Which analysis is crucial for determining the longest path in a project?

The analysis that is crucial for determining the longest path in a project is Critical Path Analysis. This technique is essential in project management as it identifies the sequence of dependent tasks that directly affect the project's duration. By calculating the longest stretch of dependent activities, it allows project managers to determine the shortest time in which the project can be completed.

In Critical Path Analysis, tasks that are on the critical path have zero slack, meaning any delay in these tasks will result in a delay in the entire project. This analysis not only highlights the critical activities that need close monitoring but also helps in resource allocation to ensure timely project completion. The identification of the longest path helps in effective time management, ensuring that deadlines are met and resources are utilized efficiently.

Other analyses like Cost-Benefit Analysis, Sensitivity Analysis, and Regression Analysis serve different purposes. Cost-Benefit Analysis evaluates the financial aspects of a project, Sensitivity Analysis assesses how different variables impact the project outcomes, and Regression Analysis is used for forecasting trends and relationships. However, none of these analyses focus specifically on determining the longest path in project scheduling like Critical Path Analysis does.