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Cellular network technologies have traditionally evolved to meet the ever-increasing need for capacity and coverage. Particularly, there has been a significant focus on exploiting the use of small cells and heterogeneous networks (HetNets). In the latter, the economic and environmental impact of the energy consumption is a key concern. Although much research has been done to address the energy consumption in HetNets, existing approaches have failed to capture the key factors affecting it. In this paper, the energy consumption in HetNets is analyzed with a focus on their multi-layer nature and the dependence of the energy consumption on the spatio-temporal traffic demands and the internal base station hardware components. The problem of minimizing the energy consumption is then studied and characterized in terms of a 0-1 Knapsack-like problem. Due to the differences with the classical 0-1 Knapsack …