Users and developers of grid applications have access to increasing numbers of resources. While more resources generally mean higher capabilities for an application, they also raise the issue of application scheduling scalability. First, even polynomial time scheduling heuristics may take a prohibitively long time to compute a schedule. Second, and perhaps more critical, it may not be possible to gather all the resource information needed by a scheduling algorithm in a scalable manner. Our application focus is scientific workflows, which can be represented as Directed Acyclic Graphs (DAGs). Our claim is that, in future resource-rich environments, simple scheduling algorithms may be sufficient to achieve good workflow performances. We introduce a scalable scheduling approach that uses a resource abstraction called a virtual grid (VG). Our simulations of a range of typical DAG structures and resources demonstrate that a simple greedy scheduling heuristic combined with the virtual grid abstraction is as effective and more scalable than more complex heuristic DAG scheduling algorithms on large-scale platforms.