According to the PMBOK® Guide, both the Critical Path Method (CPM) and the Critical Chain Method (CCM) are used to develop the project schedule, but they differ fundamentally in how they handle project constraints.

Critical Path Method (CPM): This technique calculates the theoretical shortest duration of the project based on logical dependencies (sequences) between activities. It assumes that resources are available when needed. The critical path is the longest sequence of activities in a network diagram and determines the shortest possible project duration.

Critical Chain Method (CCM): This is a schedule network analysis technique that modifies the project schedule to account for limited resources. It recognizes that a schedule is not just a sequence of tasks but also a sequence of resource assignments.

The Key Difference: While the critical path focuses only on task order (logic), the critical chain considers both logical dependencies and resource availability. If a resource is required by two tasks simultaneously, the critical chain will adjust the schedule to resolve the conflict, often changing the " path " of the project.

Buffers vs. Float: The critical path uses Total Float (slack) to manage flexibility. The critical chain uses Buffers (Project Buffers and Feeding Buffers) placed at strategic points to protect the project completion date from uncertainty and resource fluctuations.

Comparison with other options:

A. Scope changes: Both methods are affected by scope changes, but scope is not the distinguishing factor between the two mathematical models.

C. Risk analysis: While the Critical Chain Method is often considered a more " risk-aware " approach due to its use of buffers, the primary mechanical difference between the two is the inclusion of resource limitations.

D. Quality audits: This is a tool used in Manage Quality to ensure processes are being followed. It has no direct impact on the calculation of the critical path or critical chain.