Fuzzy Performance Evaluation for Network Structures

The objective of two-stage data envelopment analysis (DEA) models is to assess the performance of a group of production systems with two operational stages. This internal structure can be typically found in numerous situations such as seller-buyer supply chain, health care provision and banking systems. The vital advantage of two-stage DEA is to provide further insight into sources of inefficiencies and take the appropriate actions for improvement the system as a whole. In addition, setting aside the qualitative and subjective information leads to biased evaluations, both for the processes and the system efficiency. In this paper, we present the fuzzy input and output-oriented two-stage DEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are characterised by fuzzy numbers. To this end, a possibilistic programming problem is first adapted and then transformed into a deterministic interval programming problem using the α-level based method. Compellingly, the method proposed in this study maintains the connection between two stages in a way that the total efficiency of the system is equal to the product of the efficiencies calculated from two stages. We illustrate the applicability of the proposed approach by an empirical study.