Supply Chain Management (SCM) involves managing and optimizing the flow of products across a network of interconnected companies while mitigating the bullwhip effect, wherein demand fluctuations amplify as they propagate upstream in the supply chain (SC). Existing studies have applied the Heterogeneous-Agent Proximal Policy Optimization (HAPPO), a multi-agent reinforcement learning (MARL) approach, to inventory management in SC. HAPPO enables centralized training with decentralized execution (CTDE), allowing agents deployed in different companies to learn collaboratively while maintaining information confidentiality, making it a promising approach for real-world applications. Building upon this decentralized execution framework, this study proposes the integration of automated negotiations among agents in SCM using HAPPO to further suppress the bullwhip effect. Through evaluation experiments, we demonstrate that our proposed method, incorporating automated negotiations, reduces the occurrence of the bullwhip effect more effectively than previous studies and exhibits robustness in scenarios different from those encountered during training.