A fuzzy DEA approach

Abstract

The theoretical concept of data envelopment analysis (DEA) was published by Charnes, Cooper and Rhodes in 1978. It is a powerful tool for assessing the efficiency of decision making units (DMUs) by comparing their respective inputfactors and output quantities. More precisely, the efficiency of a DMU is measured as the relation between the sum of weighted outputs and of weighted inputs, where the weights for a DMU are the solution of a linear optimization problem. But this approach suffers from a lack of objectivity due to the fact that every DMU wants an advantageous evaluation for itself, called self-appraisal in the respective literature. The purpose of this paper is to present an extension of the evaluation process in such a way that every DMU’s performance will be calculated in an objective and fair manner. For this a fuzzy oriented approach will be formulated which yields a nonlinear optimization problem. The resulting input/output weights are a compromise of all DMU’s individual interests. The so far developed theoretical concept will be applied to a company of Taiwanese semiconductor industry. Five DMUs’ efficiencies will be calculated over three years. Professional software solves the nonlinear program and the results permit meaningful economical interpretations.