Project Management Notes
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Transcript of Project Management Notes
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Project Management and scheduling
Objectives of project scheduling
Network analysis
Scheduling techniques
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Objectives of project scheduling Produce an optimal project schedule in
terms of cost, time, or risk.
Usually, it is difficult to optimize the three
variables at the same time. Thus,
setting an acceptable limit for two of the
three varaibles and optimizing the project in
terms of the third variable.
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Critical Path Method (CPM) Produce the earliest and lastest starting and
finishing times for each task or activity.
Calculate the amount of slack associated
with each activity.
Determine the critical tasks (Critical path).
Forward pass and backward pass
computational procedures.
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Network control Track the progress of a project on the basis
of the network schedule and taking
corrective actions when necessary.
Evaluate the actual performance against
expected performance.
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3
5
6 7 8
4
PERT/CPM
Node
Arrow
Predecessor
SuccessorMerge point
Burst point
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Two models of PERT/CPM Activity-on-Arrow (AOA): Arrows are used
to represent activities or tasks. Nodes
represent starting and ending points of
activities.
Activity-on-Node (AON): Nodes are used
to represent activities or tasks, while arrows
represent precedence relationships.
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Recap - purpose of CPM Critical path
Earliest starting time ES Earliest completion time EC
Latest starting time LS
Latest completion time LC Activity Capital letter
Duration t
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Example Activity Predecessor Duration A - 2
B - 6 C - 4
D A 3
E C 5
F A 4
G B, D, E 2
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Activity on Node Network
Start B
6
A
2
C
4
G
2
EndD
3
F4
E
5
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Start B
6
A
2
C
4
G
2
EndD
3
F
4
E
5
0 0
0 2
2 6
2 5
0 6
04 4 9
9 11
11 11
Forward pass analysis
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Start B
6
A
2
C
4
G
2
EndD3
F4
E
5
0 0
0 2
2
6
2 5
0 6
04 4 9
9 11
11 11
1111
119
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64
9
3
00
117
Backward pass analysis
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Slack Time in Triangles
Start B
6
A
2
C
4
G
2
EndD
3
F
4
E
5
0 0
0 2
2 6
2 5
0 6
04 4 9
9 11
11 11
1111
119
9440
96
64
93
00
117
00
0 0
0
4
5
4
4
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Critical path
Start B
6
A
2
C
4
G
2
EndD
3
F4
E
5
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Computational analysis
of network Forward pass: each activity begins at its
earliest time. An activity can begin as soon
as the last of its predecessors is finished.
Backward pass: begins at its latest
completion time and ends at the latest
starting time of the first activity in the
project network.
R l f i l i
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Rules for implementation -
forward pass
The earliest start time (ES) for any node (j)is equal to the maximum of the earliest
completion times (EC) of the immediate
predecessors of the node. The earliest completion time (EC) of any
activity is its earliest start time plus its
estimated time (its duration). The earliest completion time of the project
is equal to the earliest completion time the
very last activity.
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Rules for implementation -
backward pass The latest completion time (LC) of any
activity is the smallest of the latest start
times of the activitys immediate
successors.
The latest start time for any activity is the
latest completion time minus the activity
time.
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Calculate slack time for each
activity Slack time: the difference in time between
the two dates at the beginning of a job or
the two dates at the end of the job. Slack
time represents the flexiblity of the job.
Thus, slack time = LS - ES or LC - EC
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PERT
PERT is an extension of CPM. In reality, activities are usually subjected to
uncertainty which determine the actual
durations of the activities. It incorporates variabilities in activity
duration into project entwork analysis.
The poetntial uncertainties in activity areaccounted for by using three time estimates
for each activity
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Variation of Task Completion TimeTask A
2
4
6
4
Task B
34
5
4Average 4 4
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PERT Estimates & Formulas
te= a+4m+b6 s
2= (b-a)2
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a = optimistic time estimatem = most likely time estimate
b = pessimistic time estimate (a < m < b)
te= expected time for the activitys2=variance of the duration of the activity
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PERT
Calculate the expected time for eachactivity
Calculate the variance of the duration of
each activity
Follow the same procedure as CPM does to
calculate the project duration, Te
Calculate the variance of the projectduration by summing up the variances of
the activities on the critical path.
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Sources of the Three Estimates Furnished by an experienced person
Extracted from standard time data
Obtained from historical data
Obtained from regression/forecasting
Generated by simulation Dictated by customer requirement
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A PERT Example
ActivityPredecessor a m b te s2
A - 1 2 4 2.17 0.2500
B - 5 6 7 6.00 0.1111 C - 2 4 5 3.83 0.2500
D A 1 3 4 2.83 0.2500
E C 4 5 7 5.17 0.2500
F A 3 4 5 4.00 0.1111
G B, D, E 1 2 3 2.00 0.1111
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What do Te& S
2
tell us? How likely to finish the project in a
specified deadline.
For example, suppose we would like to
know the probability of completing the
project on or before a deadline of 10 time
units (days)
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Probability of finishing the
project in 10 daysTe= 11 S
2= V[C] + V[E] + V[G]
= 0.25 + 0.25 + 0.1111
= 0.6111
S= 0.7817
P( T
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Probability of finishing the
project in 13 days
Te= 11 S2= V[C] + V[E] + V[G]
= 0.25 + 0.25 + 0.1111
= 0.6111
S= 0.7817
P(T
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Gantt Chart Gantt chart is a matrix of rows and columns.
The time scale is indicated along the
horizontal axis. Activities are arranged
along the vertical axis.
Gantt charts are usually used to represent
the project schedule. Gantt charts should beupdated periodically.
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Gantt Chart
A
B
C
D
E
F
G
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Gantt Chart Variations
Linked Bars
Progress - monitoring
Milestone
Task - combinations
Phase-Based Multiple-Projects
Project-Slippage-tracking
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Linked Bars Gantt Chart
A
B
C
D
E
F
G
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