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This paper addresses a two-stage stochastic model for eco-efficient reverse logistics network design (RLND). The goal of this optimization model is to maximize the expected profit and minimize landfilling activities to give more incentive for materials recycling. The model considers a source separation option that allows the separation of the collected materials at an early stage of the reverse logistics channel. The quantity of waste generated and the recycling rates at the collection centers are uncertain due to the variable quality of the collected batches. We solved the model using the combination of a Sampling Average Approximation procedure and the ε-constraint method. An application is illustrated through the case study of wood waste recycling from the construction, renovation, and demolition (CRD) industry in the province of Quebec in Canada. This research reveals that the source separation strategy provides better control of the impact of uncertainties, not only for the economic performance but also from an environmental perspective. The results highlight the necessity to evaluate the interaction between environmental policies to avoid conflicting objectives. Finally, the case study demonstrates the complexity of the reverse logistics network in the CRD industry and the challenge to achieve eco-efficiency under uncertainty. • A multi-objective stochastic model for reverse logistics network design is proposed. • The impact of the uncertain quality of the recycled materials is highlighted. • The proposed model evaluates the benefits of the recycled materials source-separation. • GHG emissions accounting is performed to comply with environmental regulations. • A case study targeting the recycled wood from the CRD* industry is proposed in Canada. [ABSTRACT FROM AUTHOR]