Document processing automation remains a critical challenge in enterprise environments, where traditional manual approaches are labor-intensive and error-prone. We present MADP, a multi-agent architecture that addresses the challenge of automating document processing in enterprise settings by combining deep learning-based classification and parsing with large language model extraction, while maintaining accuracy through selective human validation. Our system integrates five specialized agents--Classificator, Splitter, Parser, Extraction, and Validator--with a Human-in-the-Loop (HITL) mechanism and a novel Prompt Fine Tuning with Feedback Inheritance (PFTFI) approach. The operational analysis on a production use-case scenario of 100,000 invoices per year indicates a potential reduction of Full-Time Equivalent (FTE) requirements by approximately 70%. Production deployment on 955 real-world documents processed through January 2026 achieves a 97.0% full-pipeline automation rate, with only 3% requiring non-AI fallback. Ablation evaluation on a stratified 100-document subset (5 documents per each of 20 supplier/document-type categories) demonstrates that the full MADP configuration with Human-in-the-Loop supervision attains 98.5% document-level accuracy. Additionally, we present a comprehensive sustainability analysis showing that our hybrid AI+HITL approach reduces CO2 emissions by 69%, energy consumption by 69%, and water usage by 63% compared to traditional manual processing. Benchmark comparisons of multiple LLM backends (Granite-Docling, Mistral-Small, DeepSeek-OCR) provide practical insights for deployment in production environments.