On Calculating Activity Slack in Stochastic Project Networks

Problem statement: Identifying critical tasks in a project network is easily done when task times are deterministic, but doing so under stochastic task times is problematic. The few methods that have been proposed contain serious drawbacks which lead to identifying critical tasks incorrectly, leaving project managers without the means to (1) identify and rank the most probable sources of project delays, (2) assess the magnitude of each source of schedule risk, and (3) identify which tasks represent the best opportunities for successfully addressing schedule risk? Approach: In this study we considered the problem of identifying the sources of schedule risk in a stochastic project network. We developed general expressions for determining a task’s late starting and ending time distributions. We introduced the concept of stochastic slack and develop a number of metrics that help a project manager directly identify and estimate the magnitude of sources of schedule risk. Finally, we compared critical tasks identified using the activity criticality index to those found using stochastic slack metrics. Results: We have demonstrated that a task may have non-zero probability of negative stochastic slack and that expected total slack for a task may be negative. We also found that while the activity criticality index is effective for calculating the probability that a task is on a critical path, the stochastic slack based metrics discussed in this paper are better predictors of the extent to which a delay in a task will result in a project delay. Conclusion/Recommendations: Project managers should consider using stochastic slack based metrics for assessing project risk and establishing the most likely project schedule outcomes. Given the calculation complexity associated with theoretically exact stochastic slack metrics, effective heuristics are required.