Enhancing Project Scheduling with Neutrosophic Sets: New Solution Approaches for Solving Neutrosophic CPM/PERT
Abstract
The Critical Path Method (CPM) is an important tool in project management. However, the traditional
form of CPM deals with complications associated with the ambiguity and uncertainty in estimating the
duration of activities. This paper presents two new methods to solve the Neutrosophic Critical Path
Method (Neu-CPM), utilizing Triangular Neutrosophic Numbers (TNNs) to define activity durations under
indeterminacy. The methods are designed to conduct a forward pass and backward pass simultaneously to
find the earliest and latest time for each event while at the same time to find the total float for each activity,
enabling project scheduling under uncertain conditions. Neu-CPM provides a more improved approach to
handling non-precise and incomplete data compared to the traditional fuzzy or intuitionistic approaches,
based on its inclusion of membership degrees of truth, indeterminacy, and falsity. A numerical example
is provided showing the methodology’s ability to identify the project’s critical path in a neutrosophic
environment while studying the effect of various risk elements on the critical path. The results show that
Neu-CPM provides the opportunity of more flexibility, accuracy, and reliability in project scheduling in
uncertain conditions, with useful applications to practice.