CPM/PERT logic: A dummy activity becomes critical when its earliest start equals its latest finish. Is this statement correct?

Introduction / Context:Dummy activities in Activity-on-Arrow (AOA) networks have zero duration and exist only to preserve logical relationships. Understanding when any activity (including a dummy) is “critical” requires correct use of early/late times and float definitions.

Given Data / Assumptions:

• For any activity with duration d, EF = ES + d and LS = LF - d.
• Total float TF = LS - ES = LF - EF.
• Critical activities have TF = 0, i.e., ES = LS and EF = LF.

Concept / Approach:A dummy has d = 0, hence EF = ES and LS = LF. It lies on the critical path only if ES = LS (equivalently EF = LF). The statement compares ES to LF (earliest start to latest finish), which is not the criterion for criticality. ES equal to LF is neither necessary nor sufficient to establish TF = 0.

Step-by-Step Solution:

Verification / Alternative check:Construct a small network where a dummy connects two critical events; you will find ES = LS and EF = LF, not ES = LF.

Why Other Options Are Wrong:Marking the statement as “Correct” misapplies the definition of criticality.

Common Pitfalls:Mixing early and late times across different ends of an activity; forgetting that zero duration does not change the logic for float conditions.

Final Answer:Incorrect