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PERT (Program Evaluation and Review Technique)

Handles uncertainty in task durations by using three time estimates: Optimistic (O), Most Likely (M), and Pessimistic (P).

Time: O(V + E)
Space: O(V)
Use Case: Estimating project completion time when individual task durations are uncertain.

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About PERT (Program Evaluation and Review Technique)

The Program Evaluation and Review Technique (PERT) extends critical path analysis to uncertain activity durations. Each activity gets three time estimates, optimistic, most likely, and pessimistic, from which expected durations and project completion probabilities are derived.

How it works

Each activity's expected duration is computed with the beta distribution formula (optimistic + 4 times most likely + pessimistic) / 6, with variance ((pessimistic - optimistic) / 6) squared. The network is then analyzed like CPM using expected durations, and the variances along the critical path sum to give the project variance. A normal approximation converts this into the probability of finishing by any target date.

Applications

PERT was created for the US Navy Polaris missile program in 1958 and is used wherever schedules face uncertainty: research and development, defense contracting, new product launches, and large IT migrations. It teaches how probability layers onto graph-based planning models.

Read the full article: Operations Research and Graph Theory

Related algorithms: Critical Path Method (CPM), RCPSP (Resource-Constrained Project Scheduling), Topological Sort

Interactive Controls
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Nodes: 4
Edges: 4