Large language models and AI agents have ignited a surge of expectations for supply chain automation, yet the path from impressive pilots to enterprise value is often blocked by "Data Gravity." While the hype suggests total replacement of human roles, we can rather expect that ROI is found in the disciplined integration of Large Language Models (LLMs) into complex, structured data environments (ERP/BI). This paper bridges the gap between promise and practice by outlining critical pillars for SCM leaders: · Reliable Architectures: Moving beyond conversational interfaces to grounded systems. We explore how to anchor LLMs in deterministic data access and Retrieval-Augmented Generation (RAG) to ensure "process truth." · Use cases and best practices for implementing AI agents. These will allow you to embed your initiatives into the strategic context of your company. Beyond reaching break-even with your solutions, you can thus set priorities about data quality and integration. · The Strategic Evolution (LPM): We introduce the concept of Large Process Models (LPMs) - an emerging framework that combines LLMs with process mining and knowledge graphs to orchestrate end-to-end supply chain intelligence. · Governance as an Enabler: Shifting the view of governance from a constraint to a control layer that ensures auditability, security, and human-in-the-loop accountability. Small percentage improvements in inventory, transportation, and planning accuracy translate into millions in financial impact. This document provides a pragmatic guide for IT strategies, helping managers transition from siloed "MVP-ing" to scalable, agentic SCM solutions.