The most critical path in a PERT network: A heuristic approach

The classical PERT approach uses a deterministic critical path to estimate the probability of completing a project by a given deadline. In general, such a path is not the ‘most critical’ path and does not provide the lowest probability of completion time. This paper studies the ‘most critical path’ problem and formulates it as an optimal path problem through a deterministic network with a two-attribute fractional objective function. A heuristic approach is developed for the optimal path problem which gives a solution to the most critical path problem. The illustrative examples and computational results demonstrate that the proposed procedure provides critical activities and estimates for the probabilities of completion time that are more accurate than those resulting from the classical PERT approach. Further, our computational experiments show that the proposed heuristic performs well in identifying the most critical paths.