Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application

This paper describes how the recent, published DEA/AR theory, in conjunction with software, provides measures of radial efficiency and profit ratios, This new DEA theory does not require use of the non-Archimedean principle, i.e., positive infinitesimals, and it allows for analysis of zero data entries. Further, this theory provides a comprehensive classification of the measures for both the efficient and inefficient decision-making units (DMUs). As programmed in the software, the efficiency principles are relative to the Charnes-Cooper-Rhodes ratio model and the Banker-Charnes-Cooper convex model, and the profitability principles are relative to the Thompson-Thrall profit ratio model. An illustrative application to 48 large U.S. banks illustrates some of the most fundamental computations, which are developed for a base option. Additional options may be exercised by the user to more fully utilize the theory. Additions to the software are being made to computer analytic centers and to make multiplier sensitivity analyses. Software utility updates and new DEA theory contributions continue to complement this computational capability.DEA is an advanced operations research method called Data Envelopment Analysis, and AR is an assurance region method used to bound the multipliers in the DEA model. Underlying data have been deposited with the editors.