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Grids are emerging as a promising solution for resource and computation demanding applications. However, the heterogeneity of resources in Grid computing, complicates resource management and scheduling of applications. In addition, the commercialization of the Grid requires policies that can take into account user requirements, and budget considerations in particular. This paper considers a basic model for workflow applications modelled as Directed Acyclic Graphs (DAGs) and investigates heuristics that allow to schedule the nodes of the DAG (or tasks of a workflow) onto resources in a way that satisfies a budget constraint and is still optimized for overall time. Two different approaches are implemented, evaluated and presented using four different types of basic DAGs.