Which methodology is utilized to determine the critical path in a project?

The Critical Path Methodology is specifically designed to identify the longest sequence of dependent tasks in a project, which determines the shortest possible duration for completing the project. This methodology involves analyzing the various paths in a project schedule to calculate the earliest start and finish times, as well as the latest start and finish times for each task. By focusing on the critical path, project managers can prioritize tasks that directly impact the project's completion time and efficiently allocate resources, ensuring that any delays in these critical tasks will affect the overall project timeline.

In contrast, the other methodologies listed do not primarily focus on critical path analysis. The Waterfall Method follows a linear sequential approach, where each phase must be completed before the next begins. Agile Methodology emphasizes flexibility and iterative progress through small increments. The Scrum Framework is a specific application of Agile principles under which teams work in time-boxed sprints to deliver functional products. While all these methodologies are effective in their own right, they do not provide the structured approach needed for determining the critical path in project management. This is why the Critical Path Methodology is the correct choice for this question.