Sustainability of agro-food supply chains has recently become the subject of greater interest from consumers, firms, governmental organizations and academia as the environment continues to deteriorate. One of the most critical factors influencing the sustainability of an agro-food supply chain is its network design. A particularly challenging aspect in this context is the broad range of influencing indicators associated with the Triple Bottom Line (TBL) of sustainability that need to be considered. However, many of these indicators could not be fully integrated or measured by single-step optimization problems. This paper presents a critical literature review of operational research methods for the design of sustainable supply chains. A novel two-stage hybrid solution methodology is proposed. In the first stage, a partner selection is performed using a hybrid multi criteria decision making based on Analytic Hierarchy Process (AHP) method and the Ordered Weighted Averaging (OWA) aggregation method. The result obtained in the first stage is used in the second stage to develop a multi-objective mathematical model to optimize the design of the supply chain network. This approach allows the simultaneous consideration of all three dimensions of sustainability including carbon footprint, water footprint, number of jobs created and the total cost of the supply chain design. The proposed approach generates a Pareto frontier to aid users in making decisions. Numerical experiments are completed utilizing data from an agro-food company to demonstrate the efficiency and effectiveness of the proposed solution methodology. The analyzes of the numerical results provide important organizational, practical and policy insights on (1) the impact of financial and environmental sustainability on supply chain network design (2) the tradeoff analysis between environmental emission, water footprint, societal implications and associated cost for making informed decision on supply chain investment.