In this paper, we consider the Parallel Machine Scheduling Problem with Additional Unit Resources, which consists in scheduling a set of n jobs on m parallel unrelated machines and subject to exactly one of r unit resources. This problem arises from the download of acquisitions from satellites to ground stations. We first introduce two baseline constraint models for this problem. Then, we build on an approximation algorithm for this problem, and we discuss about the efficiency of designing an improved constraint model based on these approximation results. In particular, we introduce new constraints that restrict search to executions of the approximation algorithm. Finally, we report experimental data demonstrating that this model significantly outperforms the two reference models.