1. Project Management (PERT/CPM) PREPARED BY CH. AVINASH
UNIT-VI
Project Management (PERT/CPM)
PREPARED BY
CH. AVINASH

2. INDEX UNIT 6 PPT SLIDES S.NO. TOPIC LECTURE NO.
Project Management ( PERT/CPM) L1
Network Analysis L2
Programme Evaluation and Review Technique L3
(PERT), Critical Path Method ( CPM ), Identify L4
Critical Path, Probability of Completing the Project L5
Within given time, Project Cost Analysis L6
Project Crashing, (simple problems) L7

3. Project Planning Given:
Statement of work
written description of goals
work & time frame of project
Work Breakdown Structure
Be able to: develop precedence relationship diagram which shows sequential relationship of project activities 3 3

4. Gantt Chart Popular tool for project scheduling
Graph with bar representing time for each task
Provides visual display of project schedule
Also shows slack for activities
(amount of time activity can be delayed without delaying project) 4 7

5. A Gantt Chart Month 2 4 6 8 10 1 3 5 7 9 Activity Design house and2 4 6 8 10
Activity
Design house and
obtain financing
Lay foundation
Order and receive
materials
Build house
Select paint
Select carpet
Finish work 1 3 5 7 9 5 8

6. CPM/PERT Critical Path Method (CPM)
- DuPont & Remington-Rand (1956)
- deterministic task times
- activity-on-node network construction (AON)
Project Evaluation & Review Technique (PERT)
- U.S. Navy, Booz, Allen & Hamilton
- multiple task time estimates( probabilistic)
- activity-on-arrow network construction (AOA) 6 9

7. Network Construction
In AON, nodes represent activities & arrows show precedence relationships
In AOA, arrows represent activities & nodes are events for points in time
An event is the completion or beginning of an activity
A dummy shows precedence for two activities with same start & end nodes 7 11

8. The Project Network Network consists of branches & nodes Node 1 2 38 10

9. Simplified Project Network
Construct forms
Pour concrete 1 2 3 9 4

10. Activity predecessors Duration A Design house and obtain financing - 3
Consider the following table which describes the activities to be done to build a house and its sequence
Activity predecessors Duration
A Design house and obtain financing
B Lay foundation A
C Order and receive materials A
D Build house B,C 3
E Select paint B,C 1
F Select carpet E
G Finish work D,F 1 10

11. Concurrent Activities3 2 3
Lay foundation
Order material
Lay
foundation
Dummy 2 4
Order material
Incorrect
precedence
relationship
Correct
precedence
relationship 11 15

12. Project Network For A House3
Dummy
Lay foundation 2
Build house
Finish work 3 1 1 2 4 6 7 3 1
Design house and obtain financing
Order and receive materials 1
Select paint 1
Select carpet 5 12 12

13. Critical Path
A path is a sequence of connected activities running from the start to the end node in a network
The critical path is the path with the longest duration in the network
A project cannot be completed in less than the time of the critical path (under normal circumstances) 13 13

14. All Possible Paths path1: 1-2-3-4-6-7 path2: 1-2-3-4-5-6-7
= 9 months; the critical path
path2:
= 8 months
path3:
= 8 months
path4:
= 7 months 14 14

15. Early Times (House building example)
ES - earliest time activity can start
Forward pass starts at beginning of network to determine ES times
EF = ES + activity time
ESij = maximum (EFi)
EFij = ESij + tij
ES12 = 0
EF12 = ES12 + t12 = = 3 months i j 15 16

16. Computing Early Times -ES23 = max (EF2) = 3 months
- ES46 = max (EF4) = max (5,4) = 5 months
- EF46 = ES46 + t46 = = 8 months
- EF67 =9 months, the project duration 16 17

17. Late Times
LS - latest time activity can be started without delaying the project
Backward pass starts at end of network to determine LS times
LF - latest time activity can be completed without delaying the project
LSij = LFij - tij
LFij = minimum (LSj) 17 18

18. Computing Late Times
If a deadline is not given take LF of the project to be EF of the last activity
LF67 = 9 months
LS67 = LF67 - t67 = = 8 months
LF56 = minimum (LS6) = 8 months
LS56 = LF56 - t56 = = 7 months
LF24 = minimum (LS4) = min(5, 6) = 5 months
LS24 = LF24 - t24 = = 4 months 18 19

19. Project cost analysis:-
ES=5, EF=5
LS=5, LF=5
ES=3, EF=5
LS=3, LF=5 3
ES=8, EF=9
LS=8, LF=9
ES=5, EF=8
LS=5, LF=8 2 3 1 1 2 4 6 7 3 1
ES=0, EF=3
LS=0, LF=3
ES=3, EF=4
LS=4, LF=5 1 1
ES=6, EF=7
LS=7, LF=8
ES=5, EF=6
LS=6, LF=7 5 19 20

20. Activity Slack Slack is defined as the LS-ES or LF-EF
Activities on critical path have ES = LS & EF = LF (slack is 0)
Activities not on critical path have slack
Sij = LSij - ESij
Sij = LFij - EFij
S24 = LS24 - ES24 = = 1 month 20 21

21. Total slack/float or Slack of an activity
Total slack/ float means the amount of time that an activity can be delayed without affecting the entire project completion time.
The activity on a given path share the maximum possible slack of the activity along that path according to its share.
Sum of the possible slacks of the activities can not exceed the maximum slack along that path. 21

22. Free slack of an activity
This is the maximum possible delay of an activity which does not affect its immediate successors.
This is evaluated as
FSij = ESj – EFij 22

23. Activity Slack Data Activity ES LS EF LF Slack (S) Free slack
1-2*
3-4*
4-6*
6-7*
* Critical path 23 22

24. Probability of completing the project within given time:-
Activity
Design house and
obtain financing
Lay foundation
Order and receive
materials
Build house
Select paint
Select carpet
Finish work 24

25. Probabilistic Time Estimates
Reflect uncertainty of activity times
Beta distribution is used in PERT
Mean (expected time):
a + 4m + b 6
t = 2
b - a 6
( )
Variance: s 2 =
where,
a = optimistic estimate
m = most likely time estimate
b = pessimistic time estimate 25 23

26. Example Beta Distributions
P (time)
P (time) a
m t b a t
m b
P (time) a b
m = t 26 24

27. PERT Example 2 6 1 3 5 8 9 4 7 Equipment testing and modification
Final debugging
Equipment installation
Dummy
System Training 1 3 5 8 9
System development
Manual Testing
System changeover
System Testing
Job training
Dummy
Position recruiting
Orientation 4 7 27 25

28. Activity Information Time estimates (wks) Mean Time Variance
Activity a m b t s2 28 26

29. Early And Late Times Activity t s2 ES EF LS LF S FS? 29 27

30. Network With Times ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( )
ES=8, EF=13
LS=16 LF=21 2 6
( )
ES=0, EF=8
LS=1, LF=9 5
( )
ES=13, EF=17
LS=21 LF=25
( )
ES=8, EF=8
LS=9, LF=9 8 4
( )
ES=0, EF=6
LS=0, LF=6
( )
ES=9, EF=16
LS=9, LF=16 3 9 1 3 5 8 9 6
( )
ES=6, EF=9
LS=6, LF=9 7
( )
ES=16, EF=25
LS=16 LF=25
( )
ES=9, EF=13
LS=12, LF=16
( )
ES=0, EF=3
LS=2, LF=5 4
( )
ES=13, EF=13
LS=16 LF=16 3
( )
ES=3, EF=7
LS=5, LF=9 4 2 4 7
( )
ES=3, EF=5
LS=14, LF=16 30 28

31. Project Variance
Project variance is the sum of the variances along the critical path
s2 = s s s s2 89 =
= weeks 31 29

32. Probabilistic Network Analysis
Determine the probability that a project is completed (project completion time is )
within a specified period of time
where
m = tp = project mean time
s = project standard deviation
x = project time (random variable)
Z = number of standard deviations of x from
the mean (standardized random variable) 
x - m
Z = s 32 30

33. Normal Distribution Of Project Time
Probability Zs
m = tp x
Time 33 31

34. Standard Normal Distribution Of transformed Project Time
Probability Z
m =0 z
Time 34 31

35. Probabilistic Analysis Example
What is the probability that the project is completed within 30 weeks?
P(X 30) = ? s2 = weeks
s = 6.89 = 2.62 weeks
Z = x - m = = 1.91
P(Z  1.91) = ? s
2.62 35 32

36. Determining Probability From Z Value … . . .
P( x < 30 weeks) = =
m = 25
x = 30
Time (weeks) 36 33

37. What is the probability that the project will be completed within 22 weeks?
Z = =
= -1.14
P(Z< -1.14) =
x = 22
m = 25 x=28
Time (weeks)
P( x< 22 weeks) = 37 34

38. Benefits of PERT/CPM Useful at many stages of project management
Mathematically simple
Uses graphical displays
Gives critical path & slack time
Provides project documentation
Useful in monitoring costs 38 50

39. Advantages of PERT/CPM
Networks generated provide valuable project documentation and graphically point out who is responsible for various project activities
Applicable to a wide variety of projects and industries
Useful in monitoring not only schedules, but costs as well 39 51

40. Limitations of PERT/CPM
Assumes clearly defined, independent, & stable activities
Specified precedence relationships
Activity times (PERT) follow beta distribution
Subjective time estimates
Over-emphasis on critical path 40 52

41. Identifying Critical path:-3
Dummy
Lay foundation 2
Build house
Finish work 3 1 1 2 4 6 7 3 1
Design house and obtain financing
Order and receive materials 1
Select paint 1
Select carpet 5 41 12

42. Project crashing:-
When the two methods like work study, trade off and other possible ones fail, we go for crashing.
Crashing includes:
Normal cost
Normal Time
Crash cost
Crash Time
Direct cost
Indirect cost
optimization cost