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Grid computing is the future computing paradigm for enterprise applications. An enterprise application running on a grid is composed of a set of SLA-constrained sub-tasks demanding different types of services and resources such as processors, data storage, service providers, and network links. The paper formalizes the resource allocation problem for SLA-constrained grid applications. The paper considers a very general case in which applications are decomposed into tasks that exhibit precedence relationships. The problem consists in finding the optimal resource allocation that minimizes total cost while preserving execution time service level agreements (SLAs). The paper provides a framework for building heuristic solutions for this NP-hard problem, presents an example of such a heuristic, and provides a numerical example.