Network Analysis MCQ with answer and solution

Concept

Fulkerson's rule for numbering network events

Formula

i < j for activity (i, j)

Step-by-step solution

1. In project network models (CPM/PERT), nodes signify events marking the start or completion of activities. 2. Fulkerson’s rule provides an algorithmic procedure to label events sequentially with numbers. 3. The rule dictates that the initial event with no incoming arrows is numbered first (e.g., 1), and subsequent events are numbered such that every activity arrow leads from a lower-numbered node i to a higher-numbered node j (i < j). 4. Hence, Fulkerson's rule is used for numbering events. Answer: B

Explanation

Fulkerson’s rule is a systematic method used in network analysis (CPM/PERT) for numbering the events (nodes) of a project network. It assigns numbers such that for every activity arrow connecting an initial node i to an end node j, the tail event number is always strictly smaller than the head event number (i < j).

Why the other options are wrong

A) Activities in arrow diagrams are identified by their start and end events (i-j), not directly by Fulkerson's rule. C) Floats (total float, free float) are computed time spans, not network entities numbered by this rule. D) Dummy activities are zero-duration arrows representing precedence dependencies.

Shortcut

Fulkerson's rule = Event numbering (always tail i < head j).

Common mistake

Confusing events (nodes) with activities (arrows); Fulkerson's rule specifically defines numbering for events, not activities.