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An optimization model is developed for assigning a fixed set of files across an assemblage of storage devices so as to maximize system throughput. Multiple levels of executable memories and distinct record sizes for separate files are allowed. Through the use of this model, a general class of file assignment problems is reduced to the optimization of a convex function over a convex feasible region. A high-speed search procedure specifically tailored to solve this optimization problem is then presented, along with numerical examples from real systems which demonstrate orders of magnitude improvement in execution time over existing routines for solving the file-assignment problem. The optimal device capacity selection problem is then solved by simply calling the file assignment routine for each candidate set of device capacities.