The classical PERT approach uses the path with the largest expected du
ration as the critical path to estimate the probability of completing
a project by a given deadline. However, in general, such a path is not
the 'most critical' path and does not provide the smallest estimate f
or the probability of completion time. This paper studies the 'most cr
itical path' problem and formulates it as an optimal path problem in a
deterministic network with a two-attribute fractional objective funct
ion. An exact solution approach is presented for the optimal path prob
lem which also gives the solution to the most critical path problem. T
he illustrative examples as well as our computational results demonstr
ate that the proposed algorithm provides estimates for the probabiliti
es of completion time that are much more accurate than those of the cl
assical approach.