Utilizing Graph Theory for Solving CPM and PERT Problems with Java Implementation

Abstract

The Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are essential techniques in project management, commonly used to schedule tasks and optimize the overall project timeline. Both methods rely on understanding the relationships and dependencies between project activities, which can be effectively represented using directed acyclic graphs (DAGs). This paper investigates how graph theory can be applied to solve CPM and PERT problems, focusing on how graph-based techniques can help identify the critical path, calculate project duration, and optimize resource allocation. We present a Java-based implementation that models project tasks and their dependencies as a graph, leveraging algorithms to compute the critical path and perform time-based analysis. By utilizing graph traversal and shortest/longest path algorithms, this approach streamlines project scheduling, providing project managers with valuable insights for decision-making. The paper outlines the process of constructing the graph, performing CPM and PERT calculations, and discusses the advantages of applying graph theory to overcome common project management challenges. Finally, the performance of the implementation is assessed, showcasing how graph theory simplifies complex scheduling tasks and improves the accuracy of project planning.