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Soe Naing Win
Email: snw1975@gmail.com
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• Identification a real need & Selection of the best
approach
• Structuring the project: WBS, OBS, LRC
• Determine the “cost” and “duration” of the tasks
and the whole project

• Project Scheduling: Gantt chart, Network model
• Project budgeting and resource planning
 Understand the importance of project scheduling.

 Understand and complete the project scheduling
using Early and late start of Gantt chart.
 Apply network technique to complete project scheduling
using forward and backward path of AON method.
 Introduction
 Precedence Relationship
 Gantt Chart

 Activity on Node (Critical Path
Method)
 Introduction

 Precedence Relationship
 Gantt Chart
 Activity on Node (Critical Path Method)
 Scheduling can be developed after WBS is

established and the time estimation for each activity is
done.
 Scheduling is the most important step in planning
because it is the basis for
 allocating resources,
 estimating revenue and spending
 controlling the cash flow
 monitoring project performance
The scheduling process will integrate:
 The estimated duration of activities.
 The technological precedence relations
among activities.
 Constraints imposed by the availability of
resources and budget.

 Due-date requirements
Activity – any task, any job or any operation which

must be completed to finish the project.
It requires time (for people to work or to wait) and
may require resources.
Have to consider logical relationships between
activities.


Calendar/ Workpattern » the days on which the

works are scheduled.


Like what days of the week will be working or How
many days a week (e.g. 5 days per week, 8 hours per
day).



The work pattern allows the activity durations to be

related to calendar dates.
Milestones are any significant events in a project.
They should represent major segments of work - should
be a natural, important control point.
Milestone chart is the skeleton for the project schedule
which senior managers should know.
Examples:
 completion of critical or difficult tasks v' availability of
crucial resources
 Completion of major tests
 How to start a schedule?

 Top down - define major task (milestones or phases)
and then decompose each milestone/phase into more
detailed activities.
 Bottom up - list all the activities in a project in any
order. Group the list into phases/milestones based on
the required sequence, constraints, and assumptions.
 Introduction

 Precedence Relationship
 Gantt Chart
 Activity on Node (Critical Path Method)
.  Precedence relations – technological constraints of the
project that limit the availability of resources to perform
activities.
 How to arrange “the order of activities”.
 Finish-to-start relationship
 Start-to-start relationship

 Finish-to-finish relationship
 Start-to-finish relationship.
.  Finish-to-start relationship: typical, generic
relationship mostly used in scheduling. Requires that an
activity can start only after its predecessor has been
completed.
 Activity 020 can not start until activity 010 is finished.

 Space shuttle can be launched after all payloads are in
place.
 Shipment can begin after the quality inspection is done.
. Start to start relationship - exists when an activity can
start only after a specified activity has already begun.
 Sequential activities can be worked in parallel and
concurrently.
 activity 060 can start after activity 050 has started.

 In the construction of a house, the foundation work can be
started even though the final design is not finished. Usually, only
the initial design plan is required for the foundation work.
.  Finish-to-finish relationship – The finish of one
activity depends on the finish of another activity.


Activity 2000 can finish, after activity 1000 is completed.



For example, if you have two tasks, "Add wiring" and "Inspect
electrical," the "Inspect electrical" task cannot be completed
until the "Add wiring" task is completed
.

 Start-to-finish relationship – an activity cannot finish

until another activity has begun (Overlap).
 After activity A100 starts, A200 can finish



For example, the roof trusses for your construction project are
built off-site. Two of the tasks in your project are "Truss delivery"
and "Assemble roof." The "Assemble roof" task cannot be
completed until the "Truss delivery" task begins.



A security guard’s shift cannot end until the
next guard has commenced his/her shift.
.  Schedules can be presented in several different ways

to match the needs of the user.
 Chart
 Milestone chart
 Gantt chart

 Networks either AOA (Activity on arrow) or AON
(activity-on-node) method.
 Critical Path Method (CPM) .
 Program Evaluation and Review Technique (PERT).
 Introduction

 Precedence Relationship
 Gantt Chart
 Activity on Node (Critical Path Method)
.

 The most widely used management tool for project
scheduling and control.
 Particularly useful to manage “critical” and “scarce”
resources.
 Possible to schedule activities by either early-start or
late-start logic. Then a range of schedules can be
generated using a combination of these two.
 Disadvantage: does not show inter-relationships
among activities - network techniques are often used
in parallel to compensate it.
Horizontal bars denote the
length of time for each activity.

.
Activity
A

1

2

A

3

A

B
C

4

5

6

7

8

C

C

C

C

D

D

D

9

10

11

E

E

F

F

12

13

14

F

F

F

BBB
C

D
E
F

Vertical Axis: Always
Activities or Jobs

C

D
E

Horizontal Axis:
Always Time


Early start or late start approach.
The early start approach - each activity is initiated as
early as possible without violating the precedence
relations.
The late start approach - each activity is delayed as
much as possible as long as the finish time of the project
is not compromised.
Activity

Immediate Predecessors

Duration (weeks)

A

--

5

B

--

3

C

A

8

D

A,B

7

E

--

7

F

C, D, E

4

G

F

5

 Activities, A, B and E do not have any predecessors and thus can start at
any time.
 Activity C can start only after A finishes, while D can start after the
completion of A and B.
 F can start only after C, D and E are finished, and G must follow F.
1.

Generate the early start schedule using activity list given
and its precedence relationships - the duration of the
whole project will be obtained,

2.

Using the duration of the whole project obtained, the late
start schedule can be generated by shifting each activity to
the right as much as possible without violation of
precedence relationships.
 When the late start is completed, make sure that the
starting date of the whole project is day (week) 1.

3.

With applying a combination of early and late start
approaches, a range of schedules can be generated on
Gantt chart - Slack management!
Activity

A
B
C
D
E
F
G

Immediate
Predecessors
--A
A,B
-C, D, E
F

 For early start:
Count from the beginning!
 Activities, A, B and E do not have any predecessors
and thus can start at Week 1.
1 2 3 4 5 6 7
A A A A A A
B B B B
C
D
E E E E E E E E
F
G

8

Duration
(weeks)
5
3
8
7
7
4
5

9 10 11 12 13 14 15 16 17 18 19 20 21 22
Activity

A
B
C
D
E
F
G

Immediate
Predecessors
--A
A,B
-C, D, E
F

 Activity C can start
only after A finishes,
While D can start after the completion of both A and B.

Duration
(weeks)
5
3
8
7
7
4
5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
A A A A A A
B B B B
C
C C C C C C C C
D
D D D D D D
E E E E E E E E
F
G
Immediate
Duration
Predecessors
(weeks)
A
-5
B
-3
C
A
8
D
A,B
7
E
-7
 F can start only after
F
C, D, E
4
C, D and E are finished,
G
F
5
and G must follow F - early start Gantt chart finished. Duration is 22 weeks.
Activity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
A A A A A A
B B B B
C
C C C C C C C C
D
D D D D D D D
E E E E E E E E
F
F F F F
G
G G G G G
Activity

Immediate
Predecessors

Duration
(weeks)

A
-5
B
-3
C
A
8
D
A,B
7
E
-7
 For Late start
F
C, D, E
4
Count form the End!
G
F
5
 Compare activity list and predecessor column -find any missing activity
- start of LS (in here G)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
A
B
C
D
E
F
G
G G G G G
Activity

A
B
C
D
E
F
G

 Activity F is
required by only G.

1
A
B
C
D
E
F
G

2

3

4

5

6

7

8

Immediate
Predecessors
--A
A,B
-C, D, E
F

Duration
(weeks)
5
3
8
7
7
4
5

9 10 11 12 13 14 15 16 17 18 19 20 21 22

F

F

F

F
G G G G G
Activity
A
B
C
D
E
F
G

Activity C, D, & E are
required by only F.

1
A
B
C
D
E
F
G

2

3

4

5

6

7

8

Immediate
Predecessors
--A
A,B
-C, D, E
F

Duration
(weeks)
5
3
8
7
7
4
5

9 10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C C C C C
D D D D D D D
E E E E E E E
F

F

F

F
G G G G G
A
B
C
D
E

Immediate
Predecessors
--A
A,B
--

Duration
(weeks)
5
3
8
7
7

F

C, D, E

4

G

F

5

Activity

Activity B is required by only D.

1
A
B
C
D
E
F
G

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22

B B B
C C C C C C C C
D D D D D D D
E E E E E E E
F

F

F

F
G G G G G
Activity

Activity A is required by both C & D.
You have to follow the earlier one!

1 2 3 4 5 6 7 8 9
A A A A A A
B
B B B
C
C C C C
D
D D D
E
E E E
F
G

A
B
C
D
E
F
G

Immediate
Predecessors
--A
A,B
-C, D, E
F

Duration
(weeks)
5
3
8
7
7
4
5

10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C
D D D D
E E E E
F

F

F

F
G G G G G
Activity

Remember!! The starting date of the
starting date of the schedule should
be “week 1”.
1 2 3 4 5 6 7 8 9
A A A A A A
B
B B B
C
C C C C
D
D D D
E
E E E
F
G

A
B
C
D
E
F
G

Immediate
Predecessors
--A
A,B
-C, D, E
F

Duration
(weeks)
5
3
8
7
7
4
5

10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C
D D D D
E E E E
F

F

F

F
G G G G G
ES

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
A A A A A A
B B B B
C
C C C C C C C C
D
D D D D D D D
E E E E E E E E
F
F F F F
G
G G G G G
LS
1 2 3 4 5 6 7 8 9
A A A A A A
B
B B B
C
C C C C
D
D D D
E
E E E
F
G

10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C
D D D D
E E E E
F F F F
G G G G G
ES
• Total Slack

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
(float) of activity A A A A A A
- the difference B B B B
C
C C C C C C C C
between the
D D D D D D D
start (or the end) D
E E E E E E E E
times of an
F
F F F F
activity on the
G G G G G
two schedules. G
LS

1 2 3 4 5 6 7 8 9
A(0), B(3), C(0), A A A A A A
B
B B B
D(1), E(6), F(0),
C
C C C C
G(0)
D
D D D
E
E E E
F
G

10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C
D D D D
E E E E
F

F

F

F
G G G G G
 Critical activities: activities not having any total slacks

 Critical Path: the sequence of critical activities
connecting the start and the end points of the project.
The duration of the whole project.

 A delay in any activity along the critical path delays the
entire project, so special attention should be made for
the delay of critical activities: Control actions.
ES
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
A A A A A A
B B B B
C
C C C C C C C C
D
D D D D D D D
E E E E E E E E
F
F F F F
G
G G G G G
LS

Critical Path: A>C>F>G

1 2 3 4 5 6 7 8 9
A A A A A A
B
B B B
C
C C C C
D
D D D
E
E E E
F
G

10 11 12 13 14 15 16 17 18 19 20 21 22

C C C C
D D D D
E E E E
F F F F
G G G G G
 Introduction

 Precedence Relationship
 Gantt Chart
 Activity on Node (Critical Path Method)


PERT (Program Evaluation and Review Technique)
◦ Views the time to complete an activity as a random variable that
can be characterised by an optimistic, a pessimistic, and a most
likely estimate of its duration.
◦ Statistical method is used to estimate time.



CPM (Critical Path Method)
◦ Assumes that activity times are deterministic.
◦ Critical path is determined and used to analyse time of a project.



Usually CPM is good enough for most projects.



Network models are to be developed for it.


Project network model is a graphical flow chart of the
project job plan.



Shows the inter-relationships of all activities :
communication channels defined.



Identify the critical paths.



Calculate the expected project completion dates.



Usually used together with Gantt chart


Activity-on-Arrow (AOA) Analysis
◦ The arrows represent the activities, while the nodes
represent events.
◦ Closely associated with PERT analysis, but it can also be
used for CPM analysis.
◦ Often requires the dummy event nodes that correct the
network function > complication also introduced.



Activity-on-Node (AON) Analysis
◦ The nodes represent the activities and the arrows identify
the precedence relationships between activities.
◦ Closely associated with CPM analysis.
◦ More popular than AOA.


TO BE CONTINUED!!
00 Introduction of project scheduling

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00 Introduction of project scheduling

  • 1. Soe Naing Win Email: snw1975@gmail.com
  • 2. 1 2 3 • Identification a real need & Selection of the best approach • Structuring the project: WBS, OBS, LRC • Determine the “cost” and “duration” of the tasks and the whole project • Project Scheduling: Gantt chart, Network model • Project budgeting and resource planning
  • 3.  Understand the importance of project scheduling.  Understand and complete the project scheduling using Early and late start of Gantt chart.  Apply network technique to complete project scheduling using forward and backward path of AON method.
  • 4.  Introduction  Precedence Relationship  Gantt Chart  Activity on Node (Critical Path Method)
  • 5.  Introduction  Precedence Relationship  Gantt Chart  Activity on Node (Critical Path Method)
  • 6.  Scheduling can be developed after WBS is established and the time estimation for each activity is done.  Scheduling is the most important step in planning because it is the basis for  allocating resources,  estimating revenue and spending  controlling the cash flow  monitoring project performance
  • 7. The scheduling process will integrate:  The estimated duration of activities.  The technological precedence relations among activities.  Constraints imposed by the availability of resources and budget.  Due-date requirements
  • 8. Activity – any task, any job or any operation which must be completed to finish the project. It requires time (for people to work or to wait) and may require resources. Have to consider logical relationships between activities.
  • 9.  Calendar/ Workpattern » the days on which the works are scheduled.  Like what days of the week will be working or How many days a week (e.g. 5 days per week, 8 hours per day).  The work pattern allows the activity durations to be related to calendar dates.
  • 10. Milestones are any significant events in a project. They should represent major segments of work - should be a natural, important control point. Milestone chart is the skeleton for the project schedule which senior managers should know. Examples:  completion of critical or difficult tasks v' availability of crucial resources  Completion of major tests
  • 11.  How to start a schedule?  Top down - define major task (milestones or phases) and then decompose each milestone/phase into more detailed activities.  Bottom up - list all the activities in a project in any order. Group the list into phases/milestones based on the required sequence, constraints, and assumptions.
  • 12.  Introduction  Precedence Relationship  Gantt Chart  Activity on Node (Critical Path Method)
  • 13. .  Precedence relations – technological constraints of the project that limit the availability of resources to perform activities.  How to arrange “the order of activities”.  Finish-to-start relationship  Start-to-start relationship  Finish-to-finish relationship  Start-to-finish relationship.
  • 14. .  Finish-to-start relationship: typical, generic relationship mostly used in scheduling. Requires that an activity can start only after its predecessor has been completed.  Activity 020 can not start until activity 010 is finished.  Space shuttle can be launched after all payloads are in place.  Shipment can begin after the quality inspection is done.
  • 15. . Start to start relationship - exists when an activity can start only after a specified activity has already begun.  Sequential activities can be worked in parallel and concurrently.  activity 060 can start after activity 050 has started.  In the construction of a house, the foundation work can be started even though the final design is not finished. Usually, only the initial design plan is required for the foundation work.
  • 16. .  Finish-to-finish relationship – The finish of one activity depends on the finish of another activity.  Activity 2000 can finish, after activity 1000 is completed.  For example, if you have two tasks, "Add wiring" and "Inspect electrical," the "Inspect electrical" task cannot be completed until the "Add wiring" task is completed
  • 17. .  Start-to-finish relationship – an activity cannot finish until another activity has begun (Overlap).  After activity A100 starts, A200 can finish  For example, the roof trusses for your construction project are built off-site. Two of the tasks in your project are "Truss delivery" and "Assemble roof." The "Assemble roof" task cannot be completed until the "Truss delivery" task begins.  A security guard’s shift cannot end until the next guard has commenced his/her shift.
  • 18. .  Schedules can be presented in several different ways to match the needs of the user.  Chart  Milestone chart  Gantt chart  Networks either AOA (Activity on arrow) or AON (activity-on-node) method.  Critical Path Method (CPM) .  Program Evaluation and Review Technique (PERT).
  • 19.  Introduction  Precedence Relationship  Gantt Chart  Activity on Node (Critical Path Method)
  • 20. .  The most widely used management tool for project scheduling and control.  Particularly useful to manage “critical” and “scarce” resources.  Possible to schedule activities by either early-start or late-start logic. Then a range of schedules can be generated using a combination of these two.  Disadvantage: does not show inter-relationships among activities - network techniques are often used in parallel to compensate it.
  • 21. Horizontal bars denote the length of time for each activity. . Activity A 1 2 A 3 A B C 4 5 6 7 8 C C C C D D D 9 10 11 E E F F 12 13 14 F F F BBB C D E F Vertical Axis: Always Activities or Jobs C D E Horizontal Axis: Always Time
  • 22.  Early start or late start approach. The early start approach - each activity is initiated as early as possible without violating the precedence relations. The late start approach - each activity is delayed as much as possible as long as the finish time of the project is not compromised.
  • 23. Activity Immediate Predecessors Duration (weeks) A -- 5 B -- 3 C A 8 D A,B 7 E -- 7 F C, D, E 4 G F 5  Activities, A, B and E do not have any predecessors and thus can start at any time.  Activity C can start only after A finishes, while D can start after the completion of A and B.  F can start only after C, D and E are finished, and G must follow F.
  • 24. 1. Generate the early start schedule using activity list given and its precedence relationships - the duration of the whole project will be obtained, 2. Using the duration of the whole project obtained, the late start schedule can be generated by shifting each activity to the right as much as possible without violation of precedence relationships.  When the late start is completed, make sure that the starting date of the whole project is day (week) 1. 3. With applying a combination of early and late start approaches, a range of schedules can be generated on Gantt chart - Slack management!
  • 25. Activity A B C D E F G Immediate Predecessors --A A,B -C, D, E F  For early start: Count from the beginning!  Activities, A, B and E do not have any predecessors and thus can start at Week 1. 1 2 3 4 5 6 7 A A A A A A B B B B C D E E E E E E E E F G 8 Duration (weeks) 5 3 8 7 7 4 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22
  • 26. Activity A B C D E F G Immediate Predecessors --A A,B -C, D, E F  Activity C can start only after A finishes, While D can start after the completion of both A and B. Duration (weeks) 5 3 8 7 7 4 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A A A A A A B B B B C C C C C C C C C D D D D D D D E E E E E E E E F G
  • 27. Immediate Duration Predecessors (weeks) A -5 B -3 C A 8 D A,B 7 E -7  F can start only after F C, D, E 4 C, D and E are finished, G F 5 and G must follow F - early start Gantt chart finished. Duration is 22 weeks. Activity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A A A A A A B B B B C C C C C C C C C D D D D D D D D E E E E E E E E F F F F F G G G G G G
  • 28. Activity Immediate Predecessors Duration (weeks) A -5 B -3 C A 8 D A,B 7 E -7  For Late start F C, D, E 4 Count form the End! G F 5  Compare activity list and predecessor column -find any missing activity - start of LS (in here G) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A B C D E F G G G G G G
  • 29. Activity A B C D E F G  Activity F is required by only G. 1 A B C D E F G 2 3 4 5 6 7 8 Immediate Predecessors --A A,B -C, D, E F Duration (weeks) 5 3 8 7 7 4 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 F F F F G G G G G
  • 30. Activity A B C D E F G Activity C, D, & E are required by only F. 1 A B C D E F G 2 3 4 5 6 7 8 Immediate Predecessors --A A,B -C, D, E F Duration (weeks) 5 3 8 7 7 4 5 9 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C C C C C D D D D D D D E E E E E E E F F F F G G G G G
  • 31. A B C D E Immediate Predecessors --A A,B -- Duration (weeks) 5 3 8 7 7 F C, D, E 4 G F 5 Activity Activity B is required by only D. 1 A B C D E F G 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 B B B C C C C C C C C D D D D D D D E E E E E E E F F F F G G G G G
  • 32. Activity Activity A is required by both C & D. You have to follow the earlier one! 1 2 3 4 5 6 7 8 9 A A A A A A B B B B C C C C C D D D D E E E E F G A B C D E F G Immediate Predecessors --A A,B -C, D, E F Duration (weeks) 5 3 8 7 7 4 5 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C D D D D E E E E F F F F G G G G G
  • 33. Activity Remember!! The starting date of the starting date of the schedule should be “week 1”. 1 2 3 4 5 6 7 8 9 A A A A A A B B B B C C C C C D D D D E E E E F G A B C D E F G Immediate Predecessors --A A,B -C, D, E F Duration (weeks) 5 3 8 7 7 4 5 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C D D D D E E E E F F F F G G G G G
  • 34. ES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A A A A A A B B B B C C C C C C C C C D D D D D D D D E E E E E E E E F F F F F G G G G G G LS 1 2 3 4 5 6 7 8 9 A A A A A A B B B B C C C C C D D D D E E E E F G 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C D D D D E E E E F F F F G G G G G
  • 35. ES • Total Slack 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 (float) of activity A A A A A A - the difference B B B B C C C C C C C C C between the D D D D D D D start (or the end) D E E E E E E E E times of an F F F F F activity on the G G G G G two schedules. G LS 1 2 3 4 5 6 7 8 9 A(0), B(3), C(0), A A A A A A B B B B D(1), E(6), F(0), C C C C C G(0) D D D D E E E E F G 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C D D D D E E E E F F F F G G G G G
  • 36.  Critical activities: activities not having any total slacks  Critical Path: the sequence of critical activities connecting the start and the end points of the project. The duration of the whole project.  A delay in any activity along the critical path delays the entire project, so special attention should be made for the delay of critical activities: Control actions.
  • 37. ES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A A A A A A B B B B C C C C C C C C C D D D D D D D D E E E E E E E E F F F F F G G G G G G LS Critical Path: A>C>F>G 1 2 3 4 5 6 7 8 9 A A A A A A B B B B C C C C C D D D D E E E E F G 10 11 12 13 14 15 16 17 18 19 20 21 22 C C C C D D D D E E E E F F F F G G G G G
  • 38.  Introduction  Precedence Relationship  Gantt Chart  Activity on Node (Critical Path Method)
  • 39.  PERT (Program Evaluation and Review Technique) ◦ Views the time to complete an activity as a random variable that can be characterised by an optimistic, a pessimistic, and a most likely estimate of its duration. ◦ Statistical method is used to estimate time.  CPM (Critical Path Method) ◦ Assumes that activity times are deterministic. ◦ Critical path is determined and used to analyse time of a project.  Usually CPM is good enough for most projects.  Network models are to be developed for it.
  • 40.  Project network model is a graphical flow chart of the project job plan.  Shows the inter-relationships of all activities : communication channels defined.  Identify the critical paths.  Calculate the expected project completion dates.  Usually used together with Gantt chart
  • 41.  Activity-on-Arrow (AOA) Analysis ◦ The arrows represent the activities, while the nodes represent events. ◦ Closely associated with PERT analysis, but it can also be used for CPM analysis. ◦ Often requires the dummy event nodes that correct the network function > complication also introduced.  Activity-on-Node (AON) Analysis ◦ The nodes represent the activities and the arrows identify the precedence relationships between activities. ◦ Closely associated with CPM analysis. ◦ More popular than AOA.