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In this paper, we present algorithms for Grid resource provisioning that employ agreement-based resource management. These algorithms allow userlevel resource allocation and scheduling of applications that are structured as a precedenceconstrained set of tasks. We present a provisioning model where the resource availability in the Grid can be enumerated as a set of slots. A slot is defined as a number of processors available from a certain start time for a certain duration at a certain cost. Using a cost model that combines the cost of resource allocation and the expected application runtime, we evaluate the performance of the Min-Min and of the Genetic algorithm (GA)-based heuristics for a range of synthetic applications. We show that the GA paired with a list scheduling algorithm can obtain significantly better solutions than the Min-Min heuristic alone.