Two-stage cross-efficiency evaluation based on prospect theory

Abstract

Cross-efficiency evaluation in data envelopment analysis (DEA) is effective for evaluating the efficiency of decision-making units (DMUs). The use of cross-efficiency evaluation methods based on prospect theory has recently increased. However, the internal structure of DMUs is often ignored in efficiency evaluation; further, a fixed status quo is often selected as the reference point to calculate relative gains and losses, which is not ideal in the context of prospect theory. To address these issues, we investigate the basic two-stage cross-efficiency evaluation in DEA based on prospect theory. An optimism coefficient is introduced to formulate parameterised dynamic reference points, and a target identification model is developed to obtain target efficiency values that are attainable for all DMUs. Based on the prospect value and target efficiency values, we propose multiple novel aggressive, benevolent, and neutral two-stage cross-efficiency evaluation models. The models proposed herein can be applied to various decision environments and arbitrarily extended to other network system structures. A case study in sustainable supplier selection is performed to demonstrate the effectiveness of the proposed models for DMU ranking. The sensitivity analysis results show that the psychological characteristics of the decision maker under risk affect the evaluation results.