This research presents a Mixed-Integer Linear Programming (MILP) model for project scheduling with parallel machines, incorporating sequence-dependent setup times and dual resource constraints. The model aims to minimize delays and optimize resource utilization. Due to computational limitations, a Genetic Algorithm (GA)-based framework was developed, which outperformed the Branch-and-Cut algorithm in terms of efficiency and solution quality. The GA achieved a near-optimal makespan of 1785 minutes, while the BC algorithm required 69 hours to converge to a suboptimal solution. This research contributes to the advancement of heuristic optimization techniques for complex scheduling environments, offering insights for industries seeking efficient solutions for production planning and resource management.