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1

Project Management
2

OBJECTIVES
Definition of Project Management
 Work Breakdown Structure
 Project Control Charts
 Structuring Projects
 Critical Path Scheduling

3

Project Management
Defined




Project is a series of related jobs usually
directed towards some major output and
requiring a significant period of time to
perform
Project Management are the management
activities of planning, directing, and
controlling resources (people, equipment,
material) to meet the technical, cost, and time
constraints of a project


Introduction to Project
Management

4

Definition of Project Management

– A project can be defined as a group of tasks – which helps in
achieving an objective
– A Project : undertaken to solve a problem.
– Project Management – the process of planning, directing and
controlling resources to meet the technical, cost and time
considerations of a project.
– Project Management – as a Conversion Process.
5

The Definition of a “PROJECT”
•

Purpose – Usually a one-time activity with a well-defined
set of desired end result.

•

Life Cycle- From a slow beginning they progress to a
buildup of size, then peak, finally terminate.

•

Interdependencies- Projects always interact with the
parent organization’s standard, ongoing operations.

•

Uniqueness - Every Project has some elements that
are unique. (No two Construction or R & D projects are
precisely alike.)
6

Project Vs. Routine Activities


Project is a one time activity



It involves large investments



No revenue till the project is completed



High degree & Wide variety of skills are used.



Involves experts from various divisions of the company,
consultants & a number of contractors.



A systematic approach to problem solving – special
techniques used.



Usage of special purpose equipments – in some cases



Deals
with
planning,
scheduling,
controlling
simuttaneously with the objective of timely completion of
the project.
7

Pure Project
A pure project is where a self-contained team
works full-time on the project

Structuring Projects / Pure
Project: Advantages





The project manager has full authority
over the project
Team members report to one boss
Shortened communication lines
Team pride, motivation, and commitment
are high
8

Structuring Projects / Pure
Project: Disadvantages
Duplication of resources
 Organizational goals and policies
are ignored
 Lack of technology transfer
 Team members have no functional
area "home"

9

Functional Project
A functional project is housed within
a functional division
President
Research and
Development

Engineering

Manufacturing

Project Project Project
A
B
C

Project Project Project
D
E
F

Project Project Project
G
H
I

Example, Project “B” is in the functional
Example, Project “B” is in the functional
area of Research and Development.
area of Research and Development.
10

Structuring Projects
Functional Project :

Advantages

A team member can work on
several projects
 Technical expertise is maintained
within the functional area
 The functional area is a “home”
after the project is completed
 Critical mass of specialized
knowledge

Structuring Projects
Functional Project:
Disadvantages
Aspects of the project that are not
directly related to the functional
area get short-changed
 Motivation of team members is
often weak
 Needs of the client are secondary
and are responded to slowly


11
12

Matrix Project / Organisation
Structure
President
Research and
Engineering Manufacturing Marketing
Development
Manager
Project A
Manager
Project B
Manager
Project C
13

Structuring Projects /
Matrix: Advantages



Enhanced communications between functional
areas



Pinpointed responsibility



Duplication of resources is minimized



Functional “home” for team members



Policies of the parent organization are followed
14

Structuring Projects /
Matrix: Disadvantages


Too many bosses



Depends on project manager’s
negotiating skills



Potential for sub-optimization
15

Gantt Chart
Vertical Axis:
Vertical Axis:
Always Activities
Always Activities
or Jobs
or Jobs

Horizontal bars used to denote length
Horizontal bars used to denote length
of time for each activity or job.
of time for each activity or job.

Activity 1
Activity 2
Activity 3
Activity 4
Activity 5
Activity 6
Time

Horizontal Axis: Always Time
Horizontal Axis: Always Time
Work Breakdown Structure
A work breakdown structure defines the hierarchy of
project tasks, subtasks, and work packages
Level Program
1
2

Project 1

Project 2

Task 1.1

Task 1.2

3

Subtask 1.1.1

4

Work Package 1.1.1.1

Subtask 1.1.2
Work Package 1.1.1.2

16
17

Networ k Dia g rams

1/2/3/4/5 are Events
A/B/C/D/E are Activities.
18

Networ k Dia g rams
19

Network-Planning Models


A project is made up of a sequence of activities that
form a network representing a project



The path taking longest time through this network of
activities is called the “critical path”



The critical path provides a wide range of scheduling
information useful in managing a project



Critical Path Method (CPM) helps to identify the
critical path(s) in the project networks
20

Prerequisites for Critical
Path Methodology
A project must have:
well-defined jobs or tasks whose
completion marks the end of the project;
independent jobs or tasks;
and tasks that follow a given sequence.
Types of Critical Path
Methods






CPM with a Single Time Estimate
– Used when activity times are known with certainty
– Used to determine timing estimates for the project,
each activity in the project, and slack time for
activities
CPM with Three Activity Time Estimates
– Used when activity times are uncertain
– Used to obtain the same information as the Single
Time Estimate model and probability information
Time-Cost Models
– Used when cost trade-off information is a major
consideration in planning
– Used to determine the least cost in reducing total
project time

21
22

Steps in the CPM with
Single Time Estimate
1. Activity Identification
 2. Activity Sequencing and Network
Construction
 3. Determine the critical path


– From the critical path all of the project
and activity timing information can be
obtained
CPM with Single Time
Estimate

23

Consider the following consulting project :
Activity
Assess customer's needs
Write and submit proposal
Obtain approval
Develop service vision and goals
Train employees
Quality improvement pilot groups
Write assessment report

Designation Immed. Pred. Time (Weeks)
A
None
2
B
A
1
C
B
1
D
C
2
E
C
5
F
D, E
5
G
F
1

Develop a critical path diagram and determine
the duration of the critical path and slack times
for all activities.
24

First draw the network
Act.

Imed. Pred. Time

A
B
C

None
A
B

2
1
1

D
E
F

C
C
D,E

2
5
5

G

F

1

A(2)

B(1)

D(2)

C(1)

F(5)

E(5)

G(1)
25

Determine early starts and early
finish times
ES=4
EF=6
ES=0
EF=2

ES=2
EF=3

ES=3
EF=4

A(2)

B(1)

C(1)

Hint: Start with ES=0
Hint: Start with ES=0
and go forward in the
and go forward in the
network from A to G.
network from A to G.

D(2)

ES=4
EF=9
E(5)

ES=9
EF=14

ES=14
EF=15

F(5)

G(1)
Determine
late starts
and late
finish times
ES=0
EF=2

ES=2
EF=3

ES=3
EF=4

A(2)

B(1)

C(1)

LS=0
LF=2

LS=2
LF=3

LS=3
LF=4

26

ES=4
EF=6
D(2)
LS=7
LF=9
ES=4
EF=9
E(5)
LS=4
LF=9

Hint: Start with LF=15
Hint: Start with LF=15
or the total time of the
or the total time of the
project and go
project and go
backward in the
backward in the
network from G to A.
network from G to A.
ES=9
EF=14

ES=14
EF=15

F(5)

G(1)

LS=9
LF=14

LS=14
LF=15
27

Critical Path & Slack
ES=4
EF=6
ES=0
EF=2

ES=2
EF=3

ES=3
EF=4

A(2)

B(1)

C(1)

LS=0
LF=2

LS=2
LF=3

LS=3
LF=4

D(2)
LS=7
LF=9
ES=4
EF=9
E(5)
LS=4
LF=9

Slack=(7-4)=(9-6)= 3 Wks

ES=9
EF=14

ES=14
EF=15

F(5)

G(1)

LS=9
LF=14

LS=14
LF=15

Duration=15 weeks
Program Evaluation & Review
Technique (PERT)











28

PERT is Event oriented & CPM is Activity oriented.
PERT is used to deal unit uncertainty.
PERT has 3 time estimates – Optimistic time
– Most likely time.
– Pessimistic time.
PERT has one or more activities follow a probability
distribution – taking into account the uncertainty of the
situation.
PERT network provides a measure of the probability of
project completion by the scheduled date.
The probability concept – Only associated with PERT
and not CPM.
(time estimates in CPM are deterministic & not
probabilistic)
29

Example 2. CPM with Three
Activity Time Estimates
Immediate
Task Predecesors Optimistic Most Likely Pessimistic
A
None
3
6
15
B
None
2
4
14
C
A
6
12
30
D
A
2
5
8
E
C
5
11
17
F
D
3
6
15
G
B
3
9
27
H
E,F
1
4
7
I
G,H
4
19
28
30

Example 2. Expected
Time Calculations
ET(A)= 3+4(6)+15
ET(A)= 3+4(6)+15
Task
A
B
C
D
E
F
G
H
I

Immediate Expected
Predecesors
Time
None
7
None
5.333
A
14
A
5
C
11
D
7
B
11
E,F
4
G,H
18

6
6
ET(A)=42/6=7
ET(A)=42/6=7
Immediate
Task Predecesors Optimistic Most Likely Pessimistic
A
None
3
6
15
B
None
2
4
14
C
A
6
12
30
D
A
2
5
8
E
C
5
11
17
F
D
3
6
15
G
B
3
9
27
H
E,F
1
4
7
I
G,H
4
19
28

Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
6
Ex. 2. Expected Time
Calculations
Task
A
B
C
D
E
F
G
H
I

Immediate Expected
Predecesors
Time
None
7
None
5.333
A
14
A
5
C
11
D
7
B
11
E,F
4
G,H
18

31

ET(B)= 2+4(4)+14
ET(B)= 2+4(4)+14
6
6
ET(B)=32/6=5.333
ET(B)=32/6=5.333
Immediate
Task Predecesors Optimistic Most Likely Pessimistic
A
None
3
6
15
B
None
2
4
14
C
A
6
12
30
D
A
2
5
8
E
C
5
11
17
F
D
3
6
15
G
B
3
9
27
H
E,F
1
4
7
I
G,H
4
19
28

Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
6
Ex 2. Expected Time
Calculations
Task
A
B
C
D
E
F
G
H
I

Immediate Expected
Predecesors
Time
None
7
None
5.333
A
14
A
5
C
11
D
7
B
11
E,F
4
G,H
18

32

ET(C)= 6+4(12)+30
ET(C)= 6+4(12)+30
6
6
ET(C)=84/6=14
ET(C)=84/6=14
Immediate
Task Predecesors Optimistic Most Likely Pessimistic
A
None
3
6
15
B
None
2
4
14
C
A
6
12
30
D
A
2
5
8
E
C
5
11
17
F
D
3
6
15
G
B
3
9
27
H
E,F
1
4
7
I
G,H
4
19
28

Opt. Time + 4(Most Likely Time) + Pess. Time
Expected Time =
6
33

Example 2. Network
Duration = 54 Days
C(14)

E(11)
H(4)

A(7)
D(5)

F(7)
I(18)

B
(5.333)

G(11)
34

Example 2. Probability
Exercise

What is the probability of finishing this project in
What is the probability of finishing this project in
less than 53 days?
less than 53 days?

p(t < D)
D=53

t

TE = 54
Z =

D - TE

σ cp 2
∑
35

Pessim. - Optim. 2
Activity variance, σ = (
)
6
2

Task
A
B
C
D
E
F
G
H
I

Optimistic Most Likely Pessimistic Variance
3
6
15
4
2
4
14
6
12
30
16
2
5
8
5
11
17
4
3
6
15
3
9
27
1
4
7
1
4
19
28
16

(Sum the variance along the critical
path.)

σ 2 = 41
∑
36

p(t < D)
TE = 54

D=53

Z =

D - TE

∑σ

2
cp

53- 54
=
= -.156
41

p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156)
p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156)
There is a 43.8% probability that this project will be
There is a 43.8% probability that this project will be
completed in less than 53 weeks.
completed in less than 53 weeks.

t
37

Ex 2. Additional Probability
Exercise
 What is the probability that the
 What is the probability that the

project duration will exceed 56
project duration will exceed 56
weeks?
weeks?
38

Example 2. Additional
Exercise Solution
p(t < D)

TE = 54

Z =

D - TE

∑σ

2
cp

t
D=56

56 - 54
=
= .312
41

p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312))
p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312))
39

Time-Cost Models


Basic Assumption: Relationship
between activity completion time
and project cost



Time Cost Models: Determine the
optimum point in time-cost
tradeoffs
–
–
–

Activity direct costs
Project indirect costs
Activity completion times
40



Networ k Crashing (Project
Determine the timeCrashing) each activity in the
– cost ratio for
network – this ratio represents the increase in cost for a
unit decrease in time.
Time – Cost Ratio = crash cost – normal cost
normal time – crash time



Identify the activities on critical path & select that activity
which has smallest time cost ratio – crash that activity to
the extent possible.



Observe any change in the critical path – any other path
becomes critical – calculate time cost ratio in the new
critical path.



Repeat above steps – till the activities are crashed to
reduce the present duration to the desired time period.
CPM Assumptions /
Limitations


Project activities can be identified as entities
(There is a clear beginning and ending point
for each activity.)



Project activity sequence relationships can be
specified and networked



Project control should focus on the critical
path



The activity times follow the beta distribution,
with the variance of the project assumed to
equal the sum of the variances along the
critical path

41
42

Question Bowl
Which of the following are examples
of Graphic Project Charts?
a. Gantt
b. Bar
c. Milestone
d. All of the above
e. None of the above

Answer: d. All of the above
43

Question Bowl
Which of the following are one of the
three organizational structures of
projects?
a. Pure
b. Functional
c. Matrix
d. All of the above
e. None of the above

Answer: d. All of the above
44

Question Bowl
A project starts with a written description of the
objectives to be achieved, with a brief statement
of the work to be done and a proposed schedule
all contained in which of the following?
a.
SOW
b. WBS
c.
Early Start Schedule
d. Late Start Schedule
e.
None of the above

Answer: a. SOW (or Statement of Work)
45

Question Bowl

a.
b.
c.
d.
e.

For some activities in a project there may
be some leeway from when an activity can
start and when it must finish. What is this
period of time called when using the Critical
Path Method?
Early start time
Late start time
Slack time
All of the above
None of the above

Answer: c. Slack time
46

Question Bowl
How much “slack time” is permitted in the “critical
path” activity times?
a.
Only one unit of time per activity
b.
No slack time is permitted
c.
As much as the maximum activity time in the
network
d.
As much as is necessary to add up to the total
time of the project
e.
None of the above

Answer: b. No slack time is permitted (All
critical path activities must have zero slack
time, otherwise they would not be critical to
the project completion time.)
47

Question Bowl
When looking at the Time-Cost Trade Offs in the
Minimum-Cost Scheduling time-cost model,
we seek to reduce the total time of a project
by doing what to the least-cost activity
choices?
Answer: a. Crashing
a.
Crashing them
them (We “crash” the
b.
Adding slack time
least-cost activity
c.
Subtracting slack time times to seek a reduced
d.
Adding project time
total time for the
e.
None of the above
entire project and we
do it step-wise as
inexpensively as
possible.)

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Ch3 proj.mgt

  • 2. 2 OBJECTIVES Definition of Project Management  Work Breakdown Structure  Project Control Charts  Structuring Projects  Critical Path Scheduling 
  • 3. 3 Project Management Defined   Project is a series of related jobs usually directed towards some major output and requiring a significant period of time to perform Project Management are the management activities of planning, directing, and controlling resources (people, equipment, material) to meet the technical, cost, and time constraints of a project
  • 4.  Introduction to Project Management 4 Definition of Project Management – A project can be defined as a group of tasks – which helps in achieving an objective – A Project : undertaken to solve a problem. – Project Management – the process of planning, directing and controlling resources to meet the technical, cost and time considerations of a project. – Project Management – as a Conversion Process.
  • 5. 5 The Definition of a “PROJECT” • Purpose – Usually a one-time activity with a well-defined set of desired end result. • Life Cycle- From a slow beginning they progress to a buildup of size, then peak, finally terminate. • Interdependencies- Projects always interact with the parent organization’s standard, ongoing operations. • Uniqueness - Every Project has some elements that are unique. (No two Construction or R & D projects are precisely alike.)
  • 6. 6 Project Vs. Routine Activities  Project is a one time activity  It involves large investments  No revenue till the project is completed  High degree & Wide variety of skills are used.  Involves experts from various divisions of the company, consultants & a number of contractors.  A systematic approach to problem solving – special techniques used.  Usage of special purpose equipments – in some cases  Deals with planning, scheduling, controlling simuttaneously with the objective of timely completion of the project.
  • 7. 7 Pure Project A pure project is where a self-contained team works full-time on the project Structuring Projects / Pure Project: Advantages     The project manager has full authority over the project Team members report to one boss Shortened communication lines Team pride, motivation, and commitment are high
  • 8. 8 Structuring Projects / Pure Project: Disadvantages Duplication of resources  Organizational goals and policies are ignored  Lack of technology transfer  Team members have no functional area "home" 
  • 9. 9 Functional Project A functional project is housed within a functional division President Research and Development Engineering Manufacturing Project Project Project A B C Project Project Project D E F Project Project Project G H I Example, Project “B” is in the functional Example, Project “B” is in the functional area of Research and Development. area of Research and Development.
  • 10. 10 Structuring Projects Functional Project : Advantages A team member can work on several projects  Technical expertise is maintained within the functional area  The functional area is a “home” after the project is completed  Critical mass of specialized knowledge 
  • 11. Structuring Projects Functional Project: Disadvantages Aspects of the project that are not directly related to the functional area get short-changed  Motivation of team members is often weak  Needs of the client are secondary and are responded to slowly  11
  • 12. 12 Matrix Project / Organisation Structure President Research and Engineering Manufacturing Marketing Development Manager Project A Manager Project B Manager Project C
  • 13. 13 Structuring Projects / Matrix: Advantages  Enhanced communications between functional areas  Pinpointed responsibility  Duplication of resources is minimized  Functional “home” for team members  Policies of the parent organization are followed
  • 14. 14 Structuring Projects / Matrix: Disadvantages  Too many bosses  Depends on project manager’s negotiating skills  Potential for sub-optimization
  • 15. 15 Gantt Chart Vertical Axis: Vertical Axis: Always Activities Always Activities or Jobs or Jobs Horizontal bars used to denote length Horizontal bars used to denote length of time for each activity or job. of time for each activity or job. Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity 6 Time Horizontal Axis: Always Time Horizontal Axis: Always Time
  • 16. Work Breakdown Structure A work breakdown structure defines the hierarchy of project tasks, subtasks, and work packages Level Program 1 2 Project 1 Project 2 Task 1.1 Task 1.2 3 Subtask 1.1.1 4 Work Package 1.1.1.1 Subtask 1.1.2 Work Package 1.1.1.2 16
  • 17. 17 Networ k Dia g rams 1/2/3/4/5 are Events A/B/C/D/E are Activities.
  • 18. 18 Networ k Dia g rams
  • 19. 19 Network-Planning Models  A project is made up of a sequence of activities that form a network representing a project  The path taking longest time through this network of activities is called the “critical path”  The critical path provides a wide range of scheduling information useful in managing a project  Critical Path Method (CPM) helps to identify the critical path(s) in the project networks
  • 20. 20 Prerequisites for Critical Path Methodology A project must have: well-defined jobs or tasks whose completion marks the end of the project; independent jobs or tasks; and tasks that follow a given sequence.
  • 21. Types of Critical Path Methods    CPM with a Single Time Estimate – Used when activity times are known with certainty – Used to determine timing estimates for the project, each activity in the project, and slack time for activities CPM with Three Activity Time Estimates – Used when activity times are uncertain – Used to obtain the same information as the Single Time Estimate model and probability information Time-Cost Models – Used when cost trade-off information is a major consideration in planning – Used to determine the least cost in reducing total project time 21
  • 22. 22 Steps in the CPM with Single Time Estimate 1. Activity Identification  2. Activity Sequencing and Network Construction  3. Determine the critical path  – From the critical path all of the project and activity timing information can be obtained
  • 23. CPM with Single Time Estimate 23 Consider the following consulting project : Activity Assess customer's needs Write and submit proposal Obtain approval Develop service vision and goals Train employees Quality improvement pilot groups Write assessment report Designation Immed. Pred. Time (Weeks) A None 2 B A 1 C B 1 D C 2 E C 5 F D, E 5 G F 1 Develop a critical path diagram and determine the duration of the critical path and slack times for all activities.
  • 24. 24 First draw the network Act. Imed. Pred. Time A B C None A B 2 1 1 D E F C C D,E 2 5 5 G F 1 A(2) B(1) D(2) C(1) F(5) E(5) G(1)
  • 25. 25 Determine early starts and early finish times ES=4 EF=6 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 A(2) B(1) C(1) Hint: Start with ES=0 Hint: Start with ES=0 and go forward in the and go forward in the network from A to G. network from A to G. D(2) ES=4 EF=9 E(5) ES=9 EF=14 ES=14 EF=15 F(5) G(1)
  • 26. Determine late starts and late finish times ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 A(2) B(1) C(1) LS=0 LF=2 LS=2 LF=3 LS=3 LF=4 26 ES=4 EF=6 D(2) LS=7 LF=9 ES=4 EF=9 E(5) LS=4 LF=9 Hint: Start with LF=15 Hint: Start with LF=15 or the total time of the or the total time of the project and go project and go backward in the backward in the network from G to A. network from G to A. ES=9 EF=14 ES=14 EF=15 F(5) G(1) LS=9 LF=14 LS=14 LF=15
  • 27. 27 Critical Path & Slack ES=4 EF=6 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 A(2) B(1) C(1) LS=0 LF=2 LS=2 LF=3 LS=3 LF=4 D(2) LS=7 LF=9 ES=4 EF=9 E(5) LS=4 LF=9 Slack=(7-4)=(9-6)= 3 Wks ES=9 EF=14 ES=14 EF=15 F(5) G(1) LS=9 LF=14 LS=14 LF=15 Duration=15 weeks
  • 28. Program Evaluation & Review Technique (PERT)       28 PERT is Event oriented & CPM is Activity oriented. PERT is used to deal unit uncertainty. PERT has 3 time estimates – Optimistic time – Most likely time. – Pessimistic time. PERT has one or more activities follow a probability distribution – taking into account the uncertainty of the situation. PERT network provides a measure of the probability of project completion by the scheduled date. The probability concept – Only associated with PERT and not CPM. (time estimates in CPM are deterministic & not probabilistic)
  • 29. 29 Example 2. CPM with Three Activity Time Estimates Immediate Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 B None 2 4 14 C A 6 12 30 D A 2 5 8 E C 5 11 17 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28
  • 30. 30 Example 2. Expected Time Calculations ET(A)= 3+4(6)+15 ET(A)= 3+4(6)+15 Task A B C D E F G H I Immediate Expected Predecesors Time None 7 None 5.333 A 14 A 5 C 11 D 7 B 11 E,F 4 G,H 18 6 6 ET(A)=42/6=7 ET(A)=42/6=7 Immediate Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 B None 2 4 14 C A 6 12 30 D A 2 5 8 E C 5 11 17 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 31. Ex. 2. Expected Time Calculations Task A B C D E F G H I Immediate Expected Predecesors Time None 7 None 5.333 A 14 A 5 C 11 D 7 B 11 E,F 4 G,H 18 31 ET(B)= 2+4(4)+14 ET(B)= 2+4(4)+14 6 6 ET(B)=32/6=5.333 ET(B)=32/6=5.333 Immediate Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 B None 2 4 14 C A 6 12 30 D A 2 5 8 E C 5 11 17 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 32. Ex 2. Expected Time Calculations Task A B C D E F G H I Immediate Expected Predecesors Time None 7 None 5.333 A 14 A 5 C 11 D 7 B 11 E,F 4 G,H 18 32 ET(C)= 6+4(12)+30 ET(C)= 6+4(12)+30 6 6 ET(C)=84/6=14 ET(C)=84/6=14 Immediate Task Predecesors Optimistic Most Likely Pessimistic A None 3 6 15 B None 2 4 14 C A 6 12 30 D A 2 5 8 E C 5 11 17 F D 3 6 15 G B 3 9 27 H E,F 1 4 7 I G,H 4 19 28 Opt. Time + 4(Most Likely Time) + Pess. Time Expected Time = 6
  • 33. 33 Example 2. Network Duration = 54 Days C(14) E(11) H(4) A(7) D(5) F(7) I(18) B (5.333) G(11)
  • 34. 34 Example 2. Probability Exercise What is the probability of finishing this project in What is the probability of finishing this project in less than 53 days? less than 53 days? p(t < D) D=53 t TE = 54 Z = D - TE σ cp 2 ∑
  • 35. 35 Pessim. - Optim. 2 Activity variance, σ = ( ) 6 2 Task A B C D E F G H I Optimistic Most Likely Pessimistic Variance 3 6 15 4 2 4 14 6 12 30 16 2 5 8 5 11 17 4 3 6 15 3 9 27 1 4 7 1 4 19 28 16 (Sum the variance along the critical path.) σ 2 = 41 ∑
  • 36. 36 p(t < D) TE = 54 D=53 Z = D - TE ∑σ 2 cp 53- 54 = = -.156 41 p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156) p(Z < -.156) = .438, or 43.8 % (NORMSDIST(-.156) There is a 43.8% probability that this project will be There is a 43.8% probability that this project will be completed in less than 53 weeks. completed in less than 53 weeks. t
  • 37. 37 Ex 2. Additional Probability Exercise  What is the probability that the  What is the probability that the project duration will exceed 56 project duration will exceed 56 weeks? weeks?
  • 38. 38 Example 2. Additional Exercise Solution p(t < D) TE = 54 Z = D - TE ∑σ 2 cp t D=56 56 - 54 = = .312 41 p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312)) p(Z > .312) = .378, or 37.8 % (1-NORMSDIST(.312))
  • 39. 39 Time-Cost Models  Basic Assumption: Relationship between activity completion time and project cost  Time Cost Models: Determine the optimum point in time-cost tradeoffs – – – Activity direct costs Project indirect costs Activity completion times
  • 40. 40  Networ k Crashing (Project Determine the timeCrashing) each activity in the – cost ratio for network – this ratio represents the increase in cost for a unit decrease in time. Time – Cost Ratio = crash cost – normal cost normal time – crash time  Identify the activities on critical path & select that activity which has smallest time cost ratio – crash that activity to the extent possible.  Observe any change in the critical path – any other path becomes critical – calculate time cost ratio in the new critical path.  Repeat above steps – till the activities are crashed to reduce the present duration to the desired time period.
  • 41. CPM Assumptions / Limitations  Project activities can be identified as entities (There is a clear beginning and ending point for each activity.)  Project activity sequence relationships can be specified and networked  Project control should focus on the critical path  The activity times follow the beta distribution, with the variance of the project assumed to equal the sum of the variances along the critical path 41
  • 42. 42 Question Bowl Which of the following are examples of Graphic Project Charts? a. Gantt b. Bar c. Milestone d. All of the above e. None of the above Answer: d. All of the above
  • 43. 43 Question Bowl Which of the following are one of the three organizational structures of projects? a. Pure b. Functional c. Matrix d. All of the above e. None of the above Answer: d. All of the above
  • 44. 44 Question Bowl A project starts with a written description of the objectives to be achieved, with a brief statement of the work to be done and a proposed schedule all contained in which of the following? a. SOW b. WBS c. Early Start Schedule d. Late Start Schedule e. None of the above Answer: a. SOW (or Statement of Work)
  • 45. 45 Question Bowl a. b. c. d. e. For some activities in a project there may be some leeway from when an activity can start and when it must finish. What is this period of time called when using the Critical Path Method? Early start time Late start time Slack time All of the above None of the above Answer: c. Slack time
  • 46. 46 Question Bowl How much “slack time” is permitted in the “critical path” activity times? a. Only one unit of time per activity b. No slack time is permitted c. As much as the maximum activity time in the network d. As much as is necessary to add up to the total time of the project e. None of the above Answer: b. No slack time is permitted (All critical path activities must have zero slack time, otherwise they would not be critical to the project completion time.)
  • 47. 47 Question Bowl When looking at the Time-Cost Trade Offs in the Minimum-Cost Scheduling time-cost model, we seek to reduce the total time of a project by doing what to the least-cost activity choices? Answer: a. Crashing a. Crashing them them (We “crash” the b. Adding slack time least-cost activity c. Subtracting slack time times to seek a reduced d. Adding project time total time for the e. None of the above entire project and we do it step-wise as inexpensively as possible.)