fit the Gantt chart on one page.
3.
A table with calendar dates for start and end of each activity
and the project
completion date using the most likely duration.
4.
Calculate the expected time, the variance and the standard
deviation for each
task on the critical path.
5.
Using the project completion date from 3 as the desired
completion, calculate
the likelihood that the project will complete by that date.
6.
In a couple of paragraphs, in about half a page, explain to a
client who has
known only the Critical Path Method what you have done to
produce the likelihood in 5,
above. Assuming a mature project management organization,

how were the various
durations (i.e., optimistic, most likely, and pessimistic) for each
task produced? What
assumptions go into a PERT calculation?
All Durations Are In Weeks.
No. Task Name Optimistic Most Likley
Pessimistic Predecessors
1 Radar Project Authorized 0 0
0
2 Antenna Design 3 5
5 1 FS
3 Antenna H/W Design 6 8
10 2 SS + 5 (lag)
4 Antenna S/W Design 12 15
20 2 FS + 5 (lag)
5 Radar Interface Unit Design 4 5
6 10FS, 9FS, 4FS,3 FS

6 Radar Interface H/W Design 5 7
7 5 FS
7 Radar Interface S/W Design 12 14
16 5 FS
8 Receiver Design 3 5
7 1 FS
9 Receiver Hardware Design 5 7
9 8 FS
10 Receiver Software Design 6 8
10 8 SS
11 Design Review 3 4
6 6 FS, 7FS
12 Radar Material Acquisition 8 10
12 11 FS
13 Prototype Manufacturing 6 9
12 12 FS

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