Recent literature on sustainable logistics networks points to two important questions: (i) How to spot the preferred solution(s) balancing environmental and business concerns? (ii) How to improve the understanding of the trade-offs between these two dimensions? We posit that a visual exploration of the efficient frontier and trade-offs between profitability and environmental impacts are particularly suitable to answer these two questions. The visual representation of the efficient frontier, however, presents two challenges. The first is to obtain a good approximation for such frontier without enumerating all extreme efficient solutions. The second is to obtain a good visual representation of the efficient frontier. We propose a two-phased heuristic to handle these two problems. The algorithm is designed for the multi-objective linear problem with three objectives: minimize costs, cumulative energy demand and waste in a reverse logistics network. We illustrate our approach by designing a complex recycling logistics network in Germany.