This paper proposes a linear programming model to design industrial symbiosis synergies in eco-industrial parks based on the exchange of waste energy among different companies. The model allows to fill two important limitations of previous studies: (1) it uses a multi-objective optimization perspective that considers economic and environmental issues simultaneously; (2) the integration of two decision-support tools, the former able to assess the amount of waste that can be effectively exchanged among companies, the latter able to suggest how to share the infrastructural costs arising from symbiotic synergies so that the economic benefits are fairly shared among the involved companies. A numerical case example is presented to show how the model works. The case highlights several applications of the model, which contribute to confirm its usefulness for companies, industrial symbiosis facilitators, and policymakers.