Question

Free float is:

• A. The time an activity can be delayed without affecting the early start of a successor activity
• B. The time an activity can be delayed without affecting the project completion date
• C. Always more than total float
• D. Used to identify Critical Path

Hint:

Float Definitions Summary:
• Total Float: Delay allowed without delaying the Final Project Delivery.
• Free Float: Delay allowed without delaying the Next Immediate Activity.

Answer 1

The Correct Option is A

Concept: In network scheduling methods like the Critical Path Method (CPM), float (or slack) measures the amount of flexibility or schedule delay available for an activity. The two most common types are Total Float and Free Float. Free float focuses specifically on preventing delays to immediate downstream activities.

Step 1: Defining Free Float Mathematically.
Free Float ($FF$) is defined as the amount of time an activity can be delayed without pushing back the earliest start time of any immediate successor activity. It is calculated using the following formula: \[ FF_{i-j} = ES_j - ES_i - t_{i-j} \] Where:
• $ES_j$ is the Earliest Start time of the immediate successor activity.
• $ES_i$ is the Earliest Start time of the current activity.
• $t_{i-j}$ is the actual duration of the current activity. This equation shows that as long as the current activity finishes within its free float window, it will not cause any delays to downstream tasks, which matches Option A.

Step 2: Differentiating from alternative options.
Let us check why the remaining options are incorrect definitions:
• Option B: The time an activity can be delayed without delaying the *overall project completion date* is the definition of Total Float, not free float.
• Option C: Free float is a subset of total float. It is mathematically impossible for free float to exceed total float; it will always be less than or equal to total float ($FF \leq TF$).
• Option D: The Critical Path is identified by finding activities where the Total Float is zero ($TF = 0$). Free float alone is not used to establish the critical path.