Choice of metric in the measurement of relative productive efficiency

In this paper different data envelope analysis (DEA) models are compared in terms of their potential to generate a quantitative measure of the degree of inefficiency. The Russell [1] measure in particularly appealing since it is not restricted to simple proportional comparisons. However, its actual value is sensitive to the choice of weights on the different inputs (or outputs) in the objective function. This may be of little significance in a simple binary classification of efficient and inefficient firms. However when evaluating the degree of efficiency, and hence the ''distance'' of a firm from the efficient envelope, choice of metric becomes critical. A number of alternative metrics are compared, including the ''stability index'' of Charnes et al. [2] and an alternative approach is suggested using the nature of the linear program itself. The paper concludes with a numerical illustration.