Overall Efficiency of Four-Stage Structure with Undesirable Outputs: A New SBM Network DEA Model

Abstract

Benchmarking is the major reason for the widespread use of DEA models for efficiency analysis. Determining the closest targets for DMUs, DEA models play a key role in benchmarking their best performance. In fact, these models help develop certain performance enhancement plans that need fewer attempts made by DMUs. Therefore, this study proposes a novel method based on the network DEA to determine the most appropriate target for every stage in addition to benchmarking the DMUs. The proposed model differs from those proposed by other studies in the fact that all DEA models of benchmarking consider input and output values to be linear. However, in real-world problems, many DMU inputs and outputs have nonlinear values (values are the coefficients of inputs or outputs in modeling and can be the price of desirable outputs or the cost of inputs and undesirable outputs), something which was taken into account in the modeling process in this study. The proposed model was employed to benchmark cement factories listed on the Tehran Stock Exchange.