Critical Path Analysis with Imprecise Activities Times

The aim of the paper is to present the conceptual framework related to critical path analysis with imprecise activity duration times. This article is motivated by the fact that most approaches to project planning are deterministic. In reality, the problem is accompanied by uncertainty and risk associated with dealing with imprecise data. Taking this uncertainty into account when performing analyses and calculations not only helps to better project planning, but also to expand the applicability of project scheduling methods under real-life or uncertain conditions. The major contribution of this paper is the development of a novel approach to critical path analysis in the presence of uncertainty. Extended Critical Path Method has been developed as a new method with approach based on ordered fuzzy numbers, preserving its basic concept. An example was solved by the algorithm considering imprecise activity times. Our results indicate that ordered fuzzy numbers may be used to represent imprecise information about projects. OFNs offer a clear, simultaneous representation of several pieces of information. Interpretation of OFNs can be compatible with the general idea of standard fuzzy numbers but by using OFNs we can additionally describe a trend of imprecise value of the real-life processes. Additionally, well-defined arithmetic operations on ordered fuzzy numbers make it easy to perform even complex calculations connected.