Calculate the Total Float, Free Float, and Independent Float for a project with the following activities and their durations:
Activity Duration (weeks)
1 ? 2 8
1 ? 3 7
1 ? 5 12
2 ? 3 4
2 ? 4 10
3 ? 4 3
3 ? 5 5
3 ? 6 10
4 ? 6 7
5 ? 6 4
Construct the network diagram for the project.
Calculate the earliest start (ES), earliest finish (EF), latest start (LS), and latest finish (LF) for each activity.
Determine the Total Float, Free Float, and Independent Float for each activity.
The correct answer and explanation is:
To calculate the Total Float (TF), Free Float (FF), and Independent Float (IF) for the given project, we need to perform the following steps systematically:
Step 1: Create the Network Diagram
The activities and their relationships can be represented as a network diagram with nodes for events and arrows for activities. Using the provided data:
- Start from Node 1.
- Draw arrows for the dependencies as specified:
- 1→21 \to 2 (8 weeks)
- 1→31 \to 3 (7 weeks)
- 1→51 \to 5 (12 weeks)
- 2→32 \to 3 (4 weeks)
- 2→42 \to 4 (10 weeks)
- 3→43 \to 4 (3 weeks)
- 3→53 \to 5 (5 weeks)
- 3→63 \to 6 (10 weeks)
- 4→64 \to 6 (7 weeks)
- 5→65 \to 6 (4 weeks)
Step 2: Perform Forward Pass (Calculate ES and EF)
- Earliest Start (ES) of the first activity is 0.
- Earliest Finish (EF) = ES+durationES + \text{duration}.
Step 3: Perform Backward Pass (Calculate LS and LF)
- The Latest Finish (LF) of the final activity is the project duration.
- Latest Start (LS) = LF−durationLF – \text{duration}.
Step 4: Calculate Floats
- Total Float (TF) = LF−EFLF – EF or LS−ESLS – ES.
- Free Float (FF) = ESsuccessor−EFcurrentES_{\text{successor}} – EF_{\text{current}}.
- Independent Float (IF) = max(0,ESsuccessor−LFcurrent−duration)\max(0, ES_{\text{successor}} – LF_{\text{current}} – \text{duration}).
I will calculate the values and construct the network diagram for the project.
I have calculated the Total Float, Free Float, and Independent Float for all activities and displayed the results in a table for your review. The table also includes the Earliest Start (ES), Earliest Finish (EF), Latest Start (LS), and Latest Finish (LF) values. Let me know if you need further explanation or assistance!