A Pentagonal Fuzzy Ranking Approach Using Nagel Point for Uncertain Scheduling Problems

Scheduling problems are critical in manufacturing, transportation, and project management. However, the efficacy of traditional deterministic techniques is frequently limited by uncertainty and inaccurate data. To overcome such challenges, we aim to solve scheduling problems using the network methodology known as the Critical Path Method (CPM). The network’s unknown parameters are represented using pentagonal fuzzy numbers rather than crisp values. Pentagonal fuzzy numbers (PFNs) are an advanced way of encoding uncertain parameters, as the basic concept of fuzzy sets offers a solid framework for handling ambiguity. This work presents a novel approach to solving the CPM that utilizes a ranking methodology relying on the Nagel point of a triangle formed by PFN centroid points. This method enhances computational performance and offers a structured approach to managing uncertainty in project scheduling, leveraging geometric principles. The results demonstrate that the proposed method is both computationally simple and practically effective, as proven by theoretical analysis and application to project networks, providing a reliable solution to fuzzy scheduling issues.