According to the PMBOK® Guide, the Project Network Diagram is the primary tool used to perform Critical Path Method (CPM) analysis. To calculate the critical path, the project manager must be able to visualize the logical relationships (dependencies) between activities, which is exactly what a network diagram provides.

The calculation involves:

Forward Pass: To determine the early start (ES) and early finish (EF) dates.

Backward Pass: To determine the late start (LS) and late finish (LF) dates.

Float Calculation: Identifying paths with " Zero Float. " The longest path through the network diagram with zero total float is the Critical Path.

Why the Project Network Diagram is the best tool: While software can automate this, the underlying tool remains the network diagram (often using the Precedence Diagramming Method - PDM). It shows the sequence of activities and how a delay in one activity impacts the entire chain, allowing for the mathematical determination of the shortest possible project duration.

Analysis of Distractors:

A (Critical chain method): This is a schedule network analysis technique that modifies the project schedule to account for limited resources and adds " buffers " to manage uncertainty. It is an alternative or an advanced evolution of the critical path method, but the baseline tool for identifying the longest path remains the network diagram.

B (Graphical evaluation and review technique - GERT): GERT is a sophisticated network analysis technique that allows for conditional branching and loops (probabilistic treatment). It is rarely used in standard project management and is not the standard tool for a traditional critical path calculation.

C (Gantt chart): While a Gantt chart (bar chart) is excellent for displaying the schedule and progress over time, it is often difficult to see complex dependencies on a Gantt chart alone. In professional project management, the network diagram calculates the path, and the Gantt chart displays the result.