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A multi-stage software router overcomes scalability issues related to a single, PC-based, software router by introducing parallel forwarding paths. However, since the architecture includes different internal components, energy inefficiency at low loads may arise if the multi-stage internal architecture does not adapt to currently offered traffic. This paper presents an energy-saving scheme to improve energy efficiency of the multi-stage router architecture by focusing on the back-end stage and sizing it to the offered load to reduce energy needs. The problem is defined as a mixed integer linear programming model, shown to be NP-hard. We tackle the scalability issues of the optimal problem by defining a two-step heuristic which takes advantage of existing Bin Packing algorithms. Our results shows that the two-step solution is within 10% relative error with respect to the optimal solution for different realistic scenarios.