This document proposes a scheduling algorithm for allocating resources in cloud computing based on the Project Evaluation and Review Technique (PERT). It aims to address issues like starvation of lower priority tasks. The algorithm models task allocation as a directed acyclic graph and uses PERT to schedule critical and non-critical tasks, prioritizing higher priority tasks. The algorithm is evaluated against other scheduling methods and shows improvements in reducing completion time and optimizing resource allocation for all tasks.