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Grid technology has been intensively developed lasting recent years, due to a need for high performance computing to process large amounts of data distributed around global networks. In addition to the improved performance obtained by parallel processing, this technology enables resources distributed among different nodes to be shared.In this study, the problem of transferring files that are generated during the execution of DAG workflows with interdependent tasks is addressed. The ineffectiveness of advanced file-transfer techniques in these cases is discussed, and a heuristic is proposed for dealing with the scheduling of interdependent and independent tasks that arrive on-line to be processes by grid infrastructure.A simulator was developed in order to simulate resources and tasks in a grid for testing the effectiveness of the new heuristic technique. The results are compared with those obtained with OLB showing that the proposed heuristic technique also leads to significant improvements in the makespan.