Multi-tiered persistent storage provides a logical view where all available storage is distributed over a number of levels of different speeds and capacities. Efficient scheduling of parallel data transfers in multi-tiered persistent storage is a significant problem for pipelined data processing. This work considers a class of database applications implemented as sequences of operations that transfer data between persistent storage tiers. We show how to partition the sets of data transfers to reduce the number of conflicts when data transfers are performed in parallel. The paper proposes the new rule-based algorithms for allocating parallel data transfer to the processors to minimize total processing time. The new algorithms evenly distribute the workload among the processors and reduce their idle times. We describe a number of experiments that validate the efficiency of parallel data transfer plans generated by the algorithms presented in the paper.