Cross-efficiency evaluation method for non-homogeneous parallel network systems with imprecise data

The existing parallel DEA models assume that all decision making units (DMUs) should contain identical subsystems. This paper proposes a cross-efficiency evaluation method to handle the non-homogeneous DMUs (NHDMUs) in the parallel network system, where the non-homogeneity of DMUs is shown in that the input and output sets of subsystems and the internal structure of DMUs are not the same. The method considers the scenario wherein quantitative and qualitative data exist in the inputs and outputs simultaneously. To do this, first, the NHDMUs are divided into different mutually exclusive unit groups according to the subsystems in which DMUs participate. Then, several interval cross-efficiency models are constructed for the cross-efficiency evaluation of DMUs in the same group and the cross-efficiency evaluation of DMUs with overlapping internal outlines in different groups to obtain the interval cross-efficiencies of NHDMUs. Further, the evidence theory and grey relation analysis method are used to determine a set of weights that aggregate the cross-efficiency matrix. Finally, the proposed method is discussed using an application case of talent introduction performance. The results show that the proposed method can improve the rationality and distinguishability of efficiency evaluation and find the reasons for the performance decline of a DMU.

Automated summary

This paper proposes a cross-efficiency evaluation method to handle the non-homogeneous DMUs in the parallel network system. The method considers the scenario wherein quantitative and qualitative data exist in the inputs and outputs simultaneously. It divides the NHDMUs into different mutually exclusive unit groups according to the subsystems and constructs interval cross-efficiency models to obtain the interval cross-efficiencies of NHDMUs.