Fuzzy non-radial measures of relative technical efficiency using DEA

Abstract

Charnes, Cooper and Rhodes [7] developed data envelopment analysis (DEA) to measure the technical efficiency of organizational units. In DEA, these units are referred to as decision making units (DMUs). Deterministic input and output data are assumed when using conventional DEA models. Based on Carlsson and Korhonen's [6] fuzzy parametric programming approach, Girod [15] developed fuzzy radial DEA models to deal with imprecise input and output data. The merits of Girod's approach were that it can be used for scenarios where the decision maker can place upper and lower bounds on the input and output data and, it introduces fuzziness directly in the input and output sets. However, radial models alone are not sufficient to judge an DMU efficient because of excess in usage of inputs and slacks in the production of outputs. Under these circumstances, non- radial DEA models are useful alternative estimates of technical efficiency performance. In this research, fuzzy non-radial models are developed by applying Girod's [15] framework to three non-radial models; the Fare-Lovell model, the Zieschang model and the asymmetric Fare model. A fuzzy two stage radial DEA model is also used to compute fuzzy technical efficiency scores. Comparison of fuzzy radial and non-radial models is carried out. The fuzzy DEA models developed in this research are used to measure technical efficiency of a packaging line in a real world manufacturing system. The specific process studied involves inserting commercial preprints in the fold of newspapers.