1. PROJECT MANAGEMENT
An Example
Building construction
© 1995 Corel Corp.
Project Organization
Works Best When
Work can be defined with a specific goal and deadline
The job is unique or somewhat unfamiliar to the existing
organization
The work contains complex interrelated tasks requiring
specialized skills
The project is temporary but critical to the organization
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2. Project Planning, Scheduling,
and Controlling
Project Planning
Time/cost estimates
1. Setting goals
Budgets
2. Defining the project
Engineering diagrams
3. Tying needs into timed project
Cash flow charts
activities
Material availability details
4. Organizing the team
Project Scheduling
1. Tying resources to specific CPM/PERT
activities Gantt charts
2. Relating activities to each other Milestone charts
3. Updating and revising on a Cash flow schedules
regular basis
Project Controlling
Reports
1. Monitoring resources, costs, quality,
• budgets
and budgets
• delayed activities
2. Revising and changing plans
• slack activities
3. Shifting resources to meet demands
Before Project During Project
Project Planning
Establishing objectives
Defining project
Creating work breakdown structure
Determining resources
Forming organization
© 1995 Corel Corp.
Work Breakdown Structure
1. Project
2. Major tasks in the project
3. Subtasks in the major tasks
4. Activities (or work packages) to
be completed
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3. Project Scheduling
Identifying precedence relationships
Sequencing activities
Determining activity times & costs
Estimating material & worker © 1995 Corel Corp.
requirements
Determining critical activities PERT
Tes J
t J
M
Bui A
ld Mo M
De nth F
sign J
Ac
tivi
ty
Project Management Techniques
Gantt chart
Critical Path Method (CPM)
Program Evaluation & Review Technique
(PERT)
© 1984-1994 T/Maker Co.
Gantt Chart
Time Period
Activity
J F M A M J J
Design
Build
Test
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4. Service Activities for A Delta Jet During a 60 Minute
Layover
PERT and CPM
Network techniques
Developed in 1950’s
CPM by DuPont for chemical plants (1957)
PERT by Booz, Allen & Hamilton with the U.S. Navy,
for Polaris missile (1958)
Consider precedence relationships and interdependencies
Each uses a different estimate of activity times
Milwaukee General Hospital’s Activities and
Predecessors
Activity Description Immediate
Predecessors
A Build internal components -
B Modify roof and floor -
C Construct collection stack A
D Pour concrete and install frame A, B
E Build high-temperature burner C
F Install pollution control system C
G Install air pollution device D, E
H Inspect and test F, G
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5. F
A C
Start E H
B D G
Activity Description Immediate
Predecessors
A Build internal components -
B Modify roof and floor -
C Construct collection stack A
D Pour concrete and install frame A, B
E Build high-temperature burner C
F Install pollution control system C
G Install air pollution device D, E
H Inspect and test F, G
Latest Start and Finish Steps
Name
Activity
Earliest Earliest
Start ES EF
Finish
Latest
LS LF
Duration
Activity
Start Latest
Finish
Critical Path Analysis
Provides activity information
Earliest (ES) & latest (LS) start
Earliest (EF) & latest (LF) finish
Slack (S): Allowable delay
Identifies critical path
Longest path in network
Shortest time project can be completed
Any delay on critical path activities delays project
Critical path activities have 0 slack
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6. Earliest Start and Finish Steps
Begin at starting event and work forward
ES = 0 for starting activities
ES is earliest start
EF = ES + Activity time
EF is earliest finish
ES = Maximum EF of all predecessors for non-starting
activities
Latest Start and Finish Steps
Begin at ending event and work backward
LF = Maximum EF for ending activities
LF is latest finish; EF is earliest finish
LS = LF - Activity time
LS is latest start
LF = Minimum LS of all successors for non-ending
activities
Latest Start and Finish Steps
Name
Activity
Earliest Earliest
Start ES EF
Finish
Latest
LS LF
Duration
Activity
Start Latest
Finish
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7. We have 13 days for this project
Earliest Latest
Earliest Finish Start
Start A B CF 7
0 2 2 4 4
H H H
6 A 8 8 C10 10 13
2 2 3 Latest
Finish
We can begin the project as early as day 0 ---immediately
Task A costs 2 days, so the earliest day we can finish it is day 2
We must finish the project in day 13, so the latest finish day for task C is
day 13
Task C takes 3 days, so the latest time that we should begin it is day
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Critical Path for
Milwaukee General Hospital
F
A C
F
Start H
B D G
w
s sho
Arrow dence
prece ships
n
relatio
Earliest Latest
Finish Start
Earliest
Start
A C F
0 2 2 4 4 F 7
H H H
0 A 2 2 C4 10 13
2 2 3
E H
Slack=0 Slack=0 4 H 8 Slack=6 13 H 15
0 0 F
H
Start 4 8 15
0 0 4 13
0 2
B D Slack=0 G
Start 0 B 3 3 D7 8 G 13 Slack=0
H H H
1 4 4 8 8 13
3 4 5 Latest
Slack=1 Slack=1 Slack=0 Finish
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8. Gantt Chart
Earliest Start and Finish
Milwaukee General Hospital
1 2 3 4 5 6 7 8 9 10 1112 13 1415 16
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install
frame
E Build high-temperature
burner
F Install pollution control
system
G Install air pollution device
H Inspect and test
Gantt Chart
Latest Start and Finish
Milwaukee General Hospital
1 2 3 4 5 6 7 8 9 10 1112 13 1415 16
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install
frame
E Build high-temperature
burner
F Install pollution control
system
G Install air pollution device
H Inspect and test
PERT Activity Times
3 time estimates
Optimistic times (a)
Most-likely time (m)
Pessimistic time (b)
Follow beta distribution
Expected time: t = (a + 4m + b)/6
Variance of times: v = (b - a)2/6
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9. Project Times
Expected project time (T) Used to obtain
Sum of critical path activity probability of project
times, t completion!
Project variance (V)
Sum of critical path activity
variances, v
PERT Probability Example
You’re a project planner for General
Dynamics. A submarine project has an
expected completion time of 40 weeks,
with a standard deviation of 5 weeks.
What is the probability of finishing the sub © 1995
Corel Corp.
in 50 weeks or less?
Converting to Standardized Variable
Due date Expected date of finish
X - T 50 - 40
Z = = = 2 .0
s 5
Normal Standardized Normal
Distribution Standard deviation Distribution
s =5 sZ = 1
T = 40 50 X mz = 0 2.0 Z
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10. Obtaining the Probability
Standardized Normal Probability
Table (Portion)
Z .00 .01 .02
0.0 .50000 .50399 .50798 sZ =1
: : : :
2.0 .97725 .97784 .97831 .97725
2.1 .98214 .98257 .98300 mz = 0 2.0 Z
Probabilities in body
Variability of Completion Time for Noncritical
Paths
Variability of times for activities on noncritical paths must be
considered when finding the probability of finishing in a
specified time.
Variation in noncritical activity may cause change in critical
path.
Steps in Project Crashing
Compute the crash cost per time period. For crash costs
assumed linear over time:
(Crash cost − Normal cost
Crash cost per period =
(Normal time − Crash time )
Using current activity times, find the critical path
If there is only one critical path, then select the activity on this
critical path that (a) can still be crashed, and (b) has the
smallest crash cost per period. Note that a single activity may
be common to more than one critical path
Update all activity times.
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