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The schedule baseline represents a snapshot of (usually) an approved project schedule. It is used as the basis for performance assessment and reporting. Over the life of the project, the start and end dates of individual activities might change, but the baseline should not be updated until a formal change is accepted at which time a new baseline snapshot can be taken.
The critical path represents the longest sequential path of activities from the start of your project to the end, which also defines the shortest duration in which the project could be completed.
To understand the relationship between the two, the schedule end date from your baseline is defined by the critical path.
Kiron has it right.
The schedule baseline contains all planned schedule information you want to measure your schedule progress against. Could be as simple as a list of milestones, and may or may not include a critical path.
The critical path is a result if you use the scheduling method CPM (critical path method - hic). Other scheduling methods might not have a critical path (e.g. CCM, MTA, Scrum/time boxing). The critical path itself often is just a snapshot and might change as the project progresses, just as actual durations are added to the schedule model, risks mitigations may change dependencies, or resources are shifted.
From the PMI´s Lexicon of Terms:
Critical Path. The sequence of activities that represents the longest path through a project, which determines the shortest possible duration.
Schedule Baseline. The approved version of a schedule model that can be changed using formal change control procedures and is used as the basis for comparison to actual results.
Kiron I support your comparison. The Charter defines expectation base on a time line, cost and scope which can be followed through the critical path which is establish to meet schedule baseline, and can only change if a change request is made through change control.
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