According to the PMBOK® Guide and the Standard for Project Management, Analytical techniques are used in the Plan Schedule Management process to define the strategic approach for the project schedule.

As per PMI standards, these techniques involve choosing between strategic options to estimate and schedule the project. This is a critical step in determining how the project ' s timeline will be developed and managed. Specific analytical techniques used in this process include:

Scheduling methodology: Choosing between various methods such as the Critical Path Method (CPM), Critical Chain, or Agile/Adaptive approaches.

Scheduling tools: Deciding on the specific software or manual systems to be used.

Estimating techniques: Determining if the project will use Analogous, Parametric, Three-point, or Bottom-up estimating.

Fast tracking or crashing: Deciding on the strategic use of schedule compression techniques if needed.

The other options are incorrect based on the following PMI definitions:

Facilitation techniques: These are used to bring stakeholders together to reach a consensus. While they are used during the Planning meetings, they are the means of communication rather than the analysis of strategic scheduling options.

Expert judgment: This refers to providing input from individuals or groups with specialized knowledge or training in previous similar projects. While experts provide advice, the " analytical technique " is the formal category for the logical process of selecting strategic options.

Variance analysis: This is a tool and technique used in the Control Schedule process (Monitoring and Controlling), not in Plan Schedule Management (Planning). It is used to compare actual progress against the baseline to identify deviations.

As per the PMI Lexicon of Project Management Terms, analytical techniques allow the project manager to evaluate the implications of different scheduling scenarios and choose the one that best fits the project ' s constraints and organizational environment.