A growing plastic production increases the pressure on waste management systems, which have to cope with greater volumes of plastic waste. Increased plastics recycling can reduce environmental impacts by lowering the need for primary plastics production and thus fossil resources demand. Current research is mainly focused on identifying environmentally friendly recycling technologies for different waste streams. However, recycling capacities must also be expanded to handle the waste generated. Therefore, this paper develops multiple exemplary multi-criteria optimization models to design an optimal recycling network. The models are deployed in a case study for plastic packaging waste in Europe for an advanced mechanical recycling process. We compare the different multi-criteria optimization approaches, how they balance environmental and economic aspects differently, and how this affects the recycling network design. Finally, we compare the optimization approaches and find goal programming the most promising approach for recycling network design that ensures a balance between economic and environmental objectives.