Computation of Critical Path Probabilities by Modified PERT

Detection of the critical path and the uncertainty of the estimated duration are important for thecontactors. PERT and Modified PERT methods can estimate the uncertainty of constructionduration. However, probability of a path being critical is not estimated by the aforementionedmethods. Monte Carlo simulation is implemented for the detection of probabilities of activitiesbeing critical. However, Monte Carlo simulation requires significant computational demandand this method is not suitable for iterative optimization procedure. In this study, ModifiedPERT method is enhanced by considering every possible path completion combinations. As aresult, probability of finishing a path at a certain time and finishing the remaining paths earlierthan the corresponding time is computed. This enabled the computation of probability of a pathbeing critical path. For large networks the number of path completion combinations increaseswhich makes the probabilistic computations burdensome. The relationship between the pathcompletion combinations and the statistical intersection operations is derived and a macro codewhich executes the intersection computations is generated. The algorithm is tested on foursample problems and the results are compared with Monte Carlo simulation. Analysis resultsinterpret that the method is significantly faster than Monte Carlo simulation with similarprobability estimations.

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