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The literature review shows research gaps into the food supply chain design. In that context, this paper deals with the design of a sustainable supply chain. A multi-objective mixed-integer linear programming model includes four decisions and three sustainable criteria (economic—total network costs—, environmental—carbon emissions—, and social—work conditions and societal development—). The model aims to determine the optimal location and capacity of processing and distribution facilities, to choose the suppliers from a set of potential candidates, to determine transportation modes between all the actors, and to define the quantity of product, in order to satisfy the demand of dairy products in a set of regions. The applicability of the model is tested in a realistic case in the dairy sector in the central region of Colombia. The results show the existent trade-offs between the three dimensions of sustainability. The unweighted balance results, giving more priority to the social dimension, which obtains the least deviation, affecting the environmental performance of the chain. The analysis carried out in this paper does help decision-makers that will have at hand a set of possible configurations to be chosen in order to comply with environmental and social regulations without neglecting economic performance. [ABSTRACT FROM AUTHOR]