This paper addresses the problem of maximizing network lifetime in a special class of wireless sensor networks composed by devices able to adjust the sensing range and, consequently, the energy consumption rate.Wireless sensor networks used to monitor targets located at discrete fixed positions and transmit the information collected via multi-hop communication to a single base station are considered.To address the problem, it is proposed a large scale linear programming model defined over an exponential number of variables.To avoid enumerate all columns, it is adopted a column generation approach that divides the problem into two.First, a Pricing Subproblem which is used to determine the sensing range adopted for each sensor at a given configuration so as to determine their energy consumption rates and to contribute to extend network lifetime.Second, a Master Problem used to identify the time interval during which a given set of configurations of the network should be used aiming at maximizing network lifetime.To solve the pricing subproblem it is proposed a new IP model which is efficiently solved through a Branch & Cut approach.The proposed approach is tested over a large set of experiments carried out for instances with up to 300 sensors and 180 targets.Preliminary results confirm the efficacy of the proposed approach and highlight several opportunities to extend current work to networks with similar characteristics.