According to the PMBOK® Guide, specifically within the Develop Schedule process, the Critical Path Method (CPM) is the primary analytical tool used to calculate the theoretical start and finish dates for all activities.

Mechanism: The Critical Path Method performs a Forward Pass and a Backward Pass through the project schedule network diagram.

Forward Pass: Determines the Early Start (ES) and Early Finish (EF) dates for each activity by calculating from the project start date.

Backward Pass: Determines the Late Start (LS) and Late Finish (LF) dates by calculating from the project finish date.

Purpose: By comparing these dates, the tool identifies the Total Float (LS - ES or LF - EF) for each activity. Activities with zero total float are on the Critical Path, which represents the longest path through the project and determines the shortest possible project duration.

Theoretical Nature: These dates are considered " theoretical " because they do not account for resource limitations; they are based solely on logic, durations, and constraints. Resource leveling is typically applied after this analysis to create a realistic schedule.

Choice B (Variance analysis): This is a tool used in Control Schedule to compare actual progress against the baseline, not to generate theoretical start/late dates.

Choice C (Schedule compression): These techniques (Crashing and Fast Tracking) are used to shorten the schedule duration, often after the initial critical path has been identified.

Choice D (Schedule comparison bar charts): These are used to visualize the difference between two versions of a schedule (e.g., baseline vs. current), not to calculate the ES/LS dates.