Measuring the Efficiency of Decision Making Units with Some New Production Functions and Estimation Methods.

Abstract : A series of linear programming models are used to clarify and extend a measure of efficiency. The duals to these models are shown to yield estimates of production coefficients from the same empirical data and computations that yield the measures of efficiency. The nature of the resulting production functions and ways in which they differ from more customary ones are discussed en route to synthesizing the associated cost functions and other such (economic) relations. Methods for adjusting observations are suggested for economic inferences and policy applications. Multiple output-multiple input extensions are effected via a new definition of efficiency which involves a nonlinear model for determining the optimal input and output weights from observational data. The theory of fractional programming is used to secure ordinary linear programming models from which the weights and efficiency measures may also be obtained.