Schedulers in radio frequency identification dense environments aim at distributing optimally a set of t slots between a group of m readers. In single-channel environments, the readers within mutual interference range must transmit at different times; otherwise, interferences prevent identification of the tags. The goal is to maximize the expected number of tags successfully identified within the t slots. This problem may be formulated as a mixed integer non-linear mathematical program, which may effectively exploit available knowledge about the number of competing tags in the reading zone of each reader. In this paper, we present this optimization problem and analyze the impact of tag estimation in the performance achieved by the scheduler. The results demonstrate that optimal solutions outperform a reference scheduler based on dividing the available slots proportionally to the number of tags in each reader. In addition, depending on the scenario load, the results reveal that there exist an optimum number of readers for the topology considered, since the total average number of identifications depend non-linearly on the load. Finally, we study the effect of imperfect tag population knowledge on the performance achieved by the readers.