IE 2030 Lecture 5: Project Management Drawing Gantt Charts

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IE 2030 Lecture 5 Project ManagementDrawing
Gantt Charts

• Time on horizontal axis,
• Activities on vertical axis. 1 bar per activity
• Length of bar required activity time
• Left end of bar at ESEarliest Start Time
• Concepts
• Slack Time
• Earliest Start Time

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IE 2030 Lecture 5 Gantt Charts
Slack time example
2
2
5
The first 2-time-unit activity has slack 0, and
the second has a slack of 1. Either (but not
both) could be delayed without delaying the
project
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IE 2030 Lecture 5 Gantt Charts

• Gantt Chart Pros and Cons
• Easy to understand, visual
• Can show how large a staff is needed
• Good for small projects
• Poor at showing precedence relations
• Poor at showing practical slack
• Doesnt deal with variability or uncertainty

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IE 2030 Lecture 5 PERT/CPM

• How to draw PERT/CPM networks
• Concepts Critical Path, Early Time, Late Time
• How to compute values. Why a good algorithmic
  method is needed.
• A model for dealing with uncertainty PERT, Beta
  distribution, central limit theorem. Formulas
  that make assumptions.

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IE 2030 Lecture 5 PERT/CPMHow to Draw Networks

• Each activity is represented by a unique arc
  (branch)
• Start node, Finish node
• Parallel arcs not permitted 2 arcs may not
  share both head and tail nodes
• Use dummy arcs as needed for precedence
• Nodes may be thought of as events such as the end
  of an activity

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9
B
C
8
4
A
F
12
10
2
D
E
7
Critical Path A,D,F. Early start time of D,F
Late time 12 Early start time of B,C 4 Late
start time5
7
10
B
C
8
4
A
F
12
10
3
D
E
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Critical Paths A,D,F A,B,C,F A,D,E,F.
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Exponentially many paths
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Earliest Start Times -- Forward Computation
1
9
5
3
10
2
2
6
7
2
2
7
Algorithm to handle
Exponentially many paths
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Earliest Start Times -- Forward Computation Note
Early Finish Time Early Start Time Activity
Time
5
17
38
1
9
5
3
10
2
0
15
29
2
6
7
2
2
2
22
7
31
Algorithm to handle
Exponentially many paths
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Latest Finish Times -- Backward Computation Note
Late Start Time Late Finish Time - Activity
Time
5
26
38
1
9
5
3
10
2
0
15
29
39
2
6
7
2
2
9
22
7
37
Algorithm to handle
Exponentially many paths
Early S (F) Time Late S (F) Time for critical
path arcs