Risk is inherent in all parts of life and brings consequences, but when it specifically emerges in supply chains, it is susceptible. Therefore, this study aims at identifying and assessing supply chain risks and developing criteria for managing these risks. Supply chain (SC) risks consist of complex, uncertain, and vague information, but risk assessment techniques in the literature have been unable to handle complexity, uncertainty, and vagueness. Therefore, this study presents a holistic approach to supply chain risk management. In this paper, neutrosophic (N) theory is merged with the analytic hierarchy process (AHP) and technique for order of preference by similarity to ideal solution (TOPSIS) to deal with complexity, uncertainty, and vagueness. Then the proposed methodology is practically implemented through a case study on the automotive industry. SC resilience, SC agility, and SC robustness were selected as criteria for managing supply chain risks and analyzed using N-AHP. Furthermore, seventeen risks were identified and assessed by using N-TOPSIS. Results suggest supply chain resilience is the most important criterion for managing supply chain risks. Moreover, supplier delivery delays, supplier quality problems, supplier communication failures, and forecasting errors are the most vulnerable risks that occur in supply chains of the automotive industry in Pakistan.