Measuring the efficiency of decision making units☆

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Abstract

A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.

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    ☆

    This paper represents a revision of earlier versions entitled, respectively, ‘Expositions, Interpretations, and Extensions of the Farrell Efficiency Measure’, and ‘Measuring the Efficiency of Decision Making Units With Some New Production Functions and Estimation Methods’. See [11], [12] and also [9]. This research was partly supported by NSF Grant No. SOC76-15876 ‘Collaborative Research on the Analytical Capabilities of a Goals Accounting System’. It is also part of the program of the Navy Personnel Research and Development Center and is partly supported by Project NR 047-021, ONR Contract N00014-75-C-0616 with the Center for Cybernetic Studies, The University of Texas, and ONR Contract N00014-76-C-0932 at Carnegie-Mellon University School of Urban and Public Affairs.

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