Critical Path Method (CPM)

Correct Answer: The task is behind schedule and threatens project completion date

In Critical Path Method (CPM), negative total float indicates that the task is already causing a delay to the project completion date. This means the project is falling behind schedule. A negative float occurs when a task has taken longer than planned, and there isn't enough buffer time in the schedule to absorb this delay. This situation threatens the project's completion date and requires immediate corrective action. The other answers are incorrect because: - Having excess time would be indicated by positive float, not negative - Extending task duration would only make the delay worse - While additional resources might be one potential solution to address negative float, it's not what negative float indicates or signifies in CPM analysis

Correct Answer: Calculate the cost-benefit ratio for each activity on the critical path

Calculating the cost-benefit ratio for activities on the critical path is the most accurate method for determining if schedule optimization techniques should be applied because: It provides a quantitative basis for decision-making by: - Measuring the cost impact of compression against potential benefits - Identifying which activities will yield the best return on acceleration investment - Allowing for optimal resource allocation decisions Why other options are less effective: Comparing parallel paths and resource requirements is incomplete as it doesn't consider the cost implications of compression. Evaluating duration compression options alone lacks the financial analysis component necessary for informed decision-making. Analyzing resource utilization patterns focuses too heavily on resources rather than the critical cost-time trade-offs needed for optimization decisions.

Correct Answer: The ratio of the number of times a path becomes critical to the total number of project iterations

The criticality index in CPM is a statistical measure that shows how often a path becomes critical across multiple project simulations or iterations. The correct answer accurately describes this concept as a ratio between the number of times a path becomes critical versus the total number of simulations run. This measure helps project managers identify which paths are most likely to impact the project's duration. The other options are incorrect because: Multiplying activity durations along a path would not indicate criticality - it would just give a total duration. Resource allocation percentage is related to resource management, not path criticality measurement. Comparing longest and shortest durations relates more to schedule variance analysis than measuring how often a path becomes critical.