#### Transcript IE 2030 Lecture 5: Project Management Drawing Gantt Charts

```IE 2030 Lecture 5: Project Management
Drawing Gantt Charts
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Time on horizontal axis,
Activities on vertical axis. 1 bar per activity
Length of bar = required activity time
Left end of bar at ES=Earliest Start Time
Concepts:
– Slack Time
– Earliest Start Time
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
IE 2030 Lecture 5: Gantt Charts
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• 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
Doesn’t deal with variability or uncertainty
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.
IE 2030 Lecture 5: PERT/CPM
How 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
B
9
C
8
4
A
F
12
10
2
D
7
E
Critical Path: A,D,F. Early start time of D,F = Late time = 12
Early start time of B,C = 4; Late start time=5
B
10
C
8
4
A
F
12
10
3
D
7
E
Critical Paths: A,D,F; A,B,C,F; A,D,E,F.
Earliest Start Times -- Forward Computation
5
2
10
2
6
7
3
9
7
2
1
2
Earliest Start Times -- Forward Computation
Note: Early Finish Time = Early Start Time +
Activity Time
5
5
17
10
0
2
15
2
2
9
3
38
1
29
6
7
22
7
2
31
2
Latest Finish Times -- Backward Computation
Note: Late Start Time = Late Finish Time Activity Time
5
5
26
10
0
2
15
2
9
9
3
38
1
29
6
7
22
7
39
2
37
Early S (F) Time = Late S (F) Time for critical path arcs
2
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