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.

A Bilevel DEA Model for Efficiency Evaluation and Target Setting with Stochastic Conditions

“…The model, which runs for each subDMU k, computes the optimal input (v ik ) and output weights (u ω rk ) for each scenario ω that maximizes the efficiency for each subDMU k. Constraint (17) restricts the values of subDMU efficiency between zero and one. Constraints (18) and (19) ensure that the weights take values larger than a nonnegative infinitesimal number for input and output respectively. The existence of the free variable l ω k imposes the variable returns to scale assumption for the efficiency of the subDMU k.…”

“…Hence, the efficiency can be overestimated by the classical models, and this problem is perpetuated as the stages increase. More comprehensive research about NDEA models can be found in [13][14][15][16][17][18]. Typically, each DMU independently optimizes its input and output levels to maximize its efficiency.…”

Research on the Measurement of Innovation Efficiency of Chinese Cultural Industry and the Influence of Environmental Factors

“…Koronakos et al (2022) improved the application of network DEA method in the efficiency calculation of commercial banks [18]. Roudabr et al (2022) proposed an improved four stage DEA efficiency measurement model and tested it with the data of Tehran stock exchange [19]. Khoveyni (2021) proposed a hyperplane DEA model method for efficiency measurement [20].…”