PROJECT MANAGEMENT
PRACTICE
M. Eng. LAO KHAI KIEN
khaikien98@hcmut.edu.vn
CONTENT
CPM
PERT
SS1
WORKLOAD
MANAGEMENT
SS2
BUDGET
MANAGEMENT
SS3
CASH FLOW
SS4
SESSION 1
Critical Path Method
1
AON/AOA Diagram
2
Program Evaluation
Review Technique
3
Project Crashing
4
CRITICAL PATH METHOD
- CPM identifies tasks that are necessary for project
completion and determine scheduling flexibilities.
- A critical path in PM is the longest sequence of activities that
must be finished on time in order for the entire project to be
complete.
- Any delays in critical tasks will delay the rest of the project.
- As for non-critical tasks, if the delay exceeds slack, the
critical path of the project will change.
FINDING CRITICAL PATH
4 steps to find Critical Path with CPM:
Step 1: Create a Network Diagram (AOA / AON)
Step 2: Estimate task duration
Step 3: Calculate task slack time. Slack = 0  Critical task
Step 4: The series of tasks with zero slack is the Critical Path
AON Diagram
AOA Diagram
A
O
A
D
I
A
G
R
A
M
CPM – AON – 40’
Task
A
B
C
D
E
F
G
H
I
J
K
L
Processing time
(day)
15
10
14
18
14
18
15
10
8
10
25
20
Predecessor
task(s)
A
a. Chart the AON diagram
C
b. Find the Critical Path and
project completion
duration
E
c. Chart the AOA diagram
G
H
B, D, I
F
J, K
https://asq.org/qualityresources/arrow-diagram
CPM – AOA – 30’
B
A
D
C
W
E
X
T
Y
Z
a. Find the Critical Path and project completion duration
b. Convert the AOA to AON diagram
Critical Path Method
VS
PERT
o Manages predictable project activities
o Manages uncertain project activities
o Deterministic
o Probabilistic
o Just one estimate for each activity
o Three estimates for each activity
o Focuses on time-cost-trade offs
o Focuses on meeting or minimizing
project duration
PERT – 30’
Task
A
B
C
D
E
F
G
H
Predecessors
A
A
A
B, C
B,C ,D
C, D
E, F, G
Optimistic
3
4
1
3
3
4
4
2
Most likely
6
7
2
5
6
5
5
3
Pessimistic
9
10
3
7
12
6
6
4
a. Draw a network diagram for the project
b. Find the Critical Path, expected completion time, and standard deviation of
time
PROJECT CRASHING – 50’
Task
A
B
C
D
E
F
G
H
Predecessor Normal time Crash time Normal cost Crash cost
A
A
A
B, C
B,C ,D
C, D
E, F, G
6
7
2
5
6
5
5
3
3
4
1
3
3
4
4
2
1000
500
1500
2000
200
200
600
300
2000
800
1800
2500
400
400
800
600
a. How much does it cost to shorten the project by 3 days?
b. How many days can the project be shortened with the crash budget of $750?