### CPM Calculation - Arrow

```Calculate the critical path
Arrow diagram
Critical
Path
Method
Edina Nagy
Lajos Kiss
Szabolcs Hornyák
Time analysis
Time analysis goals:
- How much time is needed to implement the
schedule?
- When can I start and finish the activities at the
earliest?
- When can I start and finish the activities at the latest?
Activities
A list of all activities required to complete the project.
The time that each activity will take to completion.
The dependencies between the activities.
Basic rules
•
•
•
•
•
Starting point and terminus
Arrows, circles
Activities time
ES,LS,EF,LF
Dummy
4 activities example
ES, EF, LF, LS
ES - earliest start time
EF- earliest finish time
LF- latest finish time
LS- latest start time
ES, EF, LF, LS Formulas
•
•
•
•
Ei = ESij
Ej = EFij = ESij+tij
Li = LSij = LFij-tij
Lj = LFij
The time course analysis
→
→
→
→
TFij
FFij
IFij
CFij
– total float, TFij = Lj-Ei-tij = LFij-ESij-tij
– free float, FFij = Ej-Ei-tij
– independent float IFij = Ej-Li-tij
– conditional float CFij = TFij-FFij
The time course analysis
The Forward pass (first phase) gives the turnaround
time and the earliest possible occurence of events.
The Backward pass (second phase) gives the latest
possible occurrence of events.
Example
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References
Dr. Hajdú Miklós YMMF - Construction organization and
management
Dr. Mályusz Levente BME - The CPM network
www.netmba.com/operations/project/cpm/
Thanks…
```