This paper investigates the problem of scheduling parallel I/O operations on systems that provide data replication. The objective is to direct each compute node to access data from an I/O node where the data is duplicated, in such a way that requests for data are evenly distributed among I/O nodes. We identify a necessary and sufficient condition on whether the current data request pattern can be improved, in terms of the maximum number of data requests on any I/O node. We propose an augmenting path algorithm that examines this necessary and sufficient condition, and adjusts the current data request pattern accordingly. Using network flow technique, we show that the augmenting path algorithm finds an optimal assignment in O(nm\log n + n^2 \log ^{\frac{3} {2}} n) time.