Computation of Critical Path Probabilities by Modified PERT

Detection of the critical path and the uncertainty of the estimated duration are important for the contactors. PERT and Modified PERT methods can estimate the uncertainty of construction duration. However, probability of a path being critical is not estimated by the aforementioned methods. Monte Carlo simulation is implemented for the detection of probabilities of activities being critical. However, Monte Carlo simulation requires significant computational demand and this method is not suitable for iterative optimization procedure. In this study, Modified PERT method is enhanced by considering every possible path completion combinations. As a result, probability of finishing a path at a certain time and finishing the remaining paths earlier than the corresponding time is computed. This enabled the computation of probability of a path being critical path. For large networks the number of path completion combinations increases which makes the probabilistic computations burdensome. The relationship between the path completion combinations and the statistical intersection operations is derived and a macro code which executes the intersection computations is generated. The algorithm is tested on four sample problems and the results are compared with Monte Carlo simulation. Analysis results interpret that the method is significantly faster than Monte Carlo simulation with similar probability estimations.

Keywords:

PERT, Modified PERT, Monte Carlo Simulation Uncertainty analysis,

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