International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3548 2020 2020 VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India Ranjan Ranjan VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India Ranjan Kumar Over the past few decades, the traditional critical path method and its various generalizations have become the most popular technique for managing complex projects. It plays a crucial role in differentiating between critical and non-critical tasks to enhance project schedules. For the first time in the literature, our proposed model implements two algorithms for the study of the critical path method, each addressing an advanced framework in the form of a single-valued triangular neutrosophic. The proposed algorithm 1 utilizes Python to extended Dijkstra’s algorithm under the neutrosophic framework, while the proposed algorithm 2 employs linear programming for optimality checks, which is solved using LINGO. Our comparison with previous research on the critical path method shows that the proposed algorithms are better at dealing with uncertainty, making project schedules more reliable and flexible. The findings lead to the proposed algorithm framework, combined with Python and LINGO, to enhance decision-making and improve the accuracy and efficiency of critical path identification in complex project environments. 2025 2025 357 370 10.54216/IJNS.250430 https://www.americaspg.com/articleinfo/21/show/3548