Consensus reaching for prospect cross-efficiency in data envelopment analysis with minimum adjustments

Abstract

The expected utility theory and the arithmetic average method have been widely adopted for the cross-efficiency strategy formulation and cross-efficiencies aggregation. However, traditional cross-efficiency methods often fail to consider the decision maker’s (DM’s) risk attitude and neglect the consensus among decision-making units (DMUs) in the cross-evaluation process. Thereby, this paper utilizes the prospect cross-efficiency (PCE) model to describe the DM’s subjective preference in the evaluation process and a consensus framework to manage the consensus among DMUs in the aggregation process. First, the PCE model is utilized to derive the cross-efficiency matrix, and it can reflect DMs’ psychological factors in the strategy formulation of cross-efficiency. Then, a two-stage consensus optimization framework (TSCOF) with minimum adjustments is presented to improve the consensus degree (CD) among the DMUs in the cross-evaluation process. The TSCOF generates a sequential optimization strategy that minimizes the adjustment distance and the number of modifications sequentially. Next, we develop an interactive consensus reaching process (CRP) for PCE problems based on the consensus rule. The CRP does well in helping improve the CD among DMUs. Finally, an illustrative example related to the performance of the S&T activities of 10 universities is offered to elaborate on the feasibility and effectiveness of our approach.