Supply chain management remains a strategic research area, particularly regarding sustainability and risk mitigation. This paper introduces a new multi-objective mathematical model designed to enhance supply chain resilience during pandemic conditions. The model structures the supply chain into three echelons: suppliers, a distribution center, and customers. It addresses key disruptions, such as increased demand and the closure of supply nodes, while integrating respect for the environment and maximizing levels of customer service. The proposed mathematical formulation relies on an Integer Linear Programming (ILP) framework with three main objectives: minimizing transportation and production costs, reducing CO2 emissions, and shortening supplier lead times. To strengthen resilience, the model incorporates specific constraints that prioritize the satisfaction of customer demand during crises, even under limited supply capacity. This work highlights how combining sustainability and risk management objectives can lead to more robust supply chain performance during global disruptions such as pandemics.