PERT Analysis MCQ with answer and solution

Concept

Slack is the difference between the latest allowable time and the earliest expected time for an event. A negative slack means the project is running behind schedule, which usually happens due to a shortage of resources.

Formula

Slack = T_L - T_E

Step-by-step solution

1. Understand the definition of slack in PERT: Slack = Latest Allowable Occurrence Time (T_L) - Earliest Expected Occurrence Time (T_E). 2. When T_L is less than T_E, slack becomes negative (Slack < 0). 3. Negative slack indicates that the event is delayed and will not meet the target completion date. 4. This delay occurs when activities take longer than planned, often caused by a deficiency or shortage of resources (like labor, machinery, or materials). Answer: (C) there is deficiency of resources

Explanation

Slack measures the spare time available for an event. Negative slack means the project is behind schedule and critical deadlines cannot be met with current progress. This delay is typically caused by a lack or deficiency of resources like men, money, and machinery.

Why the other options are wrong

A: Dummy activities represent logic and have zero time or resource, so their number does not cause negative slack. B: When events happen on schedule, slack is zero. D: Excess availability of resources speeds up the project and gives positive slack.

Shortcut

Negative slack = Project is behind schedule = Shortage or deficiency of resources.

Common mistake

Students often confuse negative slack with excess resources, but excess resources actually lead to positive slack (ahead of schedule).