This study addresses the Weighted Multi-Skill Resource Constrained Project Scheduling Problem (W-MSRCSPSP) with the aim of minimizing software project makespan. Unlike previous works, our investigation regards heterogeneous resources characterized by varying skill proficiency levels. Another major problem with existing methodologies is the potential underutilization of human resources due to varying task durations. This work introduces an innovative scheduling approach known as the Greedy and Parallel Scheduling (GPS) algorithm to handle the said issues. GPS focuses on assigning the most suitable resources available to project activities at each scheduling point. The fundamental goal of our proposed approach is to reduce resource wastage while efficiently allocating surplus resources, if any, to project tasks, ultimately leading to a decrease in the makespan. To empirically evaluate the efficacy of the GPS algorithm, we conduct a comparative analysis against the Parallel Scheduling Scheme (PSS). The advantage of our proposed approach lies in its ability to optimize the utilization of available resources, resulting in accelerated project completion. Results from extensive simulations substantiate this claim, demonstrating that the GPS scheme outperforms the PSS approach in minimizing project duration.