Wireless sensor networks consist of a large number of low-power, limited-processing capability sensors that are deployed in afield to measure physical variables or detect events like intrusion or movement. In surveillance applications, ensuring a high area coverage is an important issue requiring a certain number of sensors to be turned on to report events. In this paper, we address the problem of maximizing the sensor network lifetime under area coverage constraint. For that, we propose a scheduling mechanism that calculates, for every time slot of the network operating period, an optimal covering subset of sensors that will be activated while all other sensors will go on sleep. We model this problem as an integer linear programming (ILP) problem, that we resolve using ILOG CPLEX  and we show that the obtained solutions provide for a more balanced energy consumption when we increase a balancing exponent lambda, which increases network lifetime.