by Sotskov, Y. N.; Werner, F..

**Series:** 2014-12, Preprints

- MSC:
- 90C35 Programming involving graphs or networks

**Abstract:**

In project management, it is usually difficult to obtain the exact values of the activity durations and the assumption is more realistic that the activity duration may remain uncertain until the activity completion. We assume that lower and upper bounds on a factual activity duration are given at the stage of project planning, the probability distribution of a random duration being unknown before the activity completion. Therefore, one cannot find a priory a critical path in the given project-network G. We propose a two-step approach, where the initial project-network G is minimized in the first step and the resulting minimized project-network determines a minimal dominant set of the critical paths in the second step. A fuzzy logic procedure (or another heuristic

technique) may be used to choose a single potentially critical path from the minimal dominant set.

**Keywords:**

project management, uncertain activity, dominant paths