software engineering

1. Project Management
Part 5
Project Scheduling

2. Topic Outline: Project Scheduling
• Identifying relationships among activities
• Project network diagrams
• Identifying critical paths and critical activities
• Determining activity slack times
• Gantt charts
• Project scheduling exercise
• Other precedence relationships
• Management of project schedules

3. Identifying Activity Relationships
In addition to estimating activity time duration and cost,
relationships among activities must also be identified
Relationships:
• What task immediately precedes this task?
• What task immediately follows this task?
• What tasks can be done concurrently?
These are referred to as precedence relationships
The main relationship for scheduling is ‘what task
immediately precedes the current task,’ which is
referred to as the immediate predecessor task

4. Project Network Diagrams
• Network diagrams show the precedence
relationships among activities
• It’s easier to understand these relationships
graphically
• Network diagrams help to understand the flow of
work in a project
• Network diagrams are a useful tool for project
planning and control, as well as for scheduling
• One (perhaps exaggerated) claim is that the
network represents ¾ of the planning process

5. 2 Versions of Network Diagrams
Activity-on-Arrow (AOA) networks
– also called Arrow Diagramming Method (ADM)
– simpler for projects with many dependencies
– emphasizes events; milestones can be easily flagged
– sometimes requires dummy activities
Activity-on-Node (AON) networks
– also called Precedence Diagramming Method (PDM)
– easier to draw for simple projects
– emphasizes activities
– no dummy activities

6. Activities vs. Events
• Activity – a chunk of work that is part of the
project; an activity may be broken down into
multiple subactivities
• Event – a significant point in time during the
project, such as a milestone event; an event
could be the time at which an activity is
completed or the time at which related
concurrent activities have all completed
• Dummy Activity – an artificial activity with zero
time duration that only shows a precedence
relationship among activities

7. Activity-on-Arrow (AOA) Networks
b
c
d
e
f
g
Activity Predecessor
m
n
r
s
_
_
m, n
n
m r
n s
k
j
k
j
j
k
or
Dashed lines are called dummy activities

8. 1 2
Excavate
& pour
footings
Pour
foundation
Install
drains
Project Network for
House Construction
(AOA network)
3
6
7
4
8
9
5
10
11
12
16
18
13
17
15
14
Install rough
electrical & plumbing
Pour
basement
floor
Install
cooling &
heating
Erect
frame & roof
Lay
brickwork
Lay
storm
drains
Install
drywall
Lay
flooring
Install
finished
plumbing
Install
kitchen
equipment
Paint
Finish
roof
Install
roof
drainage
Finish
grading
Finish
floors
Pour
walks;
Landscape
Finish
electrical
work
Finish
carpeting

9. Project Network Example
Task Pred. Dur.Task Pred. Dur.
a -- 4 g c,d 1
b -- 3 h e 4
c a 3 i f 5
d a 2 j e,g 6
e b 6 k h,i 1
f b 4
Draw AOA and AON networks

10. Activity-on-Arrow (AOA or ADM) Network
(Initial Network)

11. Activity-on-Arrow (AOA or ADM) Network
(Final Network)
a
b
d
c
g
j
k
i
h
f
e

12. Activity-on-Node (AON or PDM) Network

13. A project has the following activities and
precedence relationships:
Predecessor Predecessor
Activity Activities Activity Activities
a -- f c,e
b a g b
c a h b,d
d a i b,d
e b j f,g,h
Draw AOA and AON networks
Project Network Example

14. Activity on Arrow
(Initial Network)

15. Activity on Arrow
(Final Network)
a
b
c
d
e
f
g
h
i
j

16. Activity on Node

17. Critical Path
path – any route along the network from start to
finish
Critical Path – path with the longest total duration
This is the shortest time in which the project can
be completed.
Critical Activity – an activity on the critical path
*If a critical activity is delayed, the entire project
will be delayed. Close attention must be given
to critical activities to prevent project delay.
There may be more than one critical path.

18. Critical Path
Brute force approach to finding critical path:
1. identify all possible paths from start to finish
2. sum up durations for each path
3. largest total indicates critical path
(This approach is inefficient, but is instructive)

19. 1
2 6
4 7
5
3
b = 2
d = 4
g = 9
h = 9

20. Slack Times
• EST—Earliest Start Time
– Largest EFT of all predecessors
• EFT—Earliest Finish Time
– EST + duration for this task
• LFT—Latest Finish Time
– Smallest LST of following tasks
• LST—Latest Start Time
– LFT – duration for this task
• Slack—LFT – EFT or LST – EST

21. Computing Slack Times
Task = duration
slack = xxxx
EST EFT
LST LFT

22. Slack Times Example
Task Pred. Dur.Task Pred. Dur.
a -- 4 g c,d 1
b -- 3 h e 4
c a 3 i f 5
d a 2 j e,g 6
e b 6 k h,i 1
f b 4
For each task, compute ES, EF, LF, LS, Slack

23. Start Finish
a=4
slack=
b=3
slack=
c=3
slack=
d=2
slack=
e=6
slack=
f=4
slack=
g=1
slack=
h=4
slack=
i=5
slack=
j=6
slack=
k=1
slack=
Task=dur
slack=xxx
EST EFT
LFT
LST

24. Gantt Charts
• The main purpose of a Gantt chart is to display
the schedule of activities
• They are easy to understand
• They are flexible in that you can also show other
information on the chart, such as resources
required, who is responsible, critical activities,
percent complete, etc.
• All project management software packages will
create Gantt charts

25. Gantt Chart
Activity
a
b
c
d
e
f
g
h
i
Time (weeks)

26. Project Scheduling Exercise
DynaTech Equipment Corp. case
• Divide into small groups
• Read case (5 minutes)
• Assignment: (40 minutes)
– List the immediate predecessors and WBS
number for each activity
– Draw project network diagram (lowest level)
– Draw Gantt chart
– Determine project completion time

27. Other Precedence Relationships
• The typical precedence relationship between
two activities is that when the first activity has
finished, then the second activity can start. In
this case the first activity is called the immediate
predecessor of the second activity.
• This is referred to as a Finish-to-Start linkage.
• Other precedence relationships, or linkages, are
also possible.
• Lead and lag times are also possible.

28. Other Precedence Relationships
Finish-to-Start
Linkage (FS)
Start-to-Start
Linkage (SS)
Finish-to-Finish
Linkage (FF)
Start-to-Finish
Linkage (SF)
Activity 1
Activity 2
Activity 1
Activity 2
Activity 1
Activity 2
Activity 1
Activity 2
Lead and Lag Times
Lead (-) and Lag (+) times are
expressed as part of the
immediate predecessor
notation. So 1FS+3 listed for
the immediate predecessor of
Activity 2 means that Activity 1
is the predecessor with a Finish-
to-Start linkage and a 3-day lag
time after Activity 1 finishes
before Activity 2 can start.
1FS-3 means that Activity 2 can
start 3 days before Activity 1
finishes.
1FF+3; 1SF-5; 1SS+4

29. Management of Project Schedules
• Meeting project deadlines is often the most
important goal in project management
• Careful scheduling of project activities is critical
to meeting the project due date
• Effective project managers should have a good
understanding of the issues involved in activity
scheduling