© 2017 Elsevier B.V. The worth of completing parallel tasks is modeled using utility functions, which monotonically-decrease with time and represent the importance and urgency of a task. These functions define the utility earned by a task at the time of its completion. The performance of a computing system is measured as the total utility earned by all completed tasks over some interval of time (e.g., 24 h). We have designed, analyzed, and compared the performance of a set of heuristic techniques to maximize system performance when scheduling dynamically arriving parallel tasks onto a high performance computing (HPC) system that is oversubscribed and energy constrained. We consider six utility-aware heuristics and four existing heuristics for comparison. A new concept of temporary place-holders is compared with scheduling using permanent reservations. We also present a novel energy filtering technique that constrains the maximum energy-per-resource used by each task. We conducted a simulation study to evaluate the performance of these heuristics and techniques in multiple energy-constrained oversubscribed HPC environments. We conduct an experiment with a subset of the heuristics on a physical testbed system for one scheduling scenario. We demonstrate that our proposed utility-aware resource management heuristics are able to significantly outperform existing techniques.