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PERT (Program Evaluation and Review Technique) is a technique for estimating that applies an average of optimistic, pessimistic and most likely estimates when there is uncertainty with the individual activity estimates. CPM (Critical Path Method) is a method used to estimate the minimum project duration and determine the amount of scheduling flexibility on the logical network paths within the schedule model.
CPM and PERT are both used in Project Management.
CPM is usually used in construction project that could be repetative some times, whereas the PERT technic is mostly used in R&D projects that are mostly non repetative.
PERT is Probabilistic model while CPM is Deterministic and depends mainly on well defined and recognizable tasks/activities.
In CPM time is estimated using a single estimate while in PERT 3 time estimates are used ( optimistic, most probable and pessimistic).
So generally CPM is used when the project has predictable activities(such as construction projects) while PERT is used on projects with upredictable activities (such as R&D projects).