An uncertainty importance measure of activities in PERT networks

Abstract

In a PERT network, the importance of each activity needs to be assessed in order to identify those that warrant more attention from the project management. For this purpose, two measures are frequently used: criticality index; and uncertainty importance measure. While the former is used to identify which activity's expected duration to decrease in order to decrease the expected project completion time, the latter can be used to identify those that deserve more attention in reducing the magnitude of the uncertainty (variability) in the project completion time (T). This paper defines an uncertainty-importance measure of an activity, or of a pair of activities, and develops a method for evaluating the defined measure under the assumption that the durations of activities are independently and symmetrically distributed. The method utilizes Taguchi tolerance design technique with modifications. First, PERT networks are classified into two types: Type A with a dominantly longer path than the others, and Type B without such a path. For a Type A network, T can be closely approximated by the sum of the duration of activities on the dominantly longer path, and the contribution of the uncertainty in each activity duration to the uncertainty in T can be analytically determined with ease. For a Type B network. however, such an analytic approach is not feasible. In addition, activity durations may have curvature and interaction effects on T. We therefore employ an appropriate experimental strategy for Type B networks, and calculate the so called contribution ratios which evaluate the main and/or interaction effects of activity durations on the variability of T. Contribution ratios are used to estimate the defined uncertainty importance measure of an activity or of a pair of activities. The proposed method is easy to use and, in particular, computationally efficient for large-sized PERT networks as compared to other existing methods which require Monte Carlo simulation.