Implementing an efficient closed-loop recovery network requires establishing appropriate logistics systems for flows of new, used, and recovered products. Reverse logistics has received increasing attention from researchers in the last few decades. This research addresses logistics network design in an integrated reverse logistics context. We present a multi-objective facility location and allocation model with multiple commodities. Three objectives are considered:​ overall cost minimization, product returns collection maximization, and product recovery maximization. The purpose is to obtain a set of nondominating solutions for facility arrangement among the potential facilities as well as the associated material flows between these facilities and customers. The facility capacities are treated as discrete parameters and are imposed on each product type independently. Numerical examples are presented to analyze the model performance while implementing the constraint method. Finally, the trade-off relationship between the three competing objectives are presented and analyzed.