Abstract
The critical path method is one of the oldest and most important techniques used for planning and scheduling projects. The main objective of project management science is to determine the critical path through a network representation of projects. The critical path through a network can be determined by many algorithms and is useful for managing, monitoring, and controlling the time and cost of an entire project. The essential problem in this case is that activity durations are uncertain; time presents considerable uncertainty because the time of an activity is not always easily or accurately estimated. This issue increases the need to use neutrosophic theory to solve the critical path problem. Real-world problems are characterized by a lack of precision, consistency, and completeness. The concept of neutrosophic sets has been introduced as a generalization of fuzzy, intuitionistic fuzzy, and crisp sets to overcome the ambiguity surrounding real-world problems. Truth-, falsity-, and indeterminacy-membership functions are used to express neutrosophic elements. This study was performed to examine a neutrosophic event-oriented algorithm for determining the critical path in activity-on-arc networks. The activity time estimates are presented as trapezoidal neutrosophic numbers, and score and accuracy functions are used to obtain a crisp model of the problem. An appropriate numerical example is then used to explain the proposed method.
Highlights
A project is a venture to accomplish a set of interrelated jobs; when these jobs are accomplished, the project is considered completed
Care is required when deciding the type of representation to use for various activities in the project network and activity durations, as we shall see how uncertain activity times or random activity durations can be accommodated in the project scheduling framework using the neutrosophic critical path method (CPM) methodology
Neutrosophic theory is used to estimate the times of activities in a project assuming various estimates based on expert opinion; these times are expressed as trapezoidal neutrosophic numbers
Summary
A project is a venture to accomplish a set of interrelated jobs; when these jobs are accomplished, the project is considered completed. Each job requires specific amounts of time and resources, which are governed by specific relations. A project is a unique set of activities meant to produce a defined outcome within an established time frame using specific allocations of resources. The study and understanding of projects involve three axes, namely, the project objectives, the project constituents, and the basic composition of the related jobs or activities, which are important because they consume time and resources and are responsible for project completion.
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