On the latest starting times and criticality of activities in a network with imprecise durations

This paper deals with problems of computing possible values of latest starting times and determining types of criticality for all activities in a network with interval or fuzzy activity durations. Although the problem of computing the latest starting times has been solved, a novel polynomial algorithm which is easy to understand and improves complexity is proposed. In networks with interval activity durations, instead of being critical or not, three sets of critical activities exist: an activity will be either necessarily noncritical, or necessarily critical, or possibly critical. Results of determining bounds of latest starting times are used to develop lemmas that establish the possible criticality of an activity in special cases in spite of the fact that ascertaining an activity is possibly critical is NP-complete. After providing the lemmas, the idea of partitioning is used to develop an algorithm for determining these three sets. The proposed algorithms have been tested on general real world project networks and experimental results are reported. Then results obtained for networks with interval durations are extended to networks with fuzzy durations.