This paper studies autonomous generative AI agents in multi-echelon supply chains using the MIT Beer Game. We identify four inference-time levers that shape performance: model selection, policies and guardrails, centralized data sharing, and prompt engineering. Model capability is the dominant factor: an out-of-the-box reasoning model exceeds human-level performance, and optimized reasoning models reduce costs by up to 67% relative to human teams. However, strong average performance masks substantial reliability risks. We introduce agent bullwhip: the amplification of run-to-run decision instability in autonomous multi-echelon systems. A central component is decision bullwhip, the portion of order variability generated by stochastic agent decisions rather than by changes in customer demand. We show that decision instability can amplify both across facilities at a fixed point in time and within the same facility over time, even when the demand path is held fixed. Repeated sampling, a natural test-time remedy, fails to meaningfully reduce this instability, suggesting that reliability requires changing the underlying decision policy rather than merely averaging over model outputs. To address this limitation, we propose a Group Relative Policy Optimization (GRPO)-based reinforcement-learning post-training framework that trains a shared base LLM using system-level supply-chain rewards. Post-training substantially reduces tail events, curtails agent bullwhip, and improves the reliability of autonomous supply-chain agents.