PERT

Also known as: Program Evaluation Review Technique

framework · engineering · formal-scientific

Probabilistic project scheduling technique using three-point estimates to model activity duration uncertainty.

Program Evaluation and Review Technique (PERT) is the stochastic network-based project-scheduling technique developed 1957-1958 for the US Navy's Polaris fleet ballistic missile program by the Special Projects Office (Admiral William F. Raborn's program), with consulting support from Booz Allen Hamilton (D.G. Malcolm, J.H. Roseboom) and Lockheed Missile Systems Division. The technique was developed in parallel with CPM but differs in its treatment of activity duration uncertainty: PERT uses three-point estimates (optimistic O, most likely M, pessimistic P) to compute expected duration ((O + 4M + P) / 6) and variance ((P - O)/6)² for each activity, then estimates project completion-time distribution assuming activity durations follow a Beta distribution and the central limit theorem applies to the path-sum of activities. The Polaris program was completed substantially ahead of schedule, with PERT credited as contributing factor — though subsequent analysis (Sapolsky's 1972 The Polaris System Development) substantially questioned the magnitude of PERT's actual contribution. PERT and CPM converged in subsequent project-management practice as PERT/CPM.

Originators

US Navy Special Projects Office (Admiral William F. Raborn's organization, foundational organizational sponsor); Booz Allen Hamilton consultants D.G. Malcolm, J.H. Roseboom, C.E. Clark, W. Fazar (foundational technical co-authors); Lockheed Missile Systems Division (operational implementation partner); intellectual antecedents in operations research (1940s-50s), stochastic-process theory, parallel CPM development at DuPont; parallel development with CPM produced subsequent PERT/CPM convergence high

Year / Decade

1957-1958 (foundational development for Polaris program); 1959 (first publication: Malcolm et al. Operations Research) high

Primary sources

Malcolm, D.G., Roseboom, J.H., Clark, C.E. & Fazar, W. (1959). 'Application of a Technique for Research and Development Program Evaluation', Operations Research, Moder, J.J. & Phillips, C.R. (1964). Project Management with CPM and PERT, Sapolsky, H.M. (1972). The Polaris System Development (critical-historical reassessment of PERT's program contribution), Schonberger, R.J. (1981). 'Why Projects Are Always Late: A Rationale Based on Manual Simulation of a PERT/CPM Network', Interfaces high

Core components

Three-point activity duration estimates: optimistic (O), most likely (M), pessimistic (P)
Expected duration: t_e = (O + 4M + P) / 6 (weighted average approximating Beta-distribution mean)
Activity variance: ((P - O) / 6)²
Network of activities with precedence relationships (activity-on-arrow original PERT
activity-on-node common modern usage)
Forward-pass and backward-pass computation paralleling CPM, using expected durations
Critical path: longest expected-duration path through the network
Project completion-time mean: sum of expected durations on the critical path
Project completion-time variance: sum of activity variances on the critical path (assuming central limit theorem and independence)
Probability calculations: probability of completing project by specific date computed using normal approximation to the completion-time distribution
Beta-distribution assumption for activity durations (retained as theoretical foundation despite known weakness of the assumption)
PERT/Cost extension: integration with cost performance for earned-value-style analysis

Primary use case

Foundational scheduling technique for projects with substantial activity-duration uncertainty; research and development project scheduling (NASA programs, Department of Defense weapons systems development); engineering and construction projects with novel activities lacking historical duration data; academic and professional reference in project management, operations research, and industrial engineering; intellectual antecedent for modern probabilistic scheduling using Monte Carlo simulation, which substantially extends and generalizes PERT's stochastic approach without the Beta-distribution assumption; input to PMBOK and broader project-management methodology in three-point-estimating and project-risk-analysis techniques.

Common criticisms

PERT's specific assumptions have been substantially critiqued — the Beta-distribution assumption for activity durations is mathematically convenient but empirically weak, with actual activity-duration distributions often skewed and heavy-tailed in ways the Beta does not capture
the t_e = (O + 4M + P) / 6 weighted-average formula is an approximation that does not exactly produce the Beta-distribution mean and was criticized by Donald Coleman and others as introducing systematic bias
PERT's central-limit-theorem assumption — that path-sum durations approach normal distribution — fails when paths are short or when path-duration distributions are highly skewed
the assumption that activity durations are independent is empirically weak — actual project activities often have correlated durations through shared resources, weather, supplier issues, learning effects
PERT's computation of project-completion variance using only the critical-path activities ignores near-critical paths that may become critical due to schedule realization, producing systematic underestimation of schedule risk (the 'merge bias' problem documented by Schonberger and others)
the specific historical claim that PERT substantially accelerated the Polaris program has been challenged by Harvey Sapolsky's substantial 1972 study showing PERT was implemented after the program was already on accelerated trajectory and may have served more public-relations than substantive-management function
modern probabilistic scheduling using Monte Carlo simulation directly samples activity durations from arbitrary distributions, computing project-completion distributions without PERT's restrictive assumptions, and has substantially superseded PERT in rigorous schedule-risk analysis while PERT remains pedagogically prominent.

Lineage

Siblings: Critical Path Method, Gantt Chart Methodology, Monte Carlo Methods