Critical Path Analysis With Fuzzy Activity Times

Fuzzy logic has been proposed as an alternate approach for quantifying uncertainty relating to project activity duration. The fuzzy logic approach may be suitable in the situations where past data are either unavailable or not relevant, the definition of the activity itself is somewhat unclear, or the notion of the activity's completion is vague. The purpose of this paper is to present a new methodology for fuzzy critical path analysis that is consistent with the extension principle of fuzzy logic. It is the direct generalization of critical path analysis to the fuzzy domains, and resolves some of the problems expressed in the fuzzy critical path literature, especially in computing the fuzzy backward pass of the project network and fuzzy activity criticality. Here the uncertainty is represented by three possible time estimates in a way that is similar to the well-known program evaluation and review technique (PERT) approach. Another important advantage of the proposed approach is that one integrated procedure determines both the fuzzy set of critical path lengths and fuzzy activity criticality. The proposed approach constructs the membership function for the fuzzy set of critical path lengths and the fuzzy activity criticality by solving a series of mathematical programming problems. The proposed method is successfully tested on well-known problem sets, and is shown to offer computation times that should allow it to help project managers better understand and manage project schedule uncertainty.