PROJECT MANAGEMENT Time Management*

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PROJECT MANAGEMENT Time Management
Dr. L. K. GaafarThe American University in Cairo
This Presentation is Based on information from
the PMBOK Guide 2000
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Critical Path Method (CPM)

• CPM is a project network analysis technique used
  to predict total project duration
• A critical path for a project is the series of
  activities that determines the earliest time by
  which the project can be completed
• The critical path is the longest path through the
  network diagram and has the least amount of float

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Finding the Critical Path

• Develop a network diagram
• Add the durations of all activities to the
  project network diagram
• Calculate the total duration of every possible
  path from the beginning to the end of the project
• The longest path is the critical path
• Activities on the critical path have zero float

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Simple Example
Consider the following project network diagram.
Assume all times are in days.
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Simple Example
Activity-on-arrow network
a. 2 paths on this network A-B-C-E, A-B-D-F. b.
Paths have lengths of 10, 16 c. The critical
path is A-B-D-F d. The shortest duration needed
to complete this project is 16 days
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Time Management
Key
ES
EF
7
9
9
10
Slack
Dur.
Act
6
2
C
6
1
E
LS
LF
13
15
15
16
0
2
2
7
Dummy
0
2
A
0
5
B
0
2
2
7
7
14
14
16
Activity-on-node network
0
7
D
0
2
F
16
7
14
14
7
Cash Flow
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Cash Flow
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Determining the Critical Path for Project X
a. How many paths are on this network diagram?
b. How long is each path? c. Which is the
critical path? d. What is the shortest duration
needed to complete this project?
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Stochastic (non-deterministic) Activity
DurationsProject Evaluation and Review
Technique (PERT)
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Stochastic Times
Uniform
Triangular
Beta
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Important Distributions
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Stochastic Times The Central Limit Theorem
The sum of n mutually independent random
variables is well-approximated by a normal
distribution if n is large enough.
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PERT Finding the Critical Path (Stochastic Times)

• Develop a network diagram
• Calculate the mean duration and variance of each
  activity
• Calculate the total mean duration and the
  variance of every possible path from the
  beginning to the end of the project by summing
  the mean duration and variances of all activities
  on the path.
• The path with the longest mean duration is the
  critical path
• If more than one path have the longest mean
  duration, the critical path is the one with the
  largest variance.
• Calculate possible project durations using the
  normal distribution

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Example I
Assuming that all activities are beta
distributed, what is the probability that the
project duration will exceed 19 weeks?
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7
A 7, 2.8
B 4.5, 0.7
E 3.5, 0.25
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17.5
C 5,0.1
D 7, 0
F8.7, 1.8
7
G 17.5, 1.36
17
7
A 7, 2.8
B 4.5, 0.7
E 3.5, 0.25
14
17.5
C 5,0.1
D 7, 0
F8.7, 1.8
7
G 17.5, 1.36
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Example II
Duration Duration Duration Duration
Activity IPA Distribution a m b
A --- Uniform 4 NA 8
B --- Triangular 3 4 5
C --- Beta 4 5 6
D C Beta 5 7 12
E A Triangular 3 3 6
F A, B Triangular 5 8 8
G E, D Uniform 9 NA 9
Construct an activity-on-arrow network for the
project above. Provide a 95 confidence interval
on the completion time of the project.
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Example II
Duration Duration Duration Duration
Activity IPA Distribution a m b
A --- Uniform 4 NA 8
B --- Triangular 3 4 5
C --- Beta 4 5 6
D C Beta 5 7 12
E A Triangular 3 3 6
F A, B Triangular 5 8 8
G E, D Uniform 9 NA 9
F
B
A
Start
Finish
E
G
C
D
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Example II
B (4, 0.17)
F (7, 0.5)
A (6, 1.33)
Start
Finish
C (5, 0.11)
E (4, 0.5)
G (9, 0.0)
D (7.5, 1.36)
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Time Management Crashing
Consider the following project network diagram.
Assume all times are in days.
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Time Management
C(2,1,50)
E(1,1,0)
A(2,2,0)
B(5,3,100)
F(2,1,250)
D(7,4,50)
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Duration/Cost Decision Support Curve
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Time Management
C(2,1,50)
E(1,1,0)
A(2,2,0)
B(3,3,100)
F(1,1,250)
D(4,4,50)
Shortest Possible duration with crashing is 10
days.Critical path is not changed.
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Example Problem
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Project Network
A 6
B 4
E 4
C 5
D 7
F 8
G 18
Shortest possible normal duration is 18 at a cost
of 757
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Time Management
0
6
6
10
A
B
1
6
4
4
13
17
1
7
10
14
1
4
E
18
14
0
5
6
13
Dummy
2
5
C
1
7
D
14
2
7
7
6
14
0
18
Dummy
4
8
F
0
18
G
18
10
18
0
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Crashing
A(4,4,10)
B(4,3,13)
E(2,2,21)
D(7,7,0)
F(8,6,12)
C(4,4,15)
G(13,13,18)
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Final Crashed Network
A(4,4,10)
B(4,3,13)
E(2,2,21)
D(7,7,0)
F(8,6,12)
C(4,4,15)
G(13,13,18)
The shortest crashed project duration is 13 days
at a minimum total cost of 924. Further crashing
of B or F is useless
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Using Critical Path Analysis to Make Schedule
Trade-offs

• Knowing the critical path helps you make schedule
  trade-offs
• Free slack or free float is the amount of time an
  activity can be delayed without delaying the
  early start of any immediately following
  activities
• Total slack or total float is the amount of time
  an activity may be delayed from its early start
  without delaying the planned project finish date

This part is from a presentation by Kathy
Schwalbe, schwalbe_at_augsburg.edu http//www.augsbur
g.edu/depts/infotech/
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Techniques for Shortening a Project Schedule

• Shortening durations of critical tasks by adding
  more resources or changing their scope
• Crashing tasks by obtaining the greatest amount
  of schedule compression for the least incremental
  cost
• Fast tracking tasks by doing them in parallel or
  overlapping them

This part is from a presentation by Kathy
Schwalbe, schwalbe_at_augsburg.edu http//www.augsbur
g.edu/depts/infotech/
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Shortening Project Schedules
Original schedule
Shortenedduration
Overlapped tasks
This part is from a presentation by Kathy
Schwalbe, schwalbe_at_augsburg.edu http//www.augsbur
g.edu/depts/infotech/
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(No Transcript)
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Activity Definition
Activity Sequencing
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Duration Estimation
Schedule Development
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Schedule Control