Surveillance systems, such as sensor networks and surveillance camera networks, have been widely deployed to monitor events in many different scenarios. One common way to conserve resource (such as energy) usage is to have only a subset of devices activated at any give time. In this paper, we look at this classic problem from a new perspective: we do not try to cover all the event areas as usually studied, but aim to find the most valuable event areas among all the event areas (i.e., the ones leading to the most utility) to monitor, subject to resource constraints. This problem poses two major challenges. First, the utility brought by monitoring an event area is not known beforehand. Second, even if this information is known in advance, solving the problem of which event areas should be monitored to maximize the total utility, subject to resource constraints, is NP-hard. We formulate this problem as a novel programming system, called online integer linear programming, and present a polynomial time algorithm to solve this problem. For any given σ∈(0, 1), we prove a bound on the gap between the expected utility obtained by constantly using the global optimal strategy multiplied by σ and the expected utility obtained by following our algorithm.