Perishable products require special handling measures that may have social and environmental impacts along with their well-known economic aspects. Therefore, the sustainability of food supply chains has gained ground; however, the sustainability of perishable food supply chains, is still not a fully explored field of study. Therefore, in this research, a multi-objective mathematical programming model is developed to optimize the cost, energy consumption, and the traffic congestion associated with such supply chain operations. In this study, product lifetime uncertainty is explicitly modeled as a Weibull random variable, and food perishability is assumed to be affected by vehicle refrigerator utilization, which is considered as a decision variable. In addition, multiple vehicle types and multiple product types are considered. A dairy supply chain case is investigated, and the interrelations and interactions of all three aspects of sustainability, also known as the three triple bottom lines (TBL) of sustainability, are studied. The results indicate that emphasizing the economic aspect, for highly perishable products, the environmental impact of the chain may increase by 120%, and for the highly congested road networks, the social impact may rise by 51%. However, a 15% economic compromise can improve the sustainability of the supply chain network design by 150%. It is also shown that road congestion and the uncertain perishability of the products are critical factors that can, although differently, affect the operation and the design of the supply chain. This study contributes to the sustainable development goals (SDG's) such as Zero Hunger (SDG 2); Affordable and Clean Energy (SDG 7); Decent Work and Economic Growth (SDG 8); Industry, Innovation, and Infrastructure (SDG 9); Responsible Consumption and Production (SDG 12); Climate Action (SDG 13) and Peace, Justice, and Strong Institutions (SDG 16). The results suggest that decision-makers can significantly reduce the environmental and social influences of the supply chain even without drastically compromising the economic aspect.