A cross-efficiency model using bargaining theory in a two-stage network DEA

Fundamental data envelopment analysis (DEA) models fail to compare and correctly rank decision-making units (DMUs) because of the self-evaluation nature and flexibility in selecting desired optimal weights. The problem is exacerbated for network DMUs, including the ranking of stages. Cross-efficiency is a promising alternative to solve this problem. In addition to evaluating the efficiency of each DMU with the optimal weights obtained from self-evaluation, cross-efficiency also evaluates with the optimal weights selected by its peers. In previous researches, achieving efficiency from self-evaluation is considered, but this subject has attracted less attention in bargaining. To fill this gap, in this paper, a bargaining model named two stages C-B model as a secondary objective to select the favorite optimal weight between the optimal weights in evaluating the overall efficiency of each DMU and a unique cross-efficiency is obtained. For this purpose, non-linear programming is presented. Finally, this enables us to rank DMUs uniquely while assessing the performance of each DMU and its various divisions.

Automated summary

This paper introduces a bargaining model named two stages C-B model to select the optimal weights for evaluating the overall efficiency of DMUs, and uniquely ranks DMUs through cross-efficiency.