Evaluate the impact of implementing advanced project management methodologies on the overall efficiency and cost$-$effectiveness of large$-$scale civil engineering operations. Specifically, consider how integrating tools like Building Information Modeling $($BIM$),$ Lean Construction, and Critical Path Method $($CPM$)$ can influence the planning, execution, and monitoring phases of a project. Discuss the potential benefits and challenges associated with these methodologies, such as improved coordination among stakeholders, reduction in project delays and cost overruns, and enhanced quality control. Additionally, examine how the adoption of these technologies might necessitate changes in workforce training and management practices. Address the role of data analytics and real$-$time monitoring in optimizing resource allocation and decision$-$making processes. Finally, assess how these methodologies could contribute to achieving sustainability goals in civil engineering projects, and explore the potential long$-$term economic and environmental impacts of their widespread implementation.