This paper discusses effective ways to manage risks in supply chains, which can have critical impacts on businesses. Supply chain risks come from different sources such as control, process, demand, and supply, and need to be identified, assessed, and mitigated quickly to make rational decisions. However, most existing risk assessment mechanisms cannot handle the complexity, uncertainty, and incomplete information of supply chain risks in real-time. To address this, we introduce NeutroMAS4SCRM, a framework that incorporates real-time Multi-Agent Systems with Neutrosophic Data Analytic Hierarchy Processes. The proposed framework can help decision-makers adopt less risky decisions by dealing with the complexity, uncertainty, and vagueness of supply chain risk management issues. We also show how our proposed framework can be used to efficiently manage risks through a simulation-based decision support system.