Calculating Critical Path & Float for a Network

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Calculating Critical Path & Float for a Network Diagram
Late Start
(LS)
Early Start
(ES)
Task Name,
Duration (D)
Late Finish
(LF)
Early Finish
(EF)
 Find out the length of all the paths in the network diagram
 The longest path is the critical path
 Float = EF - LF
= ES - LS
Calculating Critical Path for a Network Diagram
Identify tasks, durations & dependencies.
5 days
Task 2
4 days
4 days
Task 1
Task 5
3 days
Task 3
7 days
Task 4
Step 1: Draw a Network Diagram
For forward pass, calculate the Early Start (ES) and Early Finish (EF).
Task 2,
5 days
4
Task 1,
4 days
0
9
Task 5,
4 days
14
18
4
Task 3,
3 days
4
7
Task 4,
7 days
7
14
Task 5 is dependent on Task 2 and Task 4 being complete.
So, ES for Task 5 is 14 days (dependent on Task 4, which is the longer task.
Step 2: Determine Critical Path
To determine critical path, calculate length (durations) of all the paths:
 Length of all tasks:
• Task1 → Task2 → Task5 = 4 + 5 + 4 = 13 days
• Task1 → Task3 → Task4 → Task5 = 4 + 3 + 7 + 4 = 18 days
 The longest path is the critical path
 Critical path = longest path = 18 days
 Critical Path = Task1 → Task3 → Task4 → Task5
Step 3: Calculate Float in all tasks – Backward Pass
ES = Early Start
EF = Early Finish
LS = Late Start
LF = Late Finish
0
9
14
Task 2,
5 days
4
14
18
Task 5,
4 days
14
18
9
4
Task 1,
4 days
0
4
4
Task 3,
3 days
4
7
7
14
Task 4,
7 days
7
7
14
For all tasks on Critical Path (Task1, Task 3, Task 4, Task 5), EF = LF & ES = LS
Thus, float (slack) for tasks on Critical Path = LF – EF = 0
Float for Task 2 = LF – EF = 14 – 9 = 5 days
Step 4: Calculate Project Float
 Customer requests an end date of 25 days.
 Project Float is the total amount of time that the project can be delayed
without delaying the project completion date required by the customer.
25 days – 18 days = 7 days.
 Project float can be negative when the date imposed by the customer is before
the duration required in the project schedule.
 For negative project float, the project must be crashed or fast-tracked.
 Crashing is a technique used to decrease the duration of the project by
assigning additional resources to tasks and decreasing the duration required
for those tasks.
 Fast Tracking is a technique used to shorten project time by scheduling some
activities concurrently that were originally scheduled sequentially.
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