This paper addresses the problem of target coverage for wireless sensor networks, where the sensing range of sensors can vary, thereby saving energy when only close targets need to be monitored. Two versions of this problem are addressed. In the first version, sensing ranges are supposed to be continuously adjustable (up to the maximum sensing range). In the second version, sensing ranges have to be chosen among a set of predefined values common to all sensors. An exact approach based on a column generation algorithm is proposed for solving these problems. The use of a genetic algorithm within the column generation scheme significantly decreases computation time, which results in an efficient exact approach.