Schedule Management

The strategy called when adding more resources to speed up critical tasks in a project that is falling behind is 'Crashing'. 'Crashing' involves adding more resources to the project to accomplish tasks faster, even at a higher cost. 'Fast Tracking', on the other hand, involves executing tasks simultaneously that were initially planned to be done sequentially - not adding more resources. 'Resource Leveling' is a technique used to adjust the project schedule based on resource constraintss - not speeding up tasks, while 'Schedule Compression' is a general term for techniques used to shorten the project schedule without changing project scope, which includes both 'Crashing' and 'Fast Tracking', but in this question, the exact action is adding more resources which refers strictly to 'Crashing'.

The technique the project manager is about to use is Fast tracking. This technique involves overlapping phases that are usually completed sequentially to speed up the project schedule. On the other hand, the other techniques like Crashing focuses on reducing project duration by adding more resources to project activities, Risks associated with it includes cost increment and quality reduction, it doesn't mention overlapping phases. Likewise, Resource Leveling is about managing and smoothing the assigned resources levels to avoid over-allocating or under-allocating them, it doesn't pertain to overlapping phases or accelerating project schedule. Monte Carlo Simulation is a risk assessment technique that provides a range of possible outcomes and the probabilities they will occur, it is unrelated to fast-tracking or overlapping of project tasks.

The Critical Path Method (CPM) is the most appropriate tool to use when managing and adjusting a complex project schedule. CPM allows for the identification of the most critical tasks that directly impact the project's completion date. Any delays or changes in these tasks can significantly alter the schedule. By identifying and focusing on these tasks, project managers can effectively manage schedule changes and maintain progress. The other options, Analogous Estimating, Bottom-Up Estimating, and Product Analysis are less applicable. Analogous Estimating and Bottom-Up Estimating are primarily used in the initial planning and cost estimating stages, and less so for handling mid-project changes. Product Analysis is more related to examining the quality of project outputs and deliverables, not adjusting schedules.