Network analysis (CPM/PERT): Can activity slack (float) take positive, zero, or negative values?

Introduction / Context:
Slack (float) indicates scheduling flexibility for an activity. Understanding its sign and magnitude helps managers decide where acceleration is needed and where delays are tolerable.

Given Data / Assumptions:

• Total float TF = LF - EF = LS - ES.
• Critical activities have zero total float.
• External deadline constraints can create negative float.

Concept / Approach:
In a baseline network without external constraints, floats are non-negative; zero float defines the critical path. When due-date constraints are tighter than the network's natural completion time, some activities exhibit negative float, signalling that the plan is infeasible without crashing or resequencing.

Step-by-Step Solution:

Verification / Alternative check:
Run a what-if with a deadline earlier than critical path duration; backward pass produces LS < ES for some activities, giving negative float.

Why Other Options Are Wrong:
“Disagree” ignores practical cases where contractual dates impose negative float.

Common Pitfalls:
Assuming negative float is an error; it is a diagnostic indicating the schedule must be revised or resources added.

Final Answer:
Agree