Week 3 Homework AIB ProblemsBefore starting this homewo.docx

Week 3 Homework: AIB Problems
Before starting this homework assignment, please review the
AIB simulation in this week’s Lecture. This simulation will
provide you with an understanding of how to create a network
diagram, and how to do a forward and backward pass to
determine the ES, LS, EF, LF and slack (float). You will also
learn how to determine the duration of the project, and the
critical path.
In this homework assignment, you will be working through four
Activity In Box (AIB) problems. Using the activity, duration,
and predecessor information given in this document, you should
first construct a network for each "project." [Each problem will
have its own network.]
Once you have constructed the network, please answer the
corresponding questions. Once you answer the questions,
please post your responses to the Drop Box. You do not have to
submit your network diagrams, the answers to the questions are
sufficient.
Once the homework assignment has been graded, the solution
key will be made available. The network diagrams will be
provided, along with the answers to the questions.
Good Luck!
Problem 1

The following data were obtained from a project to create a new
portable electronic.
Activity Duration Predecessors
A 5 Days ---
B 6 Days ---
C 8 Days ---
D 4 Days A, B
E 3 Days C
F 5 Days D
G 5 Days E, F
H 9 Days D
I 12 Days G
Step 1: Construct a network diagram for the project.
Step 2: Answer the following questions: (15 points total)
a) What is the Scheduled Completion of the Project? (5 points)
b) What is the Critical Path of the Project? (5 points)
c) What is the ES for Activity D? (1 points)
d) What is the LS for Activity G? (1 points)
e) What is the EF for Activity B? (1 points)

f) What is the LF for Activity H? (1 points)
g) What is the float for Activity I? (1 points)
Problem 2
The following data were obtained from a project to build a
pressure vessel:
A 6 weeks ---
B 6 weeks ---
C 5 weeks B
D 4 weeks A, C
E 5 weeks B
F 7 weeks D, E, G
G 4 weeks B
H 8 weeks F
I 5 weeks G
J 3 week I
a) Calculate the scheduled completion time. (5 points)
b) Identify the critical path (6 points)

c) What is the slack time (float) for activity A? (1 points)
d) What is the slack time (float) for activity D? (1 points)
e) What is the slack time (float) for activity E? (1 points)
f) What is the slack time (float) for activity G? (1 points)
Problem 3
The following data were obtained from a project to design a
new software package:
A 5 Days ---
B 8 Days ---
C 6 Days A
D 4 Days C, B
E 5 Days A
F 4 Days D, E, G
G 4 Days B, C
H 3 Day G

b) Identify the critical path(s) (6 points)
c) What is the slack time (float) for activity B? (1 points)
f) What is the slack time (float) for activity G? (1 points)
Problem 4
The following data were obtained from an in-house MIS project:

A 5 Days ---
B 8 Days ---
C 5 Days A
D 4 Days B
E 5 Days B
F 3 Day C, D
G 7 Days C, D
H 6 Days E, F, G
I 9 Days E, F
b) Identify the critical path (6 points)
c) What is the slack time (float) for activity A? (1 points)

f) What is the slack time (float) for activity F? (1 points)
1
PM586_ActivityInBox Page 1 of 4
Female
www.verbalink.com Page 1 of 4
Welcome to Arrow Toys, Incorporated. I’m Sandra, the lead
project manager for our
new toy division. We’ve just received the green light to start a
new project, a remote
control plane, the Biplane 3000. They want a prototype right
away, and we need to start
planning. We have a lot of work ahead of us, so let’s get
started.
To help us forecast the project schedule, we are going to build
an activity in box diagram
to help us determine how much time is allowed for each
activity, the float for each
activity, and the critical path for our project. We have
identified nine major activities for
our project, but first let’s look at the principle behind the
activity in box diagram.

An activity in box diagram represents our project. Each activity
in our project is
represented by a box, and each box contains specific
information regarding that activity.
For example, each box contains a description of the activity and
schedule information.
The schedule information includes the activity number, which is
the order in which the
activity will be completed, the person responsible for that
activity, and the duration time,
or how long it will take to complete that activity.
Let’s look at a box more closely. The box also contains
information on the start times
and finish times for that activity. The top left corner identifies
the earliest time that the
activity can start. Here is the earliest time that an activity can
finish. On the lower left of
the box is the latest time the activity can start. On the lower
right of the box is the latest
time the activity can finish.
Now that you understand the information that is contained in
each box, let’s apply it to
our Biplane 3000 project. Let’s take a look at our list of
activities.
We have nine activities that need to be completed. We also
know how long each activity
will take to complete. Before we begin building our activity in
box diagram, we need to
identify any predecessors. A predecessor is an activity that
must be completed before
another activity can begin. For example, activity four, design
remote functions, has a
predecessor. Activity one, design body of plane, must be

complete in order for activity
four to begin.
As you know, each activity will have its own box and the boxes
will be connected by
paths. We will then calculate the project schedule completion
time and critical path.
Finally, we’ll determine the float, or the window in which we
have to complete a certain
activity, using the forward pass and backward pass methods.
We’ll talk more about this
later.
I know that is a lot to take in, so let’s take a look at what we
know so far about our
project and build our activity in box diagram. The diagram
begins with a starting point
and an ending point. Now let’s start from the beginning. We
know that activities one,
two, and three do not have predecessors, and these activities
start at the beginning of our
project, so let’s place them in the beginning of our diagram.
Female
Now this gets a little tricky. Let’s add the remaining boxes.
We have to be careful; we
must pay close attention to the predecessors. Our next box is

box four, design remote
functions. This activity can only begin after the first activity
ends, so let’s place it here in
our diagram. But what about activity five, assemble
components? It has a predecessor of
both activities two and three. We’ll place it here. Activities six
and seven also have
predecessors two and three. Where would you place these
boxes? Again, these boxes
can only begin after the first activity ends. The next box is
activity eight, finalize testing.
This, too, has a predecessor. Where would you place this box?
And finally, our last box,
production of biplane. It has a predecessor, and we’ll place it
here in our diagram.
Now let’s review our activity in box project diagram. At the
beginning of our project, we
have three activities or boxes that can begin immediately
because they do not require a
predecessor. Next we added activity four, only after activity
one has completed. Next
we added activities five, six, and seven. These boxes have
predecessors of activities two
and three. Then we added our last two activities based on the
predecessor information.
Pretty straightforward, right? We’re not done yet. Remember
the project activity
information? Let’s add that now. As you recall, each box is
divided into several
sections. Let’s discuss the forward pass method and add our
project details.
The forward pass method is used to calculate the earliest start
and finish times for each

activity and to calculate the project completion time. The
earliest start time for each
activity is determined by the predecessor’s finish time. If an
activity does not have a
predecessor, then the earliest start time is zero; however, if an
activity has two or more
predecessors, then the earliest start time is the value of the
largest finish time of the
predecessors. In other words, all of the predecessors must
finish before the activity can
begin. The earliest finish time is the sum of the earliest start
time and the activity
duration. Let’s add the earliest start and finish times.
Activity information for each activity is located at the bottom of
each box. The first box
is for the activity number. Since this is our first activity, let’s
put a one in the box. Next
I will add the person responsible for completing that activity.
This can be one person or a
group of people. I will supply this information for you. In the
lower right hand box is
the duration for that activity. Looking at our project list, how
long will activity one take?
We have 20 weeks for activity one. Remember the start and
finish times? Let’s add
those now. The project start time is zero, so for our first
activity the start time is zero.
Let’s put a zero in the earliest start time area. We know from
the duration schedule that
box one takes 20 weeks, so I will put 20 in the earliest finish
time area.
Great. Now that you’ve entered the earliest start and finish
times, we can calculate how
long our project will take. So what is the final completion date

for our project? If we
follow through on all activities, and keeping in mind the weeks
allowed for each activity
to complete, our project will take 48 weeks. Pretty easy, huh?
Now it’s time for the
backward pass method.
Female
Now you try it. Enter the project information and the earliest
start and finish times.
Remember to keep in mind that the earliest start time may be
based on a predecessor.
Just like the name implies, we are going to start from the end of
our project and work our
way backwards. The backward pass method is used to calculate
the latest start and finish
times for each activity, determine the critical path, and
determine the float for each
activity. The latest finish time for an activity can be
determined by the successor’s latest
start time, so if the activity has one successor, then the latest
finish time, or OF, is the
same as the successor’s latest start time, or OST. If the
successor is end, then the latest
finish time is set to the schedule completion time already
calculated in the forward pass.

On the other hand, determining the latest finish time could get
tricky if there are multiple
successors. A rule of thumb to remember is to set the latest
finish time equal to the least
or minimum latest start time of the successors. Choosing
otherwise will cause a delay in
the project schedule time. Calculating the latest start time is
easy; just subtract the
activity duration from the activity latest finish time.
We are going to start with our schedule completion time of 48
weeks and work our way
backwards. Let’s look at the formula to determine the latest
start and finish times using
the backward pass method. Since the 48th week is the latest we
can finish our project, we
will start by calculating the latest start time by subtracting the
duration from the last
finish time. For example, production of biplane ends on week
48. The latest finish time
is 48, since we are starting from the end of our project. And
since we know that it takes
18 weeks to complete, we will subtract 18 from 48 to get the
OST, latest start time, which
is 30.
Let’s try the next one. We know that finalized testing does not
have any successors, and
this activity can end on week 48. And since we know that this
activity takes 11 weeks to
complete, then our OST, latest start time, is 37.
I know that this can get tricky. Do you remember the formula?
Remember that the latest
finish time is determined by the least or minimum successor

activity latest start time, or if
there are no successors, the latest finish time is set to the
schedule completion time
determined in the forward pass.
Great job! We’re almost done. Now that we have all of our
calculations, let’s look at the
critical path and float for our project.
Now you try it.
The critical path by definition is the path of activities which
have a float value of zero.
The critical path is especially important because if any
activities are completed later than
scheduled, then the project may not complete on time. The float
of a project tells you the
number of days, weeks, and months an activity can begin late.
It also tells you the
number of extra days, weeks, or months an activity can take
without having an impact on
the completion time of the project. The float is shared by all
activities on a path. If you
Female
use up all your slack on any activity at the beginning of a path,
subsequent activities will
have less slack, or no slack at all.

Let’s take a look at our float values for our project. We can see
that most of our activities
have some extra time to complete, and some don’t. These
activities determine our critical
path. We have three activities that are critical. If you recall,
the critical path is especially
important because if any activities are completed later than
scheduled, then the project
may not complete on time.
I know this can be complicated, but the activity in box diagram
helps project managers to
manager their projects more effectively and efficiently.
Let’s take a brief look at all the concepts we covered for our
Biplane 3000 project. First
we built an activity in box diagram based on our project details.
Then we determined the
earliest start time and earliest finish time for each activity using
the forward pass method.
Next we calculated the latest start time and latest finish time for
each activity using the
backward pass method. Finally we calculated the float values
for our activities and
determined which paths were critical to our project.
Our project schedule for the Biplane 3000 is now complete.
Fantastic job!
[End of Audio]
Print

Network Diagrams and Resource Utilization
Introduction | Building a Network Diagram | Building an AIB
Manually | AIB Simulation | Resource Constrained Planning |
Resource Leveling | Adding or Modifying Resources | Summary
Introduction
Back to Top
Last week, we learned more about how to begin planning a
project. We established the project charter, scope statement,
work breakdown structure, and created the activity list. This
week, we will talk about one of the most important aspects of
project management—building a project schedule. We'll use a
tool called a network diagram. There are several ways to build a
network diagram. In this course, we will use the Activity in Box
(AIB) method.
Building a Network Diagram
Back to Top
Now that we know what needs to be done, we need to sequence
all of the activities and establish a network diagram. With the
concept of a network diagram, you will be able to determine:
(1) a project's scheduled completion time, (2) the slack or float
of project activities, and (3) the critical path of your project.
Depending on the size of the project, the network may be built
in pieces or as a large group. Either way, the step-by-step
process to build a project network is used.
Build a Project Network (or a Partial Network)
1. Brainstorm activities that are required to complete the work
packages, recording those activities on Post-it notes (without
regard to sequencing).
2. Sequence those activities. Determine:
· The order of activities
· Which activities can occur at the same time
· Which activities need dependencies
1. Mandatory: requires the completion of another task.
2. Discretionary: a best practice or convenience. However, the
subsequent task can begin if the discretionary dependency is not

completed.
3. External: from another project or process, such as permits.
4. Internal: dependencies within the control of the project team.
3. Put the notes on a wall using the above information.
4. Build a network using the notes.
Next, the activities are assigned to the people who will be doing
the work. They build duration estimates for the activities. The
most accurate estimates are built using actuals from previous,
similar projects. Then, the activities can be loaded into an
automated scheduling tool like Microsoft Project. At that point,
you will be able to determine the project's scheduled completion
time, the slack or float of project activities, and the critical path
of your project.
Building an AIB Manually
Back to Top
The good thing about using a tool like Microsoft Project is that
it makes it easy to build a network diagram. The bad thing about
the tool is that it makes it so easy; project managers don't
always understand what they are doing, and cannot see when
they have made a mistake. They just plug in the activities and
move on.
It's like adding—you should first do it manually, and then use a
calculator. Every project manager should know how to build an
AIB manually so that he or she really understands the concepts
before working in Microsoft Project. The project managers who
understand it are much more effective and know how to use the
tools more effectively. Those who do not know how to build a
schedule manually often make mistakes and negatively impact a
project's triple constraints. Practice is required for proficiency.
Just like swimming, scheduling requires practice. You can read
about it, but you must also practice it. Let's start to practice!
When you build the network manually, you will understand the
concepts much better. This demonstration will walk you through
the process of building an AIB manually. You will conduct a
forward pass through a network to determine the early start and
early finish of each activity. A forward pass is moving from

start to finish of the project doing all necessary calculations.
When you complete the forward pass, you know which activity
will be the last one to complete. The Early Finish for that
activity is the earliest date that your project can complete. Next,
you will conduct a backward pass, by moving from finish to
start, to determine the late start and late finish for each activity.
Last of all, you calculate the slack/float for each activity.
Before you begin the AIB Simulation, let's define a few terms.
· Critical Path (CP): By definition, it is the path of activities
from start to finish that all have a slack/float of 0. This path is
especially important because if any of them complete later than
scheduled, your project may not complete on time.
· Early Start (ES): Is the EARLIEST time the activity could
possibly start.
· Early Finish (EF): Is the EARLIEST time the activity could
possibly finish.
· Late Start (LS): Is the LATEST time the activity can start and
not jeopardize the scheduled completion of the project.
· Late Finish (LF): Is the LATEST time the activity can finish
and not jeopardize the scheduled completion of the project.
· Slack/Float or Total Slack/Float: Is calculated by: LF - EF, or
LS - ES (both formulas will result in the same answer; if not,
one of your numbers is incorrect). The slack/float tells you the
number of days/weeks/months that an activity can begin late, or
the number of extra days/weeks/months that an activity can take
without impacting the completion time of the project. However,
this time is shared by all of the activities on a path. If you use
up all of your slack on an activity at the beginning of a path,
subsequent activities will have less slack or no slack.
· Free Slack/Float: This represents how much an activity can
slip without impacting a successor activity. This measure
combined with slack determines which activities receive
priority over resources.
AIB Simulation
Back to Top
Simulation

Activity in Box Diagram
Welcome to the Bi-Plane 3,000 Project! In this simulation, you
will shadow Sandra, an experienced Project Manager, as she
walks you through the construction of an Activity in Box
Diagram. You will have opportunities to practice both the
Forward and Backward Pass methods in depth. Together, you
will cover the concepts of critical path and float.
Practitioner Corner
In the project management world, you are not likely to hear the
term Activity in Box (AIB) unless you learned your project
management from a textbook. In our world, we use the term
Activity on the Node or AON. The calculations are the same but
the set up is a little different. It is also the method employed by
most project management software. So if you hear the term
AON, network diagramming or precedence diagramming from
project managers, you now know they are all talking about the
same thing.
Resource Constrained Planning
Back to Top
Now that we have our project schedule established, we need to
align the appropriate resources to accomplish the work. As
resources are applied, conflicts may arise if resources become
over-allocated.
A project manager can address resource conflicts in a variety of
ways, but the first step is to realize there is a conflict. If the
project team builds a schedule using a scheduling tool like
Microsoft Project, the PM can run an Overallocated Resources
report.
Once the over allocation is identified, there are several key
strategies to address them: (1) resource leveling, (2) adding or
modifying resources, and (3) changing the project.
Most methods for addressing resource conflicts cost the project
something, either more money, less functionality, or an
extension in the scheduled completion.
So why bother? In some cases, you have no choice—operational

necessity. For instance, if your company has two bulldozers,
and you need four on a particular week, you will have to
address that resource conflict to complete both projects.
On other projects, resource conflicts take the form of people
being over allocated. Sometimes, a team lead will say that is
what nights and weekends are for but many people would
strongly disagree. If people are overworked, something will
suffer, either the quality of the product will decrease, and
defects and re-work will increase.
Ultimately, it will result in personnel turnover. It costs a project
time and money when people are replaced. If you make people
miserable enough, they will leave either by quitting, getting
sick, transferring, or just not working up to their capacity.
Addressing resource conflicts improves morale, which increases
quality, reduces defects, reduces re-work, decreases team
turnover, and increases team commitment.
Resource Leveling
Back to Top
The first method—resource leveling is the easiest to do if you
are using an automated scheduling tool like Microsoft Project,
but only if you understand what you are doing. You can also use
the tool to try various what-ifs. For example, try plugging in
new resources and see if their addition will change your
scheduled completion time. If they are not working on a task on
the critical path, their work will not even affect the project's
scheduled completion. One must be careful with auto leveling in
project management software, as it might change the program’s
algorithm associated with the triple constraint.
This method smoothes out the peaks and valleys in your
schedule without increasing your overall budget. If you choose
a level only within available slack as an option when you level
the resources, leveling the resources will not extend your
project's schedule either. However, if there is not enough slack
in your schedule, it will not correct all of your allocation
problems, in which case, you will have to use another method to
relieve the problem.

In summary, the benefits of resource leveling are:
1. Minimizes period-by-period variations by shifting tasks
within their slack
2. Utilizes resources more efficiently
3. Resources do not have days with no work scheduled and other
days with too much work
4. Does not increase budget
5. Does not have to change scheduled completion
Here is an example:
Click on image to enlarge
Before Leveling
After Leveling
Click here for Transcript
Before leveling: The resource is over allocated on 5/2, but not
scheduled to do any work on 5/10. With this schedule, I work
for 16 straight hours on 5/2, and have nothing to do on 5/10.
After leveling: MSP moved the excess work from 5/2 onto 5/10.
With this schedule, I work a regular eight hours each day—
much more palatable! However, as I mentioned before,
sometimes there is not enough slack in the schedule to smooth
out all of your activities, so let's look at some other options.
Adding or Modifying Resources
Back to Top
Adding people to a project must be approached carefully.
Additional people are easier to absorb into projects that are
well-documented. Adding personnel to well-defined tasks is
straightforward when the plan is clear. Throwing people at
projects that are in trouble, behind, and already managed poorly
often results in an even bigger problem.
Adding resources increases the budget and rarely doubles the
work completed. This is because additional people must be
trained, which ties up their time and the time of a team member
who is training them, and adds to the communication channels.
Modifying resources can take several forms: Assign a person
with greater expertise or more experience to perform or help
with the activity, and increase productivity through improved

methods or technology.
Summary
Back to Top
Hide and Show
1. What are the different types of dependencies?
Hide Answer
There are four different types of dependencies, including:
Mandatory – requires the completion of another task.
Discretionary – a best practice or convenience. However, the
subsequent task can begin if the discretionary dependency is not
completed.
External – from another project or process.
Internal – dependencies within the control of the project team.
Hide and Show
1.
Hide Answer
The critical path is the path of activities that all have a
slack/float of 0. It is important because if any of them complete
later than scheduled, the project may not be completed on time.
Hide and Show
1. Which tasks would likely be part of the critical path for
building a canoe? Why do the other activities have float/slack?
Hide Answer
1. Obtain wood for boat
2. Build seats
3. Obtain oars or paddles
4. Cut and shape wood for boat body
5. Paint canoe with water sealant
6. Test boat in water
Hide and Show
1. Which tasks would likely be on the critical path for building
a house? Why do the other activities have float/slack?

Hide Answer
1. Obtain bricks
2. Paint Rooms
3. Install furnace
4. Obtain lumber
5. Wire for electricity
6. Obtain building permit
Hide and Show
1. What is float?
Hide Answer
Float is the number of extra days/weeks/months an activity can
take without impacting the completion time of the project. It is
calculated by subtract Earliest Finish Time (EF) from Latest
Finish Time (LF).
Hide and Show
1. Define an activity duration estimate.
Hide Answer
The duration estimate for an activity is the time required to
perform the work plus any associated waiting time.
Hide and Show
1. What are the benefits of resource leveling?
Hide Answer
· Minimizes period-by-period variations by shifting tasks within
their slack Utilizes resources more efficiently
· Resources do not have days with no work scheduled and other
days with too much work.
· Does not increase budget
· Does not have to change scheduled completion
Back to Top
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