Manuscript Number : IJSRSET24118029

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

Authors(2) :-Meenakshi Kumari, Dr. Gopal Prasad Singh

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.

Authors and Affiliations

Meenakshi Kumari
Research Scholar, Department of Computer Science & I.T., Magadh University, Bodh-Gaya, India
Dr. Gopal Prasad Singh
Department of Mathematics, Gaya College, Gaya, India

Critical Path Method, Directed Acyclic Graphs, PERT

  1. Pritsker, A. A. B., & O'Connor, R. (1966). Project Management with CPM and PERT. University of Pennsylvania Press.
  2. Lock, D. (2013). Project Management: A Systems Approach to Planning, Scheduling, and Controlling (10th ed.). John Wiley & Sons.
  3. Meyer, G. (2019). Graph-Based Optimization Algorithms for Project Scheduling. International Journal of Project Management, 37(5), 674-689.
  4. Nishihara, M., Aoyama, H., & Ogawa, Y. (2006). Application of Graph Algorithms to PERT and CPM Scheduling Problems. Journal of Computational and Applied Mathematics, 199(1), 204-215.
  5. Bovens, D., Van der Meer, J., & Garofalo, D. (2012). Graph Theory and Project Scheduling: A Java-Based Implementation. Proceedings of the International Conference on Software Engineering and Applications, 39-46.
  6. Chang, K., & Chen, W. (2017). Optimizing Resource Allocation in Project Scheduling Using Graph Theory. Computers & Operations Research, 83, 112-123.
  7. Meyer, L., & Johnson, C. (2018). Graph-Theoretic Approaches in Project Scheduling: A Comparative Analysis. Project Management Journal, 49(2), 5-16.
  8. Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice-Hall.
  9. Bovens, D., & Garofalo, D. (2013). Java-Based Scheduling Systems for Project Management. International Journal of Computer Science & Information Technology, 5(3), 76-85.
  10. Sethi, R., & Gupta, A. (2011). Graph Algorithms for Project Scheduling: Implementation and Case Study. Journal of Operations Management, 29(1-2), 12-23.

Publication Details

Published in : Volume 11 | Issue 8 | May-June 2024
Date of Publication : 2024-05-25
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 226-229
Manuscript Number : IJSRSET24118029
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

Meenakshi Kumari, Dr. Gopal Prasad Singh, " Utilizing Graph Theory for Solving CPM and PERT Problems with Java Implementation, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 11, Issue 8, pp.226-229, May-June-2024. Journal URL : https://res.ijsrset.com/IJSRSET24118029

Article Preview