Near-Critical PathsA project’s dura

Near-Critical PathsA project’s duration is a function of its critical path. However, paths that are close to the same duration as the critical path may ultimately become the critical path over the life of the project. In practice, at the start of the project, managers typically do not know the activity times with certainty and may never know which path was the critical path until the actual activity times are known at the end of the project. Nonetheless, this uncertainty does not reduce the usefulness of identifying the probability of one path or another causing a project to exceed its target completion time; it helps to identify the activities that need close management attention. To assess the chances of near-critical paths delaying the project completion, we can focus on the longest paths in the project network keeping in mind that both duration and variance along the path must be considered. Shorter paths with high variances could have just as much a chance to delay the project as longer paths with smaller variances. We can then estimate the probability that a given path will exceed the project target completion time. We demonstrate that approach using statistical analysis in Example 7.5, part (b).Alternatively, simulation can be used to estimate the probabilities. The advantage of simulation is that you are not restricted to the use of the beta distribution for activity times. Also, activity or path dependencies, such as decision points that could involve different groups of activities to be undertaken, can be incorporated in a simulation model much more easily than with the statistical analysis approach. Fortunately, regardless of the approach used, it is rarely necessary to evaluate every path in the network. In large networks, many paths will have both short durations and low variances, making them unlikely to affect the project duration.