Restricting weight flexibility in fuzzy two-stage DEA

Abstract

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. Two-stage DEA models do not require a priori specification of input and output weights (or multipliers) and by letting these weights run freely, estimates of system and process efficiencies are obtained. This paper proposes a methodology for a fuzzy two-stage DEA model, where the weights are restricted in ranges and input–output data are treated as fuzzy numbers. The assurance region approach is utilized to restrict weight flexibility in the model. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the fuzzy efficiency score. We then transform this pair of two-level mathematical programs into a pair of conventional one-level mathematical programs to calculate the bounds of the fuzzy efficiency scores. The examples of non-life insurance companies in Taiwan and IT impact on firm performance are illustrated to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy.