Abstract: This paper addresses the target coverage problem in wireless sensor networks with adjustable sensing range. Communication and sensing consume energy, therefore efficient power management can extend network lifetime. In this paper we consider a large number of sensors with adjustable sensing range that are randomly deployed to monitor a number of targets. Since targets are redundantly covered by multiple sensors, in order to conserve energy resources, sensors can be organized in sets, activated successively. In this paper we address the Adjustable Range Set Covers (AR-SC) problem that has as its objective finding a maximum number of set covers and the ranges associated with each sensor, such that each sensor set covers all the targets. A sensor can participate in multiple sensor sets, but the sum of the energy spent in each set is constrained by the initial energy resources. In this paper we mathematically model solutions to this problem and design heuristics that efficiently ...