Measuring technical efficiency in a fuzzy environment

Abstract

Data envelopment analysis (DEA) was developed by Charnes, Cooper and Rhodes (1978) to measure the technical efficiency performance of organizational units. Conventional DEA models assume input and output sets are deterministic. When input and output data are not known precisely, the decision maker may choose between three alternatives. The first alternative assumes the sets are generated by a stochastic process. This alternative introduces much subjectivity in the analysis because it requires the decision maker to assume that input and output data are distributed according to specific probability laws. Often these distributions are chosen more for computational convenience than empirical evidence. The second alternative involves traditional post-optimization techniques, such as sensitivity analysis. The major shortcoming associated with this alternative is that it generates solutions that reside near a local optimum, and thus do not always direct the decision maker towards an optimal policy for best decision. The third alternative, developed for this research, is based on fuzzy set theory.

The present dissertation proposes a methodology that can be implemented when fuzziness is directly introduced in the input and output sets. The methodology merges data envelopment analysis with the fuzzy parametric programming framework developed by Carlsson and Korhonen (1986). The approach is particularly well suited to problems where the decision maker has the capability of specifying the lower and upper bounds of the input and output sets. It is implemented for two types of DEA models: Banker, Charnes and Cooper (BCC, 1984) and Free Disposal Hull (FDH, 1984).

All theoretical concepts presented in this research are illustrated in the context of a real world manufacturing system. The system under study is a packaging line that inserts commercial pamphlets into newspapers. This illustration, at the micro level, contrasts with most DEA applications described in the technical efficiency literature. Traditionally, DEA has been applied by economists and public administrators to assess the behavior of macro systems, including government agencies, financial institutions, health care providers, and educational entities.