In network analysis, the time by which an activity's completion can be delayed without affecting the earliest start of its immediate successor(s) is called:

Introduction / Context:
Different float types quantify different flexibilities. Free float focuses on the leeway available to an activity without encroaching on the early schedule of its immediate successor(s).

Given Data / Assumptions:

• We seek the term for delay that does not impact successor earliest starts.
• Terminology must distinguish total float from free and interfering float.

Concept / Approach:
Free float (FF) = Min(EST of successors) - EFT of the activity.Free float measures how much the activity’s finish can slip without changing any successor’s earliest start. Total float is broader: TF = LFT - EFT = LST - EST. Interfering float is the portion of total float that, if used, would delay successors’ earliest starts.

Step-by-Step Solution:
Identify the definition that matches “no effect on successor earliest start”.Relate to formula: FF depends on successor EST and current activity EFT.Select Free float.

Verification / Alternative check:
Compute a small example network to confirm that a delay equal to FF keeps successor EST unchanged, while using more than FF encroaches on successor timing.

Why Other Options Are Wrong:

• Duration: Not a float type; the base length of the activity.
• Total float: Includes portions that might affect successors if used.
• Interfering float: By definition, it interferes with successor earliest starts.

Common Pitfalls:
Using TF when FF is intended; assuming all slack is harmless to successors; ignoring the distinction between local (free) and global (total) slack.

Final Answer:
Free float