Automated Log Rotation and Compression Pipeline

Design a comprehensive Bash script that implements an advanced log management system for multiple application logs. The script should dynamically rotate logs daily, compress older logs using optimal compression algorithms, implement retention policies (keep last 30 days), and generate a detailed compression report. Include error handling for disk space monitoring, with automatic alerts if log directories exceed 80% capacity. Ensure the script is idempotent and can be safely run via cron without duplicate actions.