When the epidemic comes, in addition to eliminating people’s panic, quickly enacting corresponding laws and implementing corresponding policies, and isolating infected people, providing emergency supplies are of course essential. The purpose of this article is to study the robustness and sustainability of the port logistics system for outbreak emergency supplies from overseas. This paper analyzes the sustainable development capability of the port logistics system for outbreak emergency supplies from overseas and formulates response strategies and robust collaborative optimization methods. The optimized and robust system is obtained through formula derivation and analysis, which realizes the coordinated optimization of emergency logistics infrastructure positioning and emergency rescue vehicle path positioning and minimizes the economic loss caused by the outbreak. Research data show that the shortest path can be planned between each material supply location. The research results show that the proportion of demand fluctuations during the outbreak is 6.5%, the time window needs to be controlled between 0 and 600, and the robustness and sustainability of the port logistics system have saved the time of the entire process by about 45%, greatly optimizing the delivery route and delivery time. The robustness of the logistics system can be widely used in emergency events.