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Efficient transfer of bulk data requires routing that minimizes the net transfer time instead of providing flow level bandwidth guarantees. In this work, we consider a realistic scenario where available bandwidth for each link in a given network is time varying. In such a network and for a given file size, we provide an optimal algorithm that minimizes the total time required to transfer the file from source to destination. We further consider the problem where path shifting is allowed to increase the net throughput for bulk data transfer. For this problem, we provide a dynamic programming based optimal algorithm that minimizes the number of path shifts required to transfer the file in the specified time. Solution to the above problems addresses both the performance and scalability issues that arise in large bulk data transfer for long duration of time.