Confident-DEA: A Unified Approach For Efficiency Analysis With Cardinal, Bounded And Ordinal Data

Abstract

This paper proposes an extension to the existing literature in DEA, the authors call Confident-DEA approach. The proposed new approach involves a bi-level convex optimization model, and hence NP-hard, to which a solution method is suggested. Confident-DEA constitutes a generalization of DEA for dealing with imprecise data and hence a potential method for forecasting efficiency. Imprecision in data is defined as two forms, one is bounded data and the second is cardinal data. Complementing the methodology proposed by Cooper et al (1999) which provides single valued efficiency measures, Confident-DEA provides a range of values for the efficiency measures, e.g. an efficiency confidence interval, reflecting the imprecision in data. For the case of bounded data, a theorem defining the bounds of the efficiency confidence interval is provided. For the general case of imprecise data, that is a mixture of ordinal and cardinal data, a Genetic-Algorithm-based meta-heuristic is used to determine the upper and lower bounds defining the efficiency confidence interval. To the best knowledge of the authors, this is the first work combining Genetic algorithms with DEA. In both cases of imprecision, a Monte-Carlo type simulation is used to determine the distribution of the efficiency measures, taking into account the distribution of the bounded imprecise data over their corresponding intervals. Most of previous DEA works dealing with imprecise data implicitly assumed a uniform distribution. Confident-DEA, on the other hand, allows for any type of distribution and hence expands the scope of the analysis. The bounded data used in the illustrative examples are assumed to have truncated normal distributions. However, the methodology suggested here allows for any other distribution for the data.