Recharging wireless sensor nodes has recently attracted significant research attention (see e.g., [1], [2], [3]) as an alternative way to tackle the difficult problem of prolonging network’s lifetime. This is made possible due to recent technological advances in wireless battering charging, e.g. through wireless energy transfer [4], [5]). Since their early appearance almost two decades ago [6], [7], wireless sensor networks have seen an exceptional growth and recent technological advancements have permitted the creation of small and low cost devices capable of sensing a wide range of natural phenomena and wirelessly transmitting the corresponding data. Given that nodes of these networks are typically small devices supplied with tiny batteries and while being wireless, generally operate in the absence of an infrastructure, they depend on the energy supplied by their limited batteries. Therefore, even though energy consumption is of key importance in wireless networks, it becomes more intense in their sensor counterparts [8] mostly due to the energy hole problem [9]. In particular, sensor nodes also act as relays for data generated by other nodes that need to reach the sink, i.e., the particular node that is responsible to collect all sensed information. Consequently, nodes that are close to the sink have to relay a large amount of traffic load, and therefore their energy consumption is increased compared to other nodes of less intense traffic load. In this paper, the increased energy consumption, due to the energy hole problem, is tackled by the implementation of a recharging vehicle able to move within the network when a request is applied by one or more sensor nodes in need for a battery replenishment. The vehicle remains stationed at the sink node when inactive, and moves according to shortest path’s branches upon a energy request. A simple recharging policy is introduced under which a request is sent to the sink node to initiate a recharging process if the battery level of a sensor node is below a fixed recharging threshold. As it is shown in the paper, the recharging distance, i.e., the distance covered by the recharging vehicle under this recharging policy, corresponds to a facility location problem and particularly to a 1-median one [10]. This is an important contribution, since it relates battery replenishing problems in wireless networks to facility location problems.