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This paper presents a methodology for efficiently solving the file transfer scheduling problem in a distributed environment. Our solution is based on the relaxation of an objective-based time-indexed formulation of a linear programming problem. The main contributions of this paper are the following. First, we introduce a novel approach to the relaxation of the time-indexed formulation of the transfer scheduling problem in multi-server and multi-user environments. Our solution consists of reducing the complexity of the optimization by transforming it into an approximation problem, whose proximity to the optimal solution can be controlled depending on practical and computational needs. Second, we present a distributed deployment of our methodology, which leverages the inherent parallelism of the divide-and-conquer approach in order to speed-up the solving process. Third, we demonstrate that our methodology is able to considerably reduce the schedule length and idle time in a computationally tractable way.